/*M///////////////////////////////////////////////////////////////////////////////////////
|
//
|
// IMPORTANT: READ BEFORE DOWNLOADING, COPYING, INSTALLING OR USING.
|
//
|
// By downloading, copying, installing or using the software you agree to this license.
|
// If you do not agree to this license, do not download, install,
|
// copy or use the software.
|
//
|
//
|
// License Agreement
|
// For Open Source Computer Vision Library
|
//
|
// Copyright (C) 2000-2008, Intel Corporation, all rights reserved.
|
// Copyright (C) 2009, Willow Garage Inc., all rights reserved.
|
// Copyright (C) 2013, OpenCV Foundation, all rights reserved.
|
// Third party copyrights are property of their respective owners.
|
//
|
// Redistribution and use in source and binary forms, with or without modification,
|
// are permitted provided that the following conditions are met:
|
//
|
// * Redistribution's of source code must retain the above copyright notice,
|
// this list of conditions and the following disclaimer.
|
//
|
// * Redistribution's in binary form must reproduce the above copyright notice,
|
// this list of conditions and the following disclaimer in the documentation
|
// and/or other materials provided with the distribution.
|
//
|
// * The name of the copyright holders may not be used to endorse or promote products
|
// derived from this software without specific prior written permission.
|
//
|
// This software is provided by the copyright holders and contributors "as is" and
|
// any express or implied warranties, including, but not limited to, the implied
|
// warranties of merchantability and fitness for a particular purpose are disclaimed.
|
// In no event shall the Intel Corporation or contributors be liable for any direct,
|
// indirect, incidental, special, exemplary, or consequential damages
|
// (including, but not limited to, procurement of substitute goods or services;
|
// loss of use, data, or profits; or business interruption) however caused
|
// and on any theory of liability, whether in contract, strict liability,
|
// or tort (including negligence or otherwise) arising in any way out of
|
// the use of this software, even if advised of the possibility of such damage.
|
//
|
//M*/
|
|
#ifndef OPENCV_CALIB3D_HPP
|
#define OPENCV_CALIB3D_HPP
|
|
#include "opencv2/core.hpp"
|
#include "opencv2/features2d.hpp"
|
#include "opencv2/core/affine.hpp"
|
|
/**
|
@defgroup calib3d Camera Calibration and 3D Reconstruction
|
|
The functions in this section use a so-called pinhole camera model. In this model, a scene view is
|
formed by projecting 3D points into the image plane using a perspective transformation.
|
|
\f[s \; m' = A [R|t] M'\f]
|
|
or
|
|
\f[s \vecthree{u}{v}{1} = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}
|
\begin{bmatrix}
|
r_{11} & r_{12} & r_{13} & t_x \\
|
r_{21} & r_{22} & r_{23} & t_y \\
|
r_{31} & r_{32} & r_{33} & t_z
|
\end{bmatrix}
|
\begin{bmatrix}
|
X_w \\
|
Y_w \\
|
Z_w \\
|
1
|
\end{bmatrix}\f]
|
|
where:
|
|
- \f$(X_w, Y_w, Z_w)\f$ are the coordinates of a 3D point in the world coordinate space
|
- \f$(u, v)\f$ are the coordinates of the projection point in pixels
|
- \f$A\f$ is a camera matrix, or a matrix of intrinsic parameters
|
- \f$(c_x, c_y)\f$ is a principal point that is usually at the image center
|
- \f$f_x, f_y\f$ are the focal lengths expressed in pixel units.
|
|
Thus, if an image from the camera is scaled by a factor, all of these parameters should be scaled
|
(multiplied/divided, respectively) by the same factor. The matrix of intrinsic parameters does not
|
depend on the scene viewed. So, once estimated, it can be re-used as long as the focal length is
|
fixed (in case of zoom lens). The joint rotation-translation matrix \f$[R|t]\f$ is called a matrix of
|
extrinsic parameters. It is used to describe the camera motion around a static scene, or vice versa,
|
rigid motion of an object in front of a still camera. That is, \f$[R|t]\f$ translates coordinates of a
|
world point \f$(X_w, Y_w, Z_w)\f$ to a coordinate system, fixed with respect to the camera.
|
The transformation above is equivalent to the following (when \f$z \ne 0\f$ ):
|
|
\f[\begin{array}{l}
|
\vecthree{X_c}{Y_c}{Z_c} = R \vecthree{X_w}{Y_w}{Z_w} + t \\
|
x' = X_c/Z_c \\
|
y' = Y_c/Z_c \\
|
u = f_x \times x' + c_x \\
|
v = f_y \times y' + c_y
|
\end{array}\f]
|
|
The following figure illustrates the pinhole camera model.
|
|
|
|
Real lenses usually have some distortion, mostly radial distortion and slight tangential distortion.
|
So, the above model is extended as:
|
|
\f[\begin{array}{l}
|
\vecthree{X_c}{Y_c}{Z_c} = R \vecthree{X_w}{Y_w}{Z_w} + t \\
|
x' = X_c/Z_c \\
|
y' = Y_c/Z_c \\
|
x'' = x' \frac{1 + k_1 r^2 + k_2 r^4 + k_3 r^6}{1 + k_4 r^2 + k_5 r^4 + k_6 r^6} + 2 p_1 x' y' + p_2(r^2 + 2 x'^2) + s_1 r^2 + s_2 r^4 \\
|
y'' = y' \frac{1 + k_1 r^2 + k_2 r^4 + k_3 r^6}{1 + k_4 r^2 + k_5 r^4 + k_6 r^6} + p_1 (r^2 + 2 y'^2) + 2 p_2 x' y' + s_3 r^2 + s_4 r^4 \\
|
\text{where} \quad r^2 = x'^2 + y'^2 \\
|
u = f_x \times x'' + c_x \\
|
v = f_y \times y'' + c_y
|
\end{array}\f]
|
|
\f$k_1\f$, \f$k_2\f$, \f$k_3\f$, \f$k_4\f$, \f$k_5\f$, and \f$k_6\f$ are radial distortion coefficients. \f$p_1\f$ and \f$p_2\f$ are
|
tangential distortion coefficients. \f$s_1\f$, \f$s_2\f$, \f$s_3\f$, and \f$s_4\f$, are the thin prism distortion
|
coefficients. Higher-order coefficients are not considered in OpenCV.
|
|
The next figures show two common types of radial distortion: barrel distortion (typically \f$ k_1 < 0 \f$) and pincushion distortion (typically \f$ k_1 > 0 \f$).
|
|
|
|
|
In some cases the image sensor may be tilted in order to focus an oblique plane in front of the
|
camera (Scheimpflug principle). This can be useful for particle image velocimetry (PIV) or
|
triangulation with a laser fan. The tilt causes a perspective distortion of \f$x''\f$ and
|
\f$y''\f$. This distortion can be modelled in the following way, see e.g. @cite Louhichi07.
|
|
\f[\begin{array}{l}
|
s\vecthree{x'''}{y'''}{1} =
|
\vecthreethree{R_{33}(\tau_x, \tau_y)}{0}{-R_{13}(\tau_x, \tau_y)}
|
{0}{R_{33}(\tau_x, \tau_y)}{-R_{23}(\tau_x, \tau_y)}
|
{0}{0}{1} R(\tau_x, \tau_y) \vecthree{x''}{y''}{1}\\
|
u = f_x \times x''' + c_x \\
|
v = f_y \times y''' + c_y
|
\end{array}\f]
|
|
where the matrix \f$R(\tau_x, \tau_y)\f$ is defined by two rotations with angular parameter \f$\tau_x\f$
|
and \f$\tau_y\f$, respectively,
|
|
\f[
|
R(\tau_x, \tau_y) =
|
\vecthreethree{\cos(\tau_y)}{0}{-\sin(\tau_y)}{0}{1}{0}{\sin(\tau_y)}{0}{\cos(\tau_y)}
|
\vecthreethree{1}{0}{0}{0}{\cos(\tau_x)}{\sin(\tau_x)}{0}{-\sin(\tau_x)}{\cos(\tau_x)} =
|
\vecthreethree{\cos(\tau_y)}{\sin(\tau_y)\sin(\tau_x)}{-\sin(\tau_y)\cos(\tau_x)}
|
{0}{\cos(\tau_x)}{\sin(\tau_x)}
|
{\sin(\tau_y)}{-\cos(\tau_y)\sin(\tau_x)}{\cos(\tau_y)\cos(\tau_x)}.
|
\f]
|
|
In the functions below the coefficients are passed or returned as
|
|
\f[(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6 [, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\f]
|
|
vector. That is, if the vector contains four elements, it means that \f$k_3=0\f$ . The distortion
|
coefficients do not depend on the scene viewed. Thus, they also belong to the intrinsic camera
|
parameters. And they remain the same regardless of the captured image resolution. If, for example, a
|
camera has been calibrated on images of 320 x 240 resolution, absolutely the same distortion
|
coefficients can be used for 640 x 480 images from the same camera while \f$f_x\f$, \f$f_y\f$, \f$c_x\f$, and
|
\f$c_y\f$ need to be scaled appropriately.
|
|
The functions below use the above model to do the following:
|
|
- Project 3D points to the image plane given intrinsic and extrinsic parameters.
|
- Compute extrinsic parameters given intrinsic parameters, a few 3D points, and their
|
projections.
|
- Estimate intrinsic and extrinsic camera parameters from several views of a known calibration
|
pattern (every view is described by several 3D-2D point correspondences).
|
- Estimate the relative position and orientation of the stereo camera "heads" and compute the
|
*rectification* transformation that makes the camera optical axes parallel.
|
|
@note
|
- A calibration sample for 3 cameras in horizontal position can be found at
|
opencv_source_code/samples/cpp/3calibration.cpp
|
- A calibration sample based on a sequence of images can be found at
|
opencv_source_code/samples/cpp/calibration.cpp
|
- A calibration sample in order to do 3D reconstruction can be found at
|
opencv_source_code/samples/cpp/build3dmodel.cpp
|
- A calibration example on stereo calibration can be found at
|
opencv_source_code/samples/cpp/stereo_calib.cpp
|
- A calibration example on stereo matching can be found at
|
opencv_source_code/samples/cpp/stereo_match.cpp
|
- (Python) A camera calibration sample can be found at
|
opencv_source_code/samples/python/calibrate.py
|
|
@{
|
@defgroup calib3d_fisheye Fisheye camera model
|
|
Definitions: Let P be a point in 3D of coordinates X in the world reference frame (stored in the
|
matrix X) The coordinate vector of P in the camera reference frame is:
|
|
\f[Xc = R X + T\f]
|
|
where R is the rotation matrix corresponding to the rotation vector om: R = rodrigues(om); call x, y
|
and z the 3 coordinates of Xc:
|
|
\f[x = Xc_1 \\ y = Xc_2 \\ z = Xc_3\f]
|
|
The pinhole projection coordinates of P is [a; b] where
|
|
\f[a = x / z \ and \ b = y / z \\ r^2 = a^2 + b^2 \\ \theta = atan(r)\f]
|
|
Fisheye distortion:
|
|
\f[\theta_d = \theta (1 + k_1 \theta^2 + k_2 \theta^4 + k_3 \theta^6 + k_4 \theta^8)\f]
|
|
The distorted point coordinates are [x'; y'] where
|
|
\f[x' = (\theta_d / r) a \\ y' = (\theta_d / r) b \f]
|
|
Finally, conversion into pixel coordinates: The final pixel coordinates vector [u; v] where:
|
|
\f[u = f_x (x' + \alpha y') + c_x \\
|
v = f_y y' + c_y\f]
|
|
@defgroup calib3d_c C API
|
|
@}
|
*/
|
|
namespace cv
|
{
|
|
//! @addtogroup calib3d
|
//! @{
|
|
//! type of the robust estimation algorithm
|
enum { LMEDS = 4, //!< least-median of squares algorithm
|
RANSAC = 8, //!< RANSAC algorithm
|
RHO = 16 //!< RHO algorithm
|
};
|
|
enum SolvePnPMethod {
|
SOLVEPNP_ITERATIVE = 0,
|
SOLVEPNP_EPNP = 1, //!< EPnP: Efficient Perspective-n-Point Camera Pose Estimation @cite lepetit2009epnp
|
SOLVEPNP_P3P = 2, //!< Complete Solution Classification for the Perspective-Three-Point Problem @cite gao2003complete
|
SOLVEPNP_DLS = 3, //!< A Direct Least-Squares (DLS) Method for PnP @cite hesch2011direct
|
SOLVEPNP_UPNP = 4, //!< Exhaustive Linearization for Robust Camera Pose and Focal Length Estimation @cite penate2013exhaustive
|
SOLVEPNP_AP3P = 5, //!< An Efficient Algebraic Solution to the Perspective-Three-Point Problem @cite Ke17
|
SOLVEPNP_IPPE = 6, //!< Infinitesimal Plane-Based Pose Estimation @cite Collins14 \n
|
//!< Object points must be coplanar.
|
SOLVEPNP_IPPE_SQUARE = 7, //!< Infinitesimal Plane-Based Pose Estimation @cite Collins14 \n
|
//!< This is a special case suitable for marker pose estimation.\n
|
//!< 4 coplanar object points must be defined in the following order:
|
//!< - point 0: [-squareLength / 2, squareLength / 2, 0]
|
//!< - point 1: [ squareLength / 2, squareLength / 2, 0]
|
//!< - point 2: [ squareLength / 2, -squareLength / 2, 0]
|
//!< - point 3: [-squareLength / 2, -squareLength / 2, 0]
|
#ifndef CV_DOXYGEN
|
SOLVEPNP_MAX_COUNT //!< Used for count
|
#endif
|
};
|
|
enum { CALIB_CB_ADAPTIVE_THRESH = 1,
|
CALIB_CB_NORMALIZE_IMAGE = 2,
|
CALIB_CB_FILTER_QUADS = 4,
|
CALIB_CB_FAST_CHECK = 8,
|
CALIB_CB_EXHAUSTIVE = 16,
|
CALIB_CB_ACCURACY = 32
|
};
|
|
enum { CALIB_CB_SYMMETRIC_GRID = 1,
|
CALIB_CB_ASYMMETRIC_GRID = 2,
|
CALIB_CB_CLUSTERING = 4
|
};
|
|
enum { CALIB_NINTRINSIC = 18,
|
CALIB_USE_INTRINSIC_GUESS = 0x00001,
|
CALIB_FIX_ASPECT_RATIO = 0x00002,
|
CALIB_FIX_PRINCIPAL_POINT = 0x00004,
|
CALIB_ZERO_TANGENT_DIST = 0x00008,
|
CALIB_FIX_FOCAL_LENGTH = 0x00010,
|
CALIB_FIX_K1 = 0x00020,
|
CALIB_FIX_K2 = 0x00040,
|
CALIB_FIX_K3 = 0x00080,
|
CALIB_FIX_K4 = 0x00800,
|
CALIB_FIX_K5 = 0x01000,
|
CALIB_FIX_K6 = 0x02000,
|
CALIB_RATIONAL_MODEL = 0x04000,
|
CALIB_THIN_PRISM_MODEL = 0x08000,
|
CALIB_FIX_S1_S2_S3_S4 = 0x10000,
|
CALIB_TILTED_MODEL = 0x40000,
|
CALIB_FIX_TAUX_TAUY = 0x80000,
|
CALIB_USE_QR = 0x100000, //!< use QR instead of SVD decomposition for solving. Faster but potentially less precise
|
CALIB_FIX_TANGENT_DIST = 0x200000,
|
// only for stereo
|
CALIB_FIX_INTRINSIC = 0x00100,
|
CALIB_SAME_FOCAL_LENGTH = 0x00200,
|
// for stereo rectification
|
CALIB_ZERO_DISPARITY = 0x00400,
|
CALIB_USE_LU = (1 << 17), //!< use LU instead of SVD decomposition for solving. much faster but potentially less precise
|
CALIB_USE_EXTRINSIC_GUESS = (1 << 22) //!< for stereoCalibrate
|
};
|
|
//! the algorithm for finding fundamental matrix
|
enum { FM_7POINT = 1, //!< 7-point algorithm
|
FM_8POINT = 2, //!< 8-point algorithm
|
FM_LMEDS = 4, //!< least-median algorithm. 7-point algorithm is used.
|
FM_RANSAC = 8 //!< RANSAC algorithm. It needs at least 15 points. 7-point algorithm is used.
|
};
|
|
enum HandEyeCalibrationMethod
|
{
|
CALIB_HAND_EYE_TSAI = 0, //!< A New Technique for Fully Autonomous and Efficient 3D Robotics Hand/Eye Calibration @cite Tsai89
|
CALIB_HAND_EYE_PARK = 1, //!< Robot Sensor Calibration: Solving AX = XB on the Euclidean Group @cite Park94
|
CALIB_HAND_EYE_HORAUD = 2, //!< Hand-eye Calibration @cite Horaud95
|
CALIB_HAND_EYE_ANDREFF = 3, //!< On-line Hand-Eye Calibration @cite Andreff99
|
CALIB_HAND_EYE_DANIILIDIS = 4 //!< Hand-Eye Calibration Using Dual Quaternions @cite Daniilidis98
|
};
|
|
|
/** @brief Converts a rotation matrix to a rotation vector or vice versa.
|
|
@param src Input rotation vector (3x1 or 1x3) or rotation matrix (3x3).
|
@param dst Output rotation matrix (3x3) or rotation vector (3x1 or 1x3), respectively.
|
@param jacobian Optional output Jacobian matrix, 3x9 or 9x3, which is a matrix of partial
|
derivatives of the output array components with respect to the input array components.
|
|
\f[\begin{array}{l} \theta \leftarrow norm(r) \\ r \leftarrow r/ \theta \\ R = \cos(\theta) I + (1- \cos{\theta} ) r r^T + \sin(\theta) \vecthreethree{0}{-r_z}{r_y}{r_z}{0}{-r_x}{-r_y}{r_x}{0} \end{array}\f]
|
|
Inverse transformation can be also done easily, since
|
|
\f[\sin ( \theta ) \vecthreethree{0}{-r_z}{r_y}{r_z}{0}{-r_x}{-r_y}{r_x}{0} = \frac{R - R^T}{2}\f]
|
|
A rotation vector is a convenient and most compact representation of a rotation matrix (since any
|
rotation matrix has just 3 degrees of freedom). The representation is used in the global 3D geometry
|
optimization procedures like @ref calibrateCamera, @ref stereoCalibrate, or @ref solvePnP .
|
|
@note More information about the computation of the derivative of a 3D rotation matrix with respect to its exponential coordinate
|
can be found in:
|
- A Compact Formula for the Derivative of a 3-D Rotation in Exponential Coordinates, Guillermo Gallego, Anthony J. Yezzi @cite Gallego2014ACF
|
|
@note Useful information on SE(3) and Lie Groups can be found in:
|
- A tutorial on SE(3) transformation parameterizations and on-manifold optimization, Jose-Luis Blanco @cite blanco2010tutorial
|
- Lie Groups for 2D and 3D Transformation, Ethan Eade @cite Eade17
|
- A micro Lie theory for state estimation in robotics, Joan Solà , Jérémie Deray, Dinesh Atchuthan @cite Sol2018AML
|
*/
|
CV_EXPORTS_W void Rodrigues( InputArray src, OutputArray dst, OutputArray jacobian = noArray() );
|
|
|
|
/** Levenberg-Marquardt solver. Starting with the specified vector of parameters it
|
optimizes the target vector criteria "err"
|
(finds local minima of each target vector component absolute value).
|
|
When needed, it calls user-provided callback.
|
*/
|
class CV_EXPORTS LMSolver : public Algorithm
|
{
|
public:
|
class CV_EXPORTS Callback
|
{
|
public:
|
virtual ~Callback() {}
|
/**
|
computes error and Jacobian for the specified vector of parameters
|
|
@param param the current vector of parameters
|
@param err output vector of errors: err_i = actual_f_i - ideal_f_i
|
@param J output Jacobian: J_ij = d(err_i)/d(param_j)
|
|
when J=noArray(), it means that it does not need to be computed.
|
Dimensionality of error vector and param vector can be different.
|
The callback should explicitly allocate (with "create" method) each output array
|
(unless it's noArray()).
|
*/
|
virtual bool compute(InputArray param, OutputArray err, OutputArray J) const = 0;
|
};
|
|
/**
|
Runs Levenberg-Marquardt algorithm using the passed vector of parameters as the start point.
|
The final vector of parameters (whether the algorithm converged or not) is stored at the same
|
vector. The method returns the number of iterations used. If it's equal to the previously specified
|
maxIters, there is a big chance the algorithm did not converge.
|
|
@param param initial/final vector of parameters.
|
|
Note that the dimensionality of parameter space is defined by the size of param vector,
|
and the dimensionality of optimized criteria is defined by the size of err vector
|
computed by the callback.
|
*/
|
virtual int run(InputOutputArray param) const = 0;
|
|
/**
|
Sets the maximum number of iterations
|
@param maxIters the number of iterations
|
*/
|
virtual void setMaxIters(int maxIters) = 0;
|
/**
|
Retrieves the current maximum number of iterations
|
*/
|
virtual int getMaxIters() const = 0;
|
|
/**
|
Creates Levenberg-Marquard solver
|
|
@param cb callback
|
@param maxIters maximum number of iterations that can be further
|
modified using setMaxIters() method.
|
*/
|
static Ptr<LMSolver> create(const Ptr<LMSolver::Callback>& cb, int maxIters);
|
static Ptr<LMSolver> create(const Ptr<LMSolver::Callback>& cb, int maxIters, double eps);
|
};
|
|
|
|
/** @example samples/cpp/tutorial_code/features2D/Homography/pose_from_homography.cpp
|
An example program about pose estimation from coplanar points
|
|
Check @ref tutorial_homography "the corresponding tutorial" for more details
|
*/
|
|
/** @brief Finds a perspective transformation between two planes.
|
|
@param srcPoints Coordinates of the points in the original plane, a matrix of the type CV_32FC2
|
or vector\<Point2f\> .
|
@param dstPoints Coordinates of the points in the target plane, a matrix of the type CV_32FC2 or
|
a vector\<Point2f\> .
|
@param method Method used to compute a homography matrix. The following methods are possible:
|
- **0** - a regular method using all the points, i.e., the least squares method
|
- **RANSAC** - RANSAC-based robust method
|
- **LMEDS** - Least-Median robust method
|
- **RHO** - PROSAC-based robust method
|
@param ransacReprojThreshold Maximum allowed reprojection error to treat a point pair as an inlier
|
(used in the RANSAC and RHO methods only). That is, if
|
\f[\| \texttt{dstPoints} _i - \texttt{convertPointsHomogeneous} ( \texttt{H} * \texttt{srcPoints} _i) \|_2 > \texttt{ransacReprojThreshold}\f]
|
then the point \f$i\f$ is considered as an outlier. If srcPoints and dstPoints are measured in pixels,
|
it usually makes sense to set this parameter somewhere in the range of 1 to 10.
|
@param mask Optional output mask set by a robust method ( RANSAC or LMEDS ). Note that the input
|
mask values are ignored.
|
@param maxIters The maximum number of RANSAC iterations.
|
@param confidence Confidence level, between 0 and 1.
|
|
The function finds and returns the perspective transformation \f$H\f$ between the source and the
|
destination planes:
|
|
\f[s_i \vecthree{x'_i}{y'_i}{1} \sim H \vecthree{x_i}{y_i}{1}\f]
|
|
so that the back-projection error
|
|
\f[\sum _i \left ( x'_i- \frac{h_{11} x_i + h_{12} y_i + h_{13}}{h_{31} x_i + h_{32} y_i + h_{33}} \right )^2+ \left ( y'_i- \frac{h_{21} x_i + h_{22} y_i + h_{23}}{h_{31} x_i + h_{32} y_i + h_{33}} \right )^2\f]
|
|
is minimized. If the parameter method is set to the default value 0, the function uses all the point
|
pairs to compute an initial homography estimate with a simple least-squares scheme.
|
|
However, if not all of the point pairs ( \f$srcPoints_i\f$, \f$dstPoints_i\f$ ) fit the rigid perspective
|
transformation (that is, there are some outliers), this initial estimate will be poor. In this case,
|
you can use one of the three robust methods. The methods RANSAC, LMeDS and RHO try many different
|
random subsets of the corresponding point pairs (of four pairs each, collinear pairs are discarded), estimate the homography matrix
|
using this subset and a simple least-squares algorithm, and then compute the quality/goodness of the
|
computed homography (which is the number of inliers for RANSAC or the least median re-projection error for
|
LMeDS). The best subset is then used to produce the initial estimate of the homography matrix and
|
the mask of inliers/outliers.
|
|
Regardless of the method, robust or not, the computed homography matrix is refined further (using
|
inliers only in case of a robust method) with the Levenberg-Marquardt method to reduce the
|
re-projection error even more.
|
|
The methods RANSAC and RHO can handle practically any ratio of outliers but need a threshold to
|
distinguish inliers from outliers. The method LMeDS does not need any threshold but it works
|
correctly only when there are more than 50% of inliers. Finally, if there are no outliers and the
|
noise is rather small, use the default method (method=0).
|
|
The function is used to find initial intrinsic and extrinsic matrices. Homography matrix is
|
determined up to a scale. Thus, it is normalized so that \f$h_{33}=1\f$. Note that whenever an \f$H\f$ matrix
|
cannot be estimated, an empty one will be returned.
|
|
@sa
|
getAffineTransform, estimateAffine2D, estimateAffinePartial2D, getPerspectiveTransform, warpPerspective,
|
perspectiveTransform
|
*/
|
CV_EXPORTS_W Mat findHomography( InputArray srcPoints, InputArray dstPoints,
|
int method = 0, double ransacReprojThreshold = 3,
|
OutputArray mask=noArray(), const int maxIters = 2000,
|
const double confidence = 0.995);
|
|
/** @overload */
|
CV_EXPORTS Mat findHomography( InputArray srcPoints, InputArray dstPoints,
|
OutputArray mask, int method = 0, double ransacReprojThreshold = 3 );
|
|
/** @brief Computes an RQ decomposition of 3x3 matrices.
|
|
@param src 3x3 input matrix.
|
@param mtxR Output 3x3 upper-triangular matrix.
|
@param mtxQ Output 3x3 orthogonal matrix.
|
@param Qx Optional output 3x3 rotation matrix around x-axis.
|
@param Qy Optional output 3x3 rotation matrix around y-axis.
|
@param Qz Optional output 3x3 rotation matrix around z-axis.
|
|
The function computes a RQ decomposition using the given rotations. This function is used in
|
decomposeProjectionMatrix to decompose the left 3x3 submatrix of a projection matrix into a camera
|
and a rotation matrix.
|
|
It optionally returns three rotation matrices, one for each axis, and the three Euler angles in
|
degrees (as the return value) that could be used in OpenGL. Note, there is always more than one
|
sequence of rotations about the three principal axes that results in the same orientation of an
|
object, e.g. see @cite Slabaugh . Returned tree rotation matrices and corresponding three Euler angles
|
are only one of the possible solutions.
|
*/
|
CV_EXPORTS_W Vec3d RQDecomp3x3( InputArray src, OutputArray mtxR, OutputArray mtxQ,
|
OutputArray Qx = noArray(),
|
OutputArray Qy = noArray(),
|
OutputArray Qz = noArray());
|
|
/** @brief Decomposes a projection matrix into a rotation matrix and a camera matrix.
|
|
@param projMatrix 3x4 input projection matrix P.
|
@param cameraMatrix Output 3x3 camera matrix K.
|
@param rotMatrix Output 3x3 external rotation matrix R.
|
@param transVect Output 4x1 translation vector T.
|
@param rotMatrixX Optional 3x3 rotation matrix around x-axis.
|
@param rotMatrixY Optional 3x3 rotation matrix around y-axis.
|
@param rotMatrixZ Optional 3x3 rotation matrix around z-axis.
|
@param eulerAngles Optional three-element vector containing three Euler angles of rotation in
|
degrees.
|
|
The function computes a decomposition of a projection matrix into a calibration and a rotation
|
matrix and the position of a camera.
|
|
It optionally returns three rotation matrices, one for each axis, and three Euler angles that could
|
be used in OpenGL. Note, there is always more than one sequence of rotations about the three
|
principal axes that results in the same orientation of an object, e.g. see @cite Slabaugh . Returned
|
tree rotation matrices and corresponding three Euler angles are only one of the possible solutions.
|
|
The function is based on RQDecomp3x3 .
|
*/
|
CV_EXPORTS_W void decomposeProjectionMatrix( InputArray projMatrix, OutputArray cameraMatrix,
|
OutputArray rotMatrix, OutputArray transVect,
|
OutputArray rotMatrixX = noArray(),
|
OutputArray rotMatrixY = noArray(),
|
OutputArray rotMatrixZ = noArray(),
|
OutputArray eulerAngles =noArray() );
|
|
/** @brief Computes partial derivatives of the matrix product for each multiplied matrix.
|
|
@param A First multiplied matrix.
|
@param B Second multiplied matrix.
|
@param dABdA First output derivative matrix d(A\*B)/dA of size
|
\f$\texttt{A.rows*B.cols} \times {A.rows*A.cols}\f$ .
|
@param dABdB Second output derivative matrix d(A\*B)/dB of size
|
\f$\texttt{A.rows*B.cols} \times {B.rows*B.cols}\f$ .
|
|
The function computes partial derivatives of the elements of the matrix product \f$A*B\f$ with regard to
|
the elements of each of the two input matrices. The function is used to compute the Jacobian
|
matrices in stereoCalibrate but can also be used in any other similar optimization function.
|
*/
|
CV_EXPORTS_W void matMulDeriv( InputArray A, InputArray B, OutputArray dABdA, OutputArray dABdB );
|
|
/** @brief Combines two rotation-and-shift transformations.
|
|
@param rvec1 First rotation vector.
|
@param tvec1 First translation vector.
|
@param rvec2 Second rotation vector.
|
@param tvec2 Second translation vector.
|
@param rvec3 Output rotation vector of the superposition.
|
@param tvec3 Output translation vector of the superposition.
|
@param dr3dr1 Optional output derivative of rvec3 with regard to rvec1
|
@param dr3dt1 Optional output derivative of rvec3 with regard to tvec1
|
@param dr3dr2 Optional output derivative of rvec3 with regard to rvec2
|
@param dr3dt2 Optional output derivative of rvec3 with regard to tvec2
|
@param dt3dr1 Optional output derivative of tvec3 with regard to rvec1
|
@param dt3dt1 Optional output derivative of tvec3 with regard to tvec1
|
@param dt3dr2 Optional output derivative of tvec3 with regard to rvec2
|
@param dt3dt2 Optional output derivative of tvec3 with regard to tvec2
|
|
The functions compute:
|
|
\f[\begin{array}{l} \texttt{rvec3} = \mathrm{rodrigues} ^{-1} \left ( \mathrm{rodrigues} ( \texttt{rvec2} ) \cdot \mathrm{rodrigues} ( \texttt{rvec1} ) \right ) \\ \texttt{tvec3} = \mathrm{rodrigues} ( \texttt{rvec2} ) \cdot \texttt{tvec1} + \texttt{tvec2} \end{array} ,\f]
|
|
where \f$\mathrm{rodrigues}\f$ denotes a rotation vector to a rotation matrix transformation, and
|
\f$\mathrm{rodrigues}^{-1}\f$ denotes the inverse transformation. See Rodrigues for details.
|
|
Also, the functions can compute the derivatives of the output vectors with regards to the input
|
vectors (see matMulDeriv ). The functions are used inside stereoCalibrate but can also be used in
|
your own code where Levenberg-Marquardt or another gradient-based solver is used to optimize a
|
function that contains a matrix multiplication.
|
*/
|
CV_EXPORTS_W void composeRT( InputArray rvec1, InputArray tvec1,
|
InputArray rvec2, InputArray tvec2,
|
OutputArray rvec3, OutputArray tvec3,
|
OutputArray dr3dr1 = noArray(), OutputArray dr3dt1 = noArray(),
|
OutputArray dr3dr2 = noArray(), OutputArray dr3dt2 = noArray(),
|
OutputArray dt3dr1 = noArray(), OutputArray dt3dt1 = noArray(),
|
OutputArray dt3dr2 = noArray(), OutputArray dt3dt2 = noArray() );
|
|
/** @brief Projects 3D points to an image plane.
|
|
@param objectPoints Array of object points, 3xN/Nx3 1-channel or 1xN/Nx1 3-channel (or
|
vector\<Point3f\> ), where N is the number of points in the view.
|
@param rvec Rotation vector. See Rodrigues for details.
|
@param tvec Translation vector.
|
@param cameraMatrix Camera matrix \f$A = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{_1}\f$ .
|
@param distCoeffs Input vector of distortion coefficients
|
\f$(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6 [, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\f$ of
|
4, 5, 8, 12 or 14 elements. If the vector is empty, the zero distortion coefficients are assumed.
|
@param imagePoints Output array of image points, 1xN/Nx1 2-channel, or
|
vector\<Point2f\> .
|
@param jacobian Optional output 2Nx(10+\<numDistCoeffs\>) jacobian matrix of derivatives of image
|
points with respect to components of the rotation vector, translation vector, focal lengths,
|
coordinates of the principal point and the distortion coefficients. In the old interface different
|
components of the jacobian are returned via different output parameters.
|
@param aspectRatio Optional "fixed aspect ratio" parameter. If the parameter is not 0, the
|
function assumes that the aspect ratio (*fx/fy*) is fixed and correspondingly adjusts the jacobian
|
matrix.
|
|
The function computes projections of 3D points to the image plane given intrinsic and extrinsic
|
camera parameters. Optionally, the function computes Jacobians - matrices of partial derivatives of
|
image points coordinates (as functions of all the input parameters) with respect to the particular
|
parameters, intrinsic and/or extrinsic. The Jacobians are used during the global optimization in
|
calibrateCamera, solvePnP, and stereoCalibrate . The function itself can also be used to compute a
|
re-projection error given the current intrinsic and extrinsic parameters.
|
|
@note By setting rvec=tvec=(0,0,0) or by setting cameraMatrix to a 3x3 identity matrix, or by
|
passing zero distortion coefficients, you can get various useful partial cases of the function. This
|
means that you can compute the distorted coordinates for a sparse set of points or apply a
|
perspective transformation (and also compute the derivatives) in the ideal zero-distortion setup.
|
*/
|
CV_EXPORTS_W void projectPoints( InputArray objectPoints,
|
InputArray rvec, InputArray tvec,
|
InputArray cameraMatrix, InputArray distCoeffs,
|
OutputArray imagePoints,
|
OutputArray jacobian = noArray(),
|
double aspectRatio = 0 );
|
|
/** @example samples/cpp/tutorial_code/features2D/Homography/homography_from_camera_displacement.cpp
|
An example program about homography from the camera displacement
|
|
Check @ref tutorial_homography "the corresponding tutorial" for more details
|
*/
|
|
/** @brief Finds an object pose from 3D-2D point correspondences.
|
This function returns the rotation and the translation vectors that transform a 3D point expressed in the object
|
coordinate frame to the camera coordinate frame, using different methods:
|
- P3P methods (@ref SOLVEPNP_P3P, @ref SOLVEPNP_AP3P): need 4 input points to return a unique solution.
|
- @ref SOLVEPNP_IPPE Input points must be >= 4 and object points must be coplanar.
|
- @ref SOLVEPNP_IPPE_SQUARE Special case suitable for marker pose estimation.
|
Number of input points must be 4. Object points must be defined in the following order:
|
- point 0: [-squareLength / 2, squareLength / 2, 0]
|
- point 1: [ squareLength / 2, squareLength / 2, 0]
|
- point 2: [ squareLength / 2, -squareLength / 2, 0]
|
- point 3: [-squareLength / 2, -squareLength / 2, 0]
|
- for all the other flags, number of input points must be >= 4 and object points can be in any configuration.
|
|
@param objectPoints Array of object points in the object coordinate space, Nx3 1-channel or
|
1xN/Nx1 3-channel, where N is the number of points. vector\<Point3d\> can be also passed here.
|
@param imagePoints Array of corresponding image points, Nx2 1-channel or 1xN/Nx1 2-channel,
|
where N is the number of points. vector\<Point2d\> can be also passed here.
|
@param cameraMatrix Input camera matrix \f$A = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\f$ .
|
@param distCoeffs Input vector of distortion coefficients
|
\f$(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6 [, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\f$ of
|
4, 5, 8, 12 or 14 elements. If the vector is NULL/empty, the zero distortion coefficients are
|
assumed.
|
@param rvec Output rotation vector (see @ref Rodrigues ) that, together with tvec, brings points from
|
the model coordinate system to the camera coordinate system.
|
@param tvec Output translation vector.
|
@param useExtrinsicGuess Parameter used for #SOLVEPNP_ITERATIVE. If true (1), the function uses
|
the provided rvec and tvec values as initial approximations of the rotation and translation
|
vectors, respectively, and further optimizes them.
|
@param flags Method for solving a PnP problem:
|
- **SOLVEPNP_ITERATIVE** Iterative method is based on a Levenberg-Marquardt optimization. In
|
this case the function finds such a pose that minimizes reprojection error, that is the sum
|
of squared distances between the observed projections imagePoints and the projected (using
|
projectPoints ) objectPoints .
|
- **SOLVEPNP_P3P** Method is based on the paper of X.S. Gao, X.-R. Hou, J. Tang, H.-F. Chang
|
"Complete Solution Classification for the Perspective-Three-Point Problem" (@cite gao2003complete).
|
In this case the function requires exactly four object and image points.
|
- **SOLVEPNP_AP3P** Method is based on the paper of T. Ke, S. Roumeliotis
|
"An Efficient Algebraic Solution to the Perspective-Three-Point Problem" (@cite Ke17).
|
In this case the function requires exactly four object and image points.
|
- **SOLVEPNP_EPNP** Method has been introduced by F. Moreno-Noguer, V. Lepetit and P. Fua in the
|
paper "EPnP: Efficient Perspective-n-Point Camera Pose Estimation" (@cite lepetit2009epnp).
|
- **SOLVEPNP_DLS** Method is based on the paper of J. Hesch and S. Roumeliotis.
|
"A Direct Least-Squares (DLS) Method for PnP" (@cite hesch2011direct).
|
- **SOLVEPNP_UPNP** Method is based on the paper of A. Penate-Sanchez, J. Andrade-Cetto,
|
F. Moreno-Noguer. "Exhaustive Linearization for Robust Camera Pose and Focal Length
|
Estimation" (@cite penate2013exhaustive). In this case the function also estimates the parameters \f$f_x\f$ and \f$f_y\f$
|
assuming that both have the same value. Then the cameraMatrix is updated with the estimated
|
focal length.
|
- **SOLVEPNP_IPPE** Method is based on the paper of T. Collins and A. Bartoli.
|
"Infinitesimal Plane-Based Pose Estimation" (@cite Collins14). This method requires coplanar object points.
|
- **SOLVEPNP_IPPE_SQUARE** Method is based on the paper of Toby Collins and Adrien Bartoli.
|
"Infinitesimal Plane-Based Pose Estimation" (@cite Collins14). This method is suitable for marker pose estimation.
|
It requires 4 coplanar object points defined in the following order:
|
- point 0: [-squareLength / 2, squareLength / 2, 0]
|
- point 1: [ squareLength / 2, squareLength / 2, 0]
|
- point 2: [ squareLength / 2, -squareLength / 2, 0]
|
- point 3: [-squareLength / 2, -squareLength / 2, 0]
|
|
The function estimates the object pose given a set of object points, their corresponding image
|
projections, as well as the camera matrix and the distortion coefficients, see the figure below
|
(more precisely, the X-axis of the camera frame is pointing to the right, the Y-axis downward
|
and the Z-axis forward).
|
|
|
|
Points expressed in the world frame \f$ \bf{X}_w \f$ are projected into the image plane \f$ \left[ u, v \right] \f$
|
using the perspective projection model \f$ \Pi \f$ and the camera intrinsic parameters matrix \f$ \bf{A} \f$:
|
|
\f[
|
\begin{align*}
|
\begin{bmatrix}
|
u \\
|
v \\
|
1
|
\end{bmatrix} &=
|
\bf{A} \hspace{0.1em} \Pi \hspace{0.2em} ^{c}\bf{T}_w
|
\begin{bmatrix}
|
X_{w} \\
|
Y_{w} \\
|
Z_{w} \\
|
1
|
\end{bmatrix} \\
|
\begin{bmatrix}
|
u \\
|
v \\
|
1
|
\end{bmatrix} &=
|
\begin{bmatrix}
|
f_x & 0 & c_x \\
|
0 & f_y & c_y \\
|
0 & 0 & 1
|
\end{bmatrix}
|
\begin{bmatrix}
|
1 & 0 & 0 & 0 \\
|
0 & 1 & 0 & 0 \\
|
0 & 0 & 1 & 0
|
\end{bmatrix}
|
\begin{bmatrix}
|
r_{11} & r_{12} & r_{13} & t_x \\
|
r_{21} & r_{22} & r_{23} & t_y \\
|
r_{31} & r_{32} & r_{33} & t_z \\
|
0 & 0 & 0 & 1
|
\end{bmatrix}
|
\begin{bmatrix}
|
X_{w} \\
|
Y_{w} \\
|
Z_{w} \\
|
1
|
\end{bmatrix}
|
\end{align*}
|
\f]
|
|
The estimated pose is thus the rotation (`rvec`) and the translation (`tvec`) vectors that allow transforming
|
a 3D point expressed in the world frame into the camera frame:
|
|
\f[
|
\begin{align*}
|
\begin{bmatrix}
|
X_c \\
|
Y_c \\
|
Z_c \\
|
1
|
\end{bmatrix} &=
|
\hspace{0.2em} ^{c}\bf{T}_w
|
\begin{bmatrix}
|
X_{w} \\
|
Y_{w} \\
|
Z_{w} \\
|
1
|
\end{bmatrix} \\
|
\begin{bmatrix}
|
X_c \\
|
Y_c \\
|
Z_c \\
|
1
|
\end{bmatrix} &=
|
\begin{bmatrix}
|
r_{11} & r_{12} & r_{13} & t_x \\
|
r_{21} & r_{22} & r_{23} & t_y \\
|
r_{31} & r_{32} & r_{33} & t_z \\
|
0 & 0 & 0 & 1
|
\end{bmatrix}
|
\begin{bmatrix}
|
X_{w} \\
|
Y_{w} \\
|
Z_{w} \\
|
1
|
\end{bmatrix}
|
\end{align*}
|
\f]
|
|
@note
|
- An example of how to use solvePnP for planar augmented reality can be found at
|
opencv_source_code/samples/python/plane_ar.py
|
- If you are using Python:
|
- Numpy array slices won't work as input because solvePnP requires contiguous
|
arrays (enforced by the assertion using cv::Mat::checkVector() around line 55 of
|
modules/calib3d/src/solvepnp.cpp version 2.4.9)
|
- The P3P algorithm requires image points to be in an array of shape (N,1,2) due
|
to its calling of cv::undistortPoints (around line 75 of modules/calib3d/src/solvepnp.cpp version 2.4.9)
|
which requires 2-channel information.
|
- Thus, given some data D = np.array(...) where D.shape = (N,M), in order to use a subset of
|
it as, e.g., imagePoints, one must effectively copy it into a new array: imagePoints =
|
np.ascontiguousarray(D[:,:2]).reshape((N,1,2))
|
- The methods **SOLVEPNP_DLS** and **SOLVEPNP_UPNP** cannot be used as the current implementations are
|
unstable and sometimes give completely wrong results. If you pass one of these two
|
flags, **SOLVEPNP_EPNP** method will be used instead.
|
- The minimum number of points is 4 in the general case. In the case of **SOLVEPNP_P3P** and **SOLVEPNP_AP3P**
|
methods, it is required to use exactly 4 points (the first 3 points are used to estimate all the solutions
|
of the P3P problem, the last one is used to retain the best solution that minimizes the reprojection error).
|
- With **SOLVEPNP_ITERATIVE** method and `useExtrinsicGuess=true`, the minimum number of points is 3 (3 points
|
are sufficient to compute a pose but there are up to 4 solutions). The initial solution should be close to the
|
global solution to converge.
|
- With **SOLVEPNP_IPPE** input points must be >= 4 and object points must be coplanar.
|
- With **SOLVEPNP_IPPE_SQUARE** this is a special case suitable for marker pose estimation.
|
Number of input points must be 4. Object points must be defined in the following order:
|
- point 0: [-squareLength / 2, squareLength / 2, 0]
|
- point 1: [ squareLength / 2, squareLength / 2, 0]
|
- point 2: [ squareLength / 2, -squareLength / 2, 0]
|
- point 3: [-squareLength / 2, -squareLength / 2, 0]
|
*/
|
CV_EXPORTS_W bool solvePnP( InputArray objectPoints, InputArray imagePoints,
|
InputArray cameraMatrix, InputArray distCoeffs,
|
OutputArray rvec, OutputArray tvec,
|
bool useExtrinsicGuess = false, int flags = SOLVEPNP_ITERATIVE );
|
|
/** @brief Finds an object pose from 3D-2D point correspondences using the RANSAC scheme.
|
|
@param objectPoints Array of object points in the object coordinate space, Nx3 1-channel or
|
1xN/Nx1 3-channel, where N is the number of points. vector\<Point3d\> can be also passed here.
|
@param imagePoints Array of corresponding image points, Nx2 1-channel or 1xN/Nx1 2-channel,
|
where N is the number of points. vector\<Point2d\> can be also passed here.
|
@param cameraMatrix Input camera matrix \f$A = \vecthreethree{fx}{0}{cx}{0}{fy}{cy}{0}{0}{1}\f$ .
|
@param distCoeffs Input vector of distortion coefficients
|
\f$(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6 [, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\f$ of
|
4, 5, 8, 12 or 14 elements. If the vector is NULL/empty, the zero distortion coefficients are
|
assumed.
|
@param rvec Output rotation vector (see @ref Rodrigues ) that, together with tvec, brings points from
|
the model coordinate system to the camera coordinate system.
|
@param tvec Output translation vector.
|
@param useExtrinsicGuess Parameter used for @ref SOLVEPNP_ITERATIVE. If true (1), the function uses
|
the provided rvec and tvec values as initial approximations of the rotation and translation
|
vectors, respectively, and further optimizes them.
|
@param iterationsCount Number of iterations.
|
@param reprojectionError Inlier threshold value used by the RANSAC procedure. The parameter value
|
is the maximum allowed distance between the observed and computed point projections to consider it
|
an inlier.
|
@param confidence The probability that the algorithm produces a useful result.
|
@param inliers Output vector that contains indices of inliers in objectPoints and imagePoints .
|
@param flags Method for solving a PnP problem (see @ref solvePnP ).
|
|
The function estimates an object pose given a set of object points, their corresponding image
|
projections, as well as the camera matrix and the distortion coefficients. This function finds such
|
a pose that minimizes reprojection error, that is, the sum of squared distances between the observed
|
projections imagePoints and the projected (using @ref projectPoints ) objectPoints. The use of RANSAC
|
makes the function resistant to outliers.
|
|
@note
|
- An example of how to use solvePNPRansac for object detection can be found at
|
opencv_source_code/samples/cpp/tutorial_code/calib3d/real_time_pose_estimation/
|
- The default method used to estimate the camera pose for the Minimal Sample Sets step
|
is #SOLVEPNP_EPNP. Exceptions are:
|
- if you choose #SOLVEPNP_P3P or #SOLVEPNP_AP3P, these methods will be used.
|
- if the number of input points is equal to 4, #SOLVEPNP_P3P is used.
|
- The method used to estimate the camera pose using all the inliers is defined by the
|
flags parameters unless it is equal to #SOLVEPNP_P3P or #SOLVEPNP_AP3P. In this case,
|
the method #SOLVEPNP_EPNP will be used instead.
|
*/
|
CV_EXPORTS_W bool solvePnPRansac( InputArray objectPoints, InputArray imagePoints,
|
InputArray cameraMatrix, InputArray distCoeffs,
|
OutputArray rvec, OutputArray tvec,
|
bool useExtrinsicGuess = false, int iterationsCount = 100,
|
float reprojectionError = 8.0, double confidence = 0.99,
|
OutputArray inliers = noArray(), int flags = SOLVEPNP_ITERATIVE );
|
|
/** @brief Finds an object pose from 3 3D-2D point correspondences.
|
|
@param objectPoints Array of object points in the object coordinate space, 3x3 1-channel or
|
1x3/3x1 3-channel. vector\<Point3f\> can be also passed here.
|
@param imagePoints Array of corresponding image points, 3x2 1-channel or 1x3/3x1 2-channel.
|
vector\<Point2f\> can be also passed here.
|
@param cameraMatrix Input camera matrix \f$A = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\f$ .
|
@param distCoeffs Input vector of distortion coefficients
|
\f$(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6 [, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\f$ of
|
4, 5, 8, 12 or 14 elements. If the vector is NULL/empty, the zero distortion coefficients are
|
assumed.
|
@param rvecs Output rotation vectors (see @ref Rodrigues ) that, together with tvecs, brings points from
|
the model coordinate system to the camera coordinate system. A P3P problem has up to 4 solutions.
|
@param tvecs Output translation vectors.
|
@param flags Method for solving a P3P problem:
|
- **SOLVEPNP_P3P** Method is based on the paper of X.S. Gao, X.-R. Hou, J. Tang, H.-F. Chang
|
"Complete Solution Classification for the Perspective-Three-Point Problem" (@cite gao2003complete).
|
- **SOLVEPNP_AP3P** Method is based on the paper of T. Ke and S. Roumeliotis.
|
"An Efficient Algebraic Solution to the Perspective-Three-Point Problem" (@cite Ke17).
|
|
The function estimates the object pose given 3 object points, their corresponding image
|
projections, as well as the camera matrix and the distortion coefficients.
|
|
@note
|
The solutions are sorted by reprojection errors (lowest to highest).
|
*/
|
CV_EXPORTS_W int solveP3P( InputArray objectPoints, InputArray imagePoints,
|
InputArray cameraMatrix, InputArray distCoeffs,
|
OutputArrayOfArrays rvecs, OutputArrayOfArrays tvecs,
|
int flags );
|
|
/** @brief Refine a pose (the translation and the rotation that transform a 3D point expressed in the object coordinate frame
|
to the camera coordinate frame) from a 3D-2D point correspondences and starting from an initial solution.
|
|
@param objectPoints Array of object points in the object coordinate space, Nx3 1-channel or 1xN/Nx1 3-channel,
|
where N is the number of points. vector\<Point3d\> can also be passed here.
|
@param imagePoints Array of corresponding image points, Nx2 1-channel or 1xN/Nx1 2-channel,
|
where N is the number of points. vector\<Point2d\> can also be passed here.
|
@param cameraMatrix Input camera matrix \f$A = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\f$ .
|
@param distCoeffs Input vector of distortion coefficients
|
\f$(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6 [, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\f$ of
|
4, 5, 8, 12 or 14 elements. If the vector is NULL/empty, the zero distortion coefficients are
|
assumed.
|
@param rvec Input/Output rotation vector (see @ref Rodrigues ) that, together with tvec, brings points from
|
the model coordinate system to the camera coordinate system. Input values are used as an initial solution.
|
@param tvec Input/Output translation vector. Input values are used as an initial solution.
|
@param criteria Criteria when to stop the Levenberg-Marquard iterative algorithm.
|
|
The function refines the object pose given at least 3 object points, their corresponding image
|
projections, an initial solution for the rotation and translation vector,
|
as well as the camera matrix and the distortion coefficients.
|
The function minimizes the projection error with respect to the rotation and the translation vectors, according
|
to a Levenberg-Marquardt iterative minimization @cite Madsen04 @cite Eade13 process.
|
*/
|
CV_EXPORTS_W void solvePnPRefineLM( InputArray objectPoints, InputArray imagePoints,
|
InputArray cameraMatrix, InputArray distCoeffs,
|
InputOutputArray rvec, InputOutputArray tvec,
|
TermCriteria criteria = TermCriteria(TermCriteria::EPS + TermCriteria::COUNT, 20, FLT_EPSILON));
|
|
/** @brief Refine a pose (the translation and the rotation that transform a 3D point expressed in the object coordinate frame
|
to the camera coordinate frame) from a 3D-2D point correspondences and starting from an initial solution.
|
|
@param objectPoints Array of object points in the object coordinate space, Nx3 1-channel or 1xN/Nx1 3-channel,
|
where N is the number of points. vector\<Point3d\> can also be passed here.
|
@param imagePoints Array of corresponding image points, Nx2 1-channel or 1xN/Nx1 2-channel,
|
where N is the number of points. vector\<Point2d\> can also be passed here.
|
@param cameraMatrix Input camera matrix \f$A = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\f$ .
|
@param distCoeffs Input vector of distortion coefficients
|
\f$(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6 [, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\f$ of
|
4, 5, 8, 12 or 14 elements. If the vector is NULL/empty, the zero distortion coefficients are
|
assumed.
|
@param rvec Input/Output rotation vector (see @ref Rodrigues ) that, together with tvec, brings points from
|
the model coordinate system to the camera coordinate system. Input values are used as an initial solution.
|
@param tvec Input/Output translation vector. Input values are used as an initial solution.
|
@param criteria Criteria when to stop the Levenberg-Marquard iterative algorithm.
|
@param VVSlambda Gain for the virtual visual servoing control law, equivalent to the \f$\alpha\f$
|
gain in the Damped Gauss-Newton formulation.
|
|
The function refines the object pose given at least 3 object points, their corresponding image
|
projections, an initial solution for the rotation and translation vector,
|
as well as the camera matrix and the distortion coefficients.
|
The function minimizes the projection error with respect to the rotation and the translation vectors, using a
|
virtual visual servoing (VVS) @cite Chaumette06 @cite Marchand16 scheme.
|
*/
|
CV_EXPORTS_W void solvePnPRefineVVS( InputArray objectPoints, InputArray imagePoints,
|
InputArray cameraMatrix, InputArray distCoeffs,
|
InputOutputArray rvec, InputOutputArray tvec,
|
TermCriteria criteria = TermCriteria(TermCriteria::EPS + TermCriteria::COUNT, 20, FLT_EPSILON),
|
double VVSlambda = 1);
|
|
/** @brief Finds an object pose from 3D-2D point correspondences.
|
This function returns a list of all the possible solutions (a solution is a <rotation vector, translation vector>
|
couple), depending on the number of input points and the chosen method:
|
- P3P methods (@ref SOLVEPNP_P3P, @ref SOLVEPNP_AP3P): 3 or 4 input points. Number of returned solutions can be between 0 and 4 with 3 input points.
|
- @ref SOLVEPNP_IPPE Input points must be >= 4 and object points must be coplanar. Returns 2 solutions.
|
- @ref SOLVEPNP_IPPE_SQUARE Special case suitable for marker pose estimation.
|
Number of input points must be 4 and 2 solutions are returned. Object points must be defined in the following order:
|
- point 0: [-squareLength / 2, squareLength / 2, 0]
|
- point 1: [ squareLength / 2, squareLength / 2, 0]
|
- point 2: [ squareLength / 2, -squareLength / 2, 0]
|
- point 3: [-squareLength / 2, -squareLength / 2, 0]
|
- for all the other flags, number of input points must be >= 4 and object points can be in any configuration.
|
Only 1 solution is returned.
|
|
@param objectPoints Array of object points in the object coordinate space, Nx3 1-channel or
|
1xN/Nx1 3-channel, where N is the number of points. vector\<Point3d\> can be also passed here.
|
@param imagePoints Array of corresponding image points, Nx2 1-channel or 1xN/Nx1 2-channel,
|
where N is the number of points. vector\<Point2d\> can be also passed here.
|
@param cameraMatrix Input camera matrix \f$A = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\f$ .
|
@param distCoeffs Input vector of distortion coefficients
|
\f$(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6 [, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\f$ of
|
4, 5, 8, 12 or 14 elements. If the vector is NULL/empty, the zero distortion coefficients are
|
assumed.
|
@param rvecs Vector of output rotation vectors (see @ref Rodrigues ) that, together with tvecs, brings points from
|
the model coordinate system to the camera coordinate system.
|
@param tvecs Vector of output translation vectors.
|
@param useExtrinsicGuess Parameter used for #SOLVEPNP_ITERATIVE. If true (1), the function uses
|
the provided rvec and tvec values as initial approximations of the rotation and translation
|
vectors, respectively, and further optimizes them.
|
@param flags Method for solving a PnP problem:
|
- **SOLVEPNP_ITERATIVE** Iterative method is based on a Levenberg-Marquardt optimization. In
|
this case the function finds such a pose that minimizes reprojection error, that is the sum
|
of squared distances between the observed projections imagePoints and the projected (using
|
projectPoints ) objectPoints .
|
- **SOLVEPNP_P3P** Method is based on the paper of X.S. Gao, X.-R. Hou, J. Tang, H.-F. Chang
|
"Complete Solution Classification for the Perspective-Three-Point Problem" (@cite gao2003complete).
|
In this case the function requires exactly four object and image points.
|
- **SOLVEPNP_AP3P** Method is based on the paper of T. Ke, S. Roumeliotis
|
"An Efficient Algebraic Solution to the Perspective-Three-Point Problem" (@cite Ke17).
|
In this case the function requires exactly four object and image points.
|
- **SOLVEPNP_EPNP** Method has been introduced by F.Moreno-Noguer, V.Lepetit and P.Fua in the
|
paper "EPnP: Efficient Perspective-n-Point Camera Pose Estimation" (@cite lepetit2009epnp).
|
- **SOLVEPNP_DLS** Method is based on the paper of Joel A. Hesch and Stergios I. Roumeliotis.
|
"A Direct Least-Squares (DLS) Method for PnP" (@cite hesch2011direct).
|
- **SOLVEPNP_UPNP** Method is based on the paper of A.Penate-Sanchez, J.Andrade-Cetto,
|
F.Moreno-Noguer. "Exhaustive Linearization for Robust Camera Pose and Focal Length
|
Estimation" (@cite penate2013exhaustive). In this case the function also estimates the parameters \f$f_x\f$ and \f$f_y\f$
|
assuming that both have the same value. Then the cameraMatrix is updated with the estimated
|
focal length.
|
- **SOLVEPNP_IPPE** Method is based on the paper of T. Collins and A. Bartoli.
|
"Infinitesimal Plane-Based Pose Estimation" (@cite Collins14). This method requires coplanar object points.
|
- **SOLVEPNP_IPPE_SQUARE** Method is based on the paper of Toby Collins and Adrien Bartoli.
|
"Infinitesimal Plane-Based Pose Estimation" (@cite Collins14). This method is suitable for marker pose estimation.
|
It requires 4 coplanar object points defined in the following order:
|
- point 0: [-squareLength / 2, squareLength / 2, 0]
|
- point 1: [ squareLength / 2, squareLength / 2, 0]
|
- point 2: [ squareLength / 2, -squareLength / 2, 0]
|
- point 3: [-squareLength / 2, -squareLength / 2, 0]
|
@param rvec Rotation vector used to initialize an iterative PnP refinement algorithm, when flag is SOLVEPNP_ITERATIVE
|
and useExtrinsicGuess is set to true.
|
@param tvec Translation vector used to initialize an iterative PnP refinement algorithm, when flag is SOLVEPNP_ITERATIVE
|
and useExtrinsicGuess is set to true.
|
@param reprojectionError Optional vector of reprojection error, that is the RMS error
|
(\f$ \text{RMSE} = \sqrt{\frac{\sum_{i}^{N} \left ( \hat{y_i} - y_i \right )^2}{N}} \f$) between the input image points
|
and the 3D object points projected with the estimated pose.
|
|
The function estimates the object pose given a set of object points, their corresponding image
|
projections, as well as the camera matrix and the distortion coefficients, see the figure below
|
(more precisely, the X-axis of the camera frame is pointing to the right, the Y-axis downward
|
and the Z-axis forward).
|
|
|
|
Points expressed in the world frame \f$ \bf{X}_w \f$ are projected into the image plane \f$ \left[ u, v \right] \f$
|
using the perspective projection model \f$ \Pi \f$ and the camera intrinsic parameters matrix \f$ \bf{A} \f$:
|
|
\f[
|
\begin{align*}
|
\begin{bmatrix}
|
u \\
|
v \\
|
1
|
\end{bmatrix} &=
|
\bf{A} \hspace{0.1em} \Pi \hspace{0.2em} ^{c}\bf{T}_w
|
\begin{bmatrix}
|
X_{w} \\
|
Y_{w} \\
|
Z_{w} \\
|
1
|
\end{bmatrix} \\
|
\begin{bmatrix}
|
u \\
|
v \\
|
1
|
\end{bmatrix} &=
|
\begin{bmatrix}
|
f_x & 0 & c_x \\
|
0 & f_y & c_y \\
|
0 & 0 & 1
|
\end{bmatrix}
|
\begin{bmatrix}
|
1 & 0 & 0 & 0 \\
|
0 & 1 & 0 & 0 \\
|
0 & 0 & 1 & 0
|
\end{bmatrix}
|
\begin{bmatrix}
|
r_{11} & r_{12} & r_{13} & t_x \\
|
r_{21} & r_{22} & r_{23} & t_y \\
|
r_{31} & r_{32} & r_{33} & t_z \\
|
0 & 0 & 0 & 1
|
\end{bmatrix}
|
\begin{bmatrix}
|
X_{w} \\
|
Y_{w} \\
|
Z_{w} \\
|
1
|
\end{bmatrix}
|
\end{align*}
|
\f]
|
|
The estimated pose is thus the rotation (`rvec`) and the translation (`tvec`) vectors that allow transforming
|
a 3D point expressed in the world frame into the camera frame:
|
|
\f[
|
\begin{align*}
|
\begin{bmatrix}
|
X_c \\
|
Y_c \\
|
Z_c \\
|
1
|
\end{bmatrix} &=
|
\hspace{0.2em} ^{c}\bf{T}_w
|
\begin{bmatrix}
|
X_{w} \\
|
Y_{w} \\
|
Z_{w} \\
|
1
|
\end{bmatrix} \\
|
\begin{bmatrix}
|
X_c \\
|
Y_c \\
|
Z_c \\
|
1
|
\end{bmatrix} &=
|
\begin{bmatrix}
|
r_{11} & r_{12} & r_{13} & t_x \\
|
r_{21} & r_{22} & r_{23} & t_y \\
|
r_{31} & r_{32} & r_{33} & t_z \\
|
0 & 0 & 0 & 1
|
\end{bmatrix}
|
\begin{bmatrix}
|
X_{w} \\
|
Y_{w} \\
|
Z_{w} \\
|
1
|
\end{bmatrix}
|
\end{align*}
|
\f]
|
|
@note
|
- An example of how to use solvePnP for planar augmented reality can be found at
|
opencv_source_code/samples/python/plane_ar.py
|
- If you are using Python:
|
- Numpy array slices won't work as input because solvePnP requires contiguous
|
arrays (enforced by the assertion using cv::Mat::checkVector() around line 55 of
|
modules/calib3d/src/solvepnp.cpp version 2.4.9)
|
- The P3P algorithm requires image points to be in an array of shape (N,1,2) due
|
to its calling of cv::undistortPoints (around line 75 of modules/calib3d/src/solvepnp.cpp version 2.4.9)
|
which requires 2-channel information.
|
- Thus, given some data D = np.array(...) where D.shape = (N,M), in order to use a subset of
|
it as, e.g., imagePoints, one must effectively copy it into a new array: imagePoints =
|
np.ascontiguousarray(D[:,:2]).reshape((N,1,2))
|
- The methods **SOLVEPNP_DLS** and **SOLVEPNP_UPNP** cannot be used as the current implementations are
|
unstable and sometimes give completely wrong results. If you pass one of these two
|
flags, **SOLVEPNP_EPNP** method will be used instead.
|
- The minimum number of points is 4 in the general case. In the case of **SOLVEPNP_P3P** and **SOLVEPNP_AP3P**
|
methods, it is required to use exactly 4 points (the first 3 points are used to estimate all the solutions
|
of the P3P problem, the last one is used to retain the best solution that minimizes the reprojection error).
|
- With **SOLVEPNP_ITERATIVE** method and `useExtrinsicGuess=true`, the minimum number of points is 3 (3 points
|
are sufficient to compute a pose but there are up to 4 solutions). The initial solution should be close to the
|
global solution to converge.
|
- With **SOLVEPNP_IPPE** input points must be >= 4 and object points must be coplanar.
|
- With **SOLVEPNP_IPPE_SQUARE** this is a special case suitable for marker pose estimation.
|
Number of input points must be 4. Object points must be defined in the following order:
|
- point 0: [-squareLength / 2, squareLength / 2, 0]
|
- point 1: [ squareLength / 2, squareLength / 2, 0]
|
- point 2: [ squareLength / 2, -squareLength / 2, 0]
|
- point 3: [-squareLength / 2, -squareLength / 2, 0]
|
*/
|
CV_EXPORTS_W int solvePnPGeneric( InputArray objectPoints, InputArray imagePoints,
|
InputArray cameraMatrix, InputArray distCoeffs,
|
OutputArrayOfArrays rvecs, OutputArrayOfArrays tvecs,
|
bool useExtrinsicGuess = false, SolvePnPMethod flags = SOLVEPNP_ITERATIVE,
|
InputArray rvec = noArray(), InputArray tvec = noArray(),
|
OutputArray reprojectionError = noArray() );
|
|
/** @brief Finds an initial camera matrix from 3D-2D point correspondences.
|
|
@param objectPoints Vector of vectors of the calibration pattern points in the calibration pattern
|
coordinate space. In the old interface all the per-view vectors are concatenated. See
|
calibrateCamera for details.
|
@param imagePoints Vector of vectors of the projections of the calibration pattern points. In the
|
old interface all the per-view vectors are concatenated.
|
@param imageSize Image size in pixels used to initialize the principal point.
|
@param aspectRatio If it is zero or negative, both \f$f_x\f$ and \f$f_y\f$ are estimated independently.
|
Otherwise, \f$f_x = f_y * \texttt{aspectRatio}\f$ .
|
|
The function estimates and returns an initial camera matrix for the camera calibration process.
|
Currently, the function only supports planar calibration patterns, which are patterns where each
|
object point has z-coordinate =0.
|
*/
|
CV_EXPORTS_W Mat initCameraMatrix2D( InputArrayOfArrays objectPoints,
|
InputArrayOfArrays imagePoints,
|
Size imageSize, double aspectRatio = 1.0 );
|
|
/** @brief Finds the positions of internal corners of the chessboard.
|
|
@param image Source chessboard view. It must be an 8-bit grayscale or color image.
|
@param patternSize Number of inner corners per a chessboard row and column
|
( patternSize = cv::Size(points_per_row,points_per_colum) = cv::Size(columns,rows) ).
|
@param corners Output array of detected corners.
|
@param flags Various operation flags that can be zero or a combination of the following values:
|
- **CALIB_CB_ADAPTIVE_THRESH** Use adaptive thresholding to convert the image to black
|
and white, rather than a fixed threshold level (computed from the average image brightness).
|
- **CALIB_CB_NORMALIZE_IMAGE** Normalize the image gamma with equalizeHist before
|
applying fixed or adaptive thresholding.
|
- **CALIB_CB_FILTER_QUADS** Use additional criteria (like contour area, perimeter,
|
square-like shape) to filter out false quads extracted at the contour retrieval stage.
|
- **CALIB_CB_FAST_CHECK** Run a fast check on the image that looks for chessboard corners,
|
and shortcut the call if none is found. This can drastically speed up the call in the
|
degenerate condition when no chessboard is observed.
|
|
The function attempts to determine whether the input image is a view of the chessboard pattern and
|
locate the internal chessboard corners. The function returns a non-zero value if all of the corners
|
are found and they are placed in a certain order (row by row, left to right in every row).
|
Otherwise, if the function fails to find all the corners or reorder them, it returns 0. For example,
|
a regular chessboard has 8 x 8 squares and 7 x 7 internal corners, that is, points where the black
|
squares touch each other. The detected coordinates are approximate, and to determine their positions
|
more accurately, the function calls cornerSubPix. You also may use the function cornerSubPix with
|
different parameters if returned coordinates are not accurate enough.
|
|
Sample usage of detecting and drawing chessboard corners: :
|
@code
|
Size patternsize(8,6); //interior number of corners
|
Mat gray = ....; //source image
|
vector<Point2f> corners; //this will be filled by the detected corners
|
|
//CALIB_CB_FAST_CHECK saves a lot of time on images
|
//that do not contain any chessboard corners
|
bool patternfound = findChessboardCorners(gray, patternsize, corners,
|
CALIB_CB_ADAPTIVE_THRESH + CALIB_CB_NORMALIZE_IMAGE
|
+ CALIB_CB_FAST_CHECK);
|
|
if(patternfound)
|
cornerSubPix(gray, corners, Size(11, 11), Size(-1, -1),
|
TermCriteria(CV_TERMCRIT_EPS + CV_TERMCRIT_ITER, 30, 0.1));
|
|
drawChessboardCorners(img, patternsize, Mat(corners), patternfound);
|
@endcode
|
@note The function requires white space (like a square-thick border, the wider the better) around
|
the board to make the detection more robust in various environments. Otherwise, if there is no
|
border and the background is dark, the outer black squares cannot be segmented properly and so the
|
square grouping and ordering algorithm fails.
|
*/
|
CV_EXPORTS_W bool findChessboardCorners( InputArray image, Size patternSize, OutputArray corners,
|
int flags = CALIB_CB_ADAPTIVE_THRESH + CALIB_CB_NORMALIZE_IMAGE );
|
|
/*
|
Checks whether the image contains chessboard of the specific size or not.
|
If yes, nonzero value is returned.
|
*/
|
CV_EXPORTS_W bool checkChessboard(InputArray img, Size size);
|
|
/** @brief Finds the positions of internal corners of the chessboard using a sector based approach.
|
|
@param image Source chessboard view. It must be an 8-bit grayscale or color image.
|
@param patternSize Number of inner corners per a chessboard row and column
|
( patternSize = cv::Size(points_per_row,points_per_colum) = cv::Size(columns,rows) ).
|
@param corners Output array of detected corners.
|
@param flags Various operation flags that can be zero or a combination of the following values:
|
- **CALIB_CB_NORMALIZE_IMAGE** Normalize the image gamma with equalizeHist before detection.
|
- **CALIB_CB_EXHAUSTIVE** Run an exhaustive search to improve detection rate.
|
- **CALIB_CB_ACCURACY** Up sample input image to improve sub-pixel accuracy due to aliasing effects.
|
This should be used if an accurate camera calibration is required.
|
|
The function is analog to findchessboardCorners but uses a localized radon
|
transformation approximated by box filters being more robust to all sort of
|
noise, faster on larger images and is able to directly return the sub-pixel
|
position of the internal chessboard corners. The Method is based on the paper
|
@cite duda2018 "Accurate Detection and Localization of Checkerboard Corners for
|
Calibration" demonstrating that the returned sub-pixel positions are more
|
accurate than the one returned by cornerSubPix allowing a precise camera
|
calibration for demanding applications.
|
|
@note The function requires a white boarder with roughly the same width as one
|
of the checkerboard fields around the whole board to improve the detection in
|
various environments. In addition, because of the localized radon
|
transformation it is beneficial to use round corners for the field corners
|
which are located on the outside of the board. The following figure illustrates
|
a sample checkerboard optimized for the detection. However, any other checkerboard
|
can be used as well.
|
|
*/
|
CV_EXPORTS_W bool findChessboardCornersSB(InputArray image,Size patternSize, OutputArray corners,int flags=0);
|
|
//! finds subpixel-accurate positions of the chessboard corners
|
CV_EXPORTS_W bool find4QuadCornerSubpix( InputArray img, InputOutputArray corners, Size region_size );
|
|
/** @brief Renders the detected chessboard corners.
|
|
@param image Destination image. It must be an 8-bit color image.
|
@param patternSize Number of inner corners per a chessboard row and column
|
(patternSize = cv::Size(points_per_row,points_per_column)).
|
@param corners Array of detected corners, the output of findChessboardCorners.
|
@param patternWasFound Parameter indicating whether the complete board was found or not. The
|
return value of findChessboardCorners should be passed here.
|
|
The function draws individual chessboard corners detected either as red circles if the board was not
|
found, or as colored corners connected with lines if the board was found.
|
*/
|
CV_EXPORTS_W void drawChessboardCorners( InputOutputArray image, Size patternSize,
|
InputArray corners, bool patternWasFound );
|
|
/** @brief Draw axes of the world/object coordinate system from pose estimation. @sa solvePnP
|
|
@param image Input/output image. It must have 1 or 3 channels. The number of channels is not altered.
|
@param cameraMatrix Input 3x3 floating-point matrix of camera intrinsic parameters.
|
\f$A = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\f$
|
@param distCoeffs Input vector of distortion coefficients
|
\f$(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6 [, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\f$ of
|
4, 5, 8, 12 or 14 elements. If the vector is empty, the zero distortion coefficients are assumed.
|
@param rvec Rotation vector (see @ref Rodrigues ) that, together with tvec, brings points from
|
the model coordinate system to the camera coordinate system.
|
@param tvec Translation vector.
|
@param length Length of the painted axes in the same unit than tvec (usually in meters).
|
@param thickness Line thickness of the painted axes.
|
|
This function draws the axes of the world/object coordinate system w.r.t. to the camera frame.
|
OX is drawn in red, OY in green and OZ in blue.
|
*/
|
CV_EXPORTS_W void drawFrameAxes(InputOutputArray image, InputArray cameraMatrix, InputArray distCoeffs,
|
InputArray rvec, InputArray tvec, float length, int thickness=3);
|
|
struct CV_EXPORTS_W_SIMPLE CirclesGridFinderParameters
|
{
|
CV_WRAP CirclesGridFinderParameters();
|
CV_PROP_RW cv::Size2f densityNeighborhoodSize;
|
CV_PROP_RW float minDensity;
|
CV_PROP_RW int kmeansAttempts;
|
CV_PROP_RW int minDistanceToAddKeypoint;
|
CV_PROP_RW int keypointScale;
|
CV_PROP_RW float minGraphConfidence;
|
CV_PROP_RW float vertexGain;
|
CV_PROP_RW float vertexPenalty;
|
CV_PROP_RW float existingVertexGain;
|
CV_PROP_RW float edgeGain;
|
CV_PROP_RW float edgePenalty;
|
CV_PROP_RW float convexHullFactor;
|
CV_PROP_RW float minRNGEdgeSwitchDist;
|
|
enum GridType
|
{
|
SYMMETRIC_GRID, ASYMMETRIC_GRID
|
};
|
GridType gridType;
|
|
CV_PROP_RW float squareSize; //!< Distance between two adjacent points. Used by CALIB_CB_CLUSTERING.
|
CV_PROP_RW float maxRectifiedDistance; //!< Max deviation from predicion. Used by CALIB_CB_CLUSTERING.
|
};
|
|
#ifndef DISABLE_OPENCV_3_COMPATIBILITY
|
typedef CirclesGridFinderParameters CirclesGridFinderParameters2;
|
#endif
|
|
/** @brief Finds centers in the grid of circles.
|
|
@param image grid view of input circles; it must be an 8-bit grayscale or color image.
|
@param patternSize number of circles per row and column
|
( patternSize = Size(points_per_row, points_per_colum) ).
|
@param centers output array of detected centers.
|
@param flags various operation flags that can be one of the following values:
|
- **CALIB_CB_SYMMETRIC_GRID** uses symmetric pattern of circles.
|
- **CALIB_CB_ASYMMETRIC_GRID** uses asymmetric pattern of circles.
|
- **CALIB_CB_CLUSTERING** uses a special algorithm for grid detection. It is more robust to
|
perspective distortions but much more sensitive to background clutter.
|
@param blobDetector feature detector that finds blobs like dark circles on light background.
|
@param parameters struct for finding circles in a grid pattern.
|
|
The function attempts to determine whether the input image contains a grid of circles. If it is, the
|
function locates centers of the circles. The function returns a non-zero value if all of the centers
|
have been found and they have been placed in a certain order (row by row, left to right in every
|
row). Otherwise, if the function fails to find all the corners or reorder them, it returns 0.
|
|
Sample usage of detecting and drawing the centers of circles: :
|
@code
|
Size patternsize(7,7); //number of centers
|
Mat gray = ....; //source image
|
vector<Point2f> centers; //this will be filled by the detected centers
|
|
bool patternfound = findCirclesGrid(gray, patternsize, centers);
|
|
drawChessboardCorners(img, patternsize, Mat(centers), patternfound);
|
@endcode
|
@note The function requires white space (like a square-thick border, the wider the better) around
|
the board to make the detection more robust in various environments.
|
*/
|
CV_EXPORTS_W bool findCirclesGrid( InputArray image, Size patternSize,
|
OutputArray centers, int flags,
|
const Ptr<FeatureDetector> &blobDetector,
|
const CirclesGridFinderParameters& parameters);
|
|
/** @overload */
|
CV_EXPORTS_W bool findCirclesGrid( InputArray image, Size patternSize,
|
OutputArray centers, int flags = CALIB_CB_SYMMETRIC_GRID,
|
const Ptr<FeatureDetector> &blobDetector = SimpleBlobDetector::create());
|
|
/** @brief Finds the camera intrinsic and extrinsic parameters from several views of a calibration pattern.
|
|
@param objectPoints In the new interface it is a vector of vectors of calibration pattern points in
|
the calibration pattern coordinate space (e.g. std::vector<std::vector<cv::Vec3f>>). The outer
|
vector contains as many elements as the number of the pattern views. If the same calibration pattern
|
is shown in each view and it is fully visible, all the vectors will be the same. Although, it is
|
possible to use partially occluded patterns, or even different patterns in different views. Then,
|
the vectors will be different. The points are 3D, but since they are in a pattern coordinate system,
|
then, if the rig is planar, it may make sense to put the model to a XY coordinate plane so that
|
Z-coordinate of each input object point is 0.
|
In the old interface all the vectors of object points from different views are concatenated
|
together.
|
@param imagePoints In the new interface it is a vector of vectors of the projections of calibration
|
pattern points (e.g. std::vector<std::vector<cv::Vec2f>>). imagePoints.size() and
|
objectPoints.size() and imagePoints[i].size() must be equal to objectPoints[i].size() for each i.
|
In the old interface all the vectors of object points from different views are concatenated
|
together.
|
@param imageSize Size of the image used only to initialize the intrinsic camera matrix.
|
@param cameraMatrix Output 3x3 floating-point camera matrix
|
\f$A = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\f$ . If CV\_CALIB\_USE\_INTRINSIC\_GUESS
|
and/or CALIB_FIX_ASPECT_RATIO are specified, some or all of fx, fy, cx, cy must be
|
initialized before calling the function.
|
@param distCoeffs Output vector of distortion coefficients
|
\f$(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6 [, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\f$ of
|
4, 5, 8, 12 or 14 elements.
|
@param rvecs Output vector of rotation vectors (see Rodrigues ) estimated for each pattern view
|
(e.g. std::vector<cv::Mat>>). That is, each k-th rotation vector together with the corresponding
|
k-th translation vector (see the next output parameter description) brings the calibration pattern
|
from the model coordinate space (in which object points are specified) to the world coordinate
|
space, that is, a real position of the calibration pattern in the k-th pattern view (k=0.. *M* -1).
|
@param tvecs Output vector of translation vectors estimated for each pattern view.
|
@param stdDeviationsIntrinsics Output vector of standard deviations estimated for intrinsic parameters.
|
Order of deviations values:
|
\f$(f_x, f_y, c_x, c_y, k_1, k_2, p_1, p_2, k_3, k_4, k_5, k_6 , s_1, s_2, s_3,
|
s_4, \tau_x, \tau_y)\f$ If one of parameters is not estimated, it's deviation is equals to zero.
|
@param stdDeviationsExtrinsics Output vector of standard deviations estimated for extrinsic parameters.
|
Order of deviations values: \f$(R_1, T_1, \dotsc , R_M, T_M)\f$ where M is number of pattern views,
|
\f$R_i, T_i\f$ are concatenated 1x3 vectors.
|
@param perViewErrors Output vector of the RMS re-projection error estimated for each pattern view.
|
@param flags Different flags that may be zero or a combination of the following values:
|
- **CALIB_USE_INTRINSIC_GUESS** cameraMatrix contains valid initial values of
|
fx, fy, cx, cy that are optimized further. Otherwise, (cx, cy) is initially set to the image
|
center ( imageSize is used), and focal distances are computed in a least-squares fashion.
|
Note, that if intrinsic parameters are known, there is no need to use this function just to
|
estimate extrinsic parameters. Use solvePnP instead.
|
- **CALIB_FIX_PRINCIPAL_POINT** The principal point is not changed during the global
|
optimization. It stays at the center or at a different location specified when
|
CALIB_USE_INTRINSIC_GUESS is set too.
|
- **CALIB_FIX_ASPECT_RATIO** The functions considers only fy as a free parameter. The
|
ratio fx/fy stays the same as in the input cameraMatrix . When
|
CALIB_USE_INTRINSIC_GUESS is not set, the actual input values of fx and fy are
|
ignored, only their ratio is computed and used further.
|
- **CALIB_ZERO_TANGENT_DIST** Tangential distortion coefficients \f$(p_1, p_2)\f$ are set
|
to zeros and stay zero.
|
- **CALIB_FIX_K1,...,CALIB_FIX_K6** The corresponding radial distortion
|
coefficient is not changed during the optimization. If CALIB_USE_INTRINSIC_GUESS is
|
set, the coefficient from the supplied distCoeffs matrix is used. Otherwise, it is set to 0.
|
- **CALIB_RATIONAL_MODEL** Coefficients k4, k5, and k6 are enabled. To provide the
|
backward compatibility, this extra flag should be explicitly specified to make the
|
calibration function use the rational model and return 8 coefficients. If the flag is not
|
set, the function computes and returns only 5 distortion coefficients.
|
- **CALIB_THIN_PRISM_MODEL** Coefficients s1, s2, s3 and s4 are enabled. To provide the
|
backward compatibility, this extra flag should be explicitly specified to make the
|
calibration function use the thin prism model and return 12 coefficients. If the flag is not
|
set, the function computes and returns only 5 distortion coefficients.
|
- **CALIB_FIX_S1_S2_S3_S4** The thin prism distortion coefficients are not changed during
|
the optimization. If CALIB_USE_INTRINSIC_GUESS is set, the coefficient from the
|
supplied distCoeffs matrix is used. Otherwise, it is set to 0.
|
- **CALIB_TILTED_MODEL** Coefficients tauX and tauY are enabled. To provide the
|
backward compatibility, this extra flag should be explicitly specified to make the
|
calibration function use the tilted sensor model and return 14 coefficients. If the flag is not
|
set, the function computes and returns only 5 distortion coefficients.
|
- **CALIB_FIX_TAUX_TAUY** The coefficients of the tilted sensor model are not changed during
|
the optimization. If CALIB_USE_INTRINSIC_GUESS is set, the coefficient from the
|
supplied distCoeffs matrix is used. Otherwise, it is set to 0.
|
@param criteria Termination criteria for the iterative optimization algorithm.
|
|
@return the overall RMS re-projection error.
|
|
The function estimates the intrinsic camera parameters and extrinsic parameters for each of the
|
views. The algorithm is based on @cite Zhang2000 and @cite BouguetMCT . The coordinates of 3D object
|
points and their corresponding 2D projections in each view must be specified. That may be achieved
|
by using an object with a known geometry and easily detectable feature points. Such an object is
|
called a calibration rig or calibration pattern, and OpenCV has built-in support for a chessboard as
|
a calibration rig (see findChessboardCorners ). Currently, initialization of intrinsic parameters
|
(when CALIB_USE_INTRINSIC_GUESS is not set) is only implemented for planar calibration
|
patterns (where Z-coordinates of the object points must be all zeros). 3D calibration rigs can also
|
be used as long as initial cameraMatrix is provided.
|
|
The algorithm performs the following steps:
|
|
- Compute the initial intrinsic parameters (the option only available for planar calibration
|
patterns) or read them from the input parameters. The distortion coefficients are all set to
|
zeros initially unless some of CALIB_FIX_K? are specified.
|
|
- Estimate the initial camera pose as if the intrinsic parameters have been already known. This is
|
done using solvePnP .
|
|
- Run the global Levenberg-Marquardt optimization algorithm to minimize the reprojection error,
|
that is, the total sum of squared distances between the observed feature points imagePoints and
|
the projected (using the current estimates for camera parameters and the poses) object points
|
objectPoints. See projectPoints for details.
|
|
@note
|
If you use a non-square (=non-NxN) grid and findChessboardCorners for calibration, and
|
calibrateCamera returns bad values (zero distortion coefficients, an image center very far from
|
(w/2-0.5,h/2-0.5), and/or large differences between \f$f_x\f$ and \f$f_y\f$ (ratios of 10:1 or more)),
|
then you have probably used patternSize=cvSize(rows,cols) instead of using
|
patternSize=cvSize(cols,rows) in findChessboardCorners .
|
|
@sa
|
calibrateCameraRO, findChessboardCorners, solvePnP, initCameraMatrix2D, stereoCalibrate, undistort
|
*/
|
CV_EXPORTS_AS(calibrateCameraExtended) double calibrateCamera( InputArrayOfArrays objectPoints,
|
InputArrayOfArrays imagePoints, Size imageSize,
|
InputOutputArray cameraMatrix, InputOutputArray distCoeffs,
|
OutputArrayOfArrays rvecs, OutputArrayOfArrays tvecs,
|
OutputArray stdDeviationsIntrinsics,
|
OutputArray stdDeviationsExtrinsics,
|
OutputArray perViewErrors,
|
int flags = 0, TermCriteria criteria = TermCriteria(
|
TermCriteria::COUNT + TermCriteria::EPS, 30, DBL_EPSILON) );
|
|
/** @overload */
|
CV_EXPORTS_W double calibrateCamera( InputArrayOfArrays objectPoints,
|
InputArrayOfArrays imagePoints, Size imageSize,
|
InputOutputArray cameraMatrix, InputOutputArray distCoeffs,
|
OutputArrayOfArrays rvecs, OutputArrayOfArrays tvecs,
|
int flags = 0, TermCriteria criteria = TermCriteria(
|
TermCriteria::COUNT + TermCriteria::EPS, 30, DBL_EPSILON) );
|
|
/** @brief Finds the camera intrinsic and extrinsic parameters from several views of a calibration pattern.
|
|
This function is an extension of calibrateCamera() with the method of releasing object which was
|
proposed in @cite strobl2011iccv. In many common cases with inaccurate, unmeasured, roughly planar
|
targets (calibration plates), this method can dramatically improve the precision of the estimated
|
camera parameters. Both the object-releasing method and standard method are supported by this
|
function. Use the parameter **iFixedPoint** for method selection. In the internal implementation,
|
calibrateCamera() is a wrapper for this function.
|
|
@param objectPoints Vector of vectors of calibration pattern points in the calibration pattern
|
coordinate space. See calibrateCamera() for details. If the method of releasing object to be used,
|
the identical calibration board must be used in each view and it must be fully visible, and all
|
objectPoints[i] must be the same and all points should be roughly close to a plane. **The calibration
|
target has to be rigid, or at least static if the camera (rather than the calibration target) is
|
shifted for grabbing images.**
|
@param imagePoints Vector of vectors of the projections of calibration pattern points. See
|
calibrateCamera() for details.
|
@param imageSize Size of the image used only to initialize the intrinsic camera matrix.
|
@param iFixedPoint The index of the 3D object point in objectPoints[0] to be fixed. It also acts as
|
a switch for calibration method selection. If object-releasing method to be used, pass in the
|
parameter in the range of [1, objectPoints[0].size()-2], otherwise a value out of this range will
|
make standard calibration method selected. Usually the top-right corner point of the calibration
|
board grid is recommended to be fixed when object-releasing method being utilized. According to
|
\cite strobl2011iccv, two other points are also fixed. In this implementation, objectPoints[0].front
|
and objectPoints[0].back.z are used. With object-releasing method, accurate rvecs, tvecs and
|
newObjPoints are only possible if coordinates of these three fixed points are accurate enough.
|
@param cameraMatrix Output 3x3 floating-point camera matrix. See calibrateCamera() for details.
|
@param distCoeffs Output vector of distortion coefficients. See calibrateCamera() for details.
|
@param rvecs Output vector of rotation vectors estimated for each pattern view. See calibrateCamera()
|
for details.
|
@param tvecs Output vector of translation vectors estimated for each pattern view.
|
@param newObjPoints The updated output vector of calibration pattern points. The coordinates might
|
be scaled based on three fixed points. The returned coordinates are accurate only if the above
|
mentioned three fixed points are accurate. If not needed, noArray() can be passed in. This parameter
|
is ignored with standard calibration method.
|
@param stdDeviationsIntrinsics Output vector of standard deviations estimated for intrinsic parameters.
|
See calibrateCamera() for details.
|
@param stdDeviationsExtrinsics Output vector of standard deviations estimated for extrinsic parameters.
|
See calibrateCamera() for details.
|
@param stdDeviationsObjPoints Output vector of standard deviations estimated for refined coordinates
|
of calibration pattern points. It has the same size and order as objectPoints[0] vector. This
|
parameter is ignored with standard calibration method.
|
@param perViewErrors Output vector of the RMS re-projection error estimated for each pattern view.
|
@param flags Different flags that may be zero or a combination of some predefined values. See
|
calibrateCamera() for details. If the method of releasing object is used, the calibration time may
|
be much longer. CALIB_USE_QR or CALIB_USE_LU could be used for faster calibration with potentially
|
less precise and less stable in some rare cases.
|
@param criteria Termination criteria for the iterative optimization algorithm.
|
|
@return the overall RMS re-projection error.
|
|
The function estimates the intrinsic camera parameters and extrinsic parameters for each of the
|
views. The algorithm is based on @cite Zhang2000, @cite BouguetMCT and @cite strobl2011iccv. See
|
calibrateCamera() for other detailed explanations.
|
@sa
|
calibrateCamera, findChessboardCorners, solvePnP, initCameraMatrix2D, stereoCalibrate, undistort
|
*/
|
CV_EXPORTS_AS(calibrateCameraROExtended) double calibrateCameraRO( InputArrayOfArrays objectPoints,
|
InputArrayOfArrays imagePoints, Size imageSize, int iFixedPoint,
|
InputOutputArray cameraMatrix, InputOutputArray distCoeffs,
|
OutputArrayOfArrays rvecs, OutputArrayOfArrays tvecs,
|
OutputArray newObjPoints,
|
OutputArray stdDeviationsIntrinsics,
|
OutputArray stdDeviationsExtrinsics,
|
OutputArray stdDeviationsObjPoints,
|
OutputArray perViewErrors,
|
int flags = 0, TermCriteria criteria = TermCriteria(
|
TermCriteria::COUNT + TermCriteria::EPS, 30, DBL_EPSILON) );
|
|
/** @overload */
|
CV_EXPORTS_W double calibrateCameraRO( InputArrayOfArrays objectPoints,
|
InputArrayOfArrays imagePoints, Size imageSize, int iFixedPoint,
|
InputOutputArray cameraMatrix, InputOutputArray distCoeffs,
|
OutputArrayOfArrays rvecs, OutputArrayOfArrays tvecs,
|
OutputArray newObjPoints,
|
int flags = 0, TermCriteria criteria = TermCriteria(
|
TermCriteria::COUNT + TermCriteria::EPS, 30, DBL_EPSILON) );
|
|
/** @brief Computes useful camera characteristics from the camera matrix.
|
|
@param cameraMatrix Input camera matrix that can be estimated by calibrateCamera or
|
stereoCalibrate .
|
@param imageSize Input image size in pixels.
|
@param apertureWidth Physical width in mm of the sensor.
|
@param apertureHeight Physical height in mm of the sensor.
|
@param fovx Output field of view in degrees along the horizontal sensor axis.
|
@param fovy Output field of view in degrees along the vertical sensor axis.
|
@param focalLength Focal length of the lens in mm.
|
@param principalPoint Principal point in mm.
|
@param aspectRatio \f$f_y/f_x\f$
|
|
The function computes various useful camera characteristics from the previously estimated camera
|
matrix.
|
|
@note
|
Do keep in mind that the unity measure 'mm' stands for whatever unit of measure one chooses for
|
the chessboard pitch (it can thus be any value).
|
*/
|
CV_EXPORTS_W void calibrationMatrixValues( InputArray cameraMatrix, Size imageSize,
|
double apertureWidth, double apertureHeight,
|
CV_OUT double& fovx, CV_OUT double& fovy,
|
CV_OUT double& focalLength, CV_OUT Point2d& principalPoint,
|
CV_OUT double& aspectRatio );
|
|
/** @brief Calibrates the stereo camera.
|
|
@param objectPoints Vector of vectors of the calibration pattern points.
|
@param imagePoints1 Vector of vectors of the projections of the calibration pattern points,
|
observed by the first camera.
|
@param imagePoints2 Vector of vectors of the projections of the calibration pattern points,
|
observed by the second camera.
|
@param cameraMatrix1 Input/output first camera matrix:
|
\f$\vecthreethree{f_x^{(j)}}{0}{c_x^{(j)}}{0}{f_y^{(j)}}{c_y^{(j)}}{0}{0}{1}\f$ , \f$j = 0,\, 1\f$ . If
|
any of CALIB_USE_INTRINSIC_GUESS , CALIB_FIX_ASPECT_RATIO ,
|
CALIB_FIX_INTRINSIC , or CALIB_FIX_FOCAL_LENGTH are specified, some or all of the
|
matrix components must be initialized. See the flags description for details.
|
@param distCoeffs1 Input/output vector of distortion coefficients
|
\f$(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6 [, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\f$ of
|
4, 5, 8, 12 or 14 elements. The output vector length depends on the flags.
|
@param cameraMatrix2 Input/output second camera matrix. The parameter is similar to cameraMatrix1
|
@param distCoeffs2 Input/output lens distortion coefficients for the second camera. The parameter
|
is similar to distCoeffs1 .
|
@param imageSize Size of the image used only to initialize intrinsic camera matrix.
|
@param R Output rotation matrix between the 1st and the 2nd camera coordinate systems.
|
@param T Output translation vector between the coordinate systems of the cameras.
|
@param E Output essential matrix.
|
@param F Output fundamental matrix.
|
@param perViewErrors Output vector of the RMS re-projection error estimated for each pattern view.
|
@param flags Different flags that may be zero or a combination of the following values:
|
- **CALIB_FIX_INTRINSIC** Fix cameraMatrix? and distCoeffs? so that only R, T, E , and F
|
matrices are estimated.
|
- **CALIB_USE_INTRINSIC_GUESS** Optimize some or all of the intrinsic parameters
|
according to the specified flags. Initial values are provided by the user.
|
- **CALIB_USE_EXTRINSIC_GUESS** R, T contain valid initial values that are optimized further.
|
Otherwise R, T are initialized to the median value of the pattern views (each dimension separately).
|
- **CALIB_FIX_PRINCIPAL_POINT** Fix the principal points during the optimization.
|
- **CALIB_FIX_FOCAL_LENGTH** Fix \f$f^{(j)}_x\f$ and \f$f^{(j)}_y\f$ .
|
- **CALIB_FIX_ASPECT_RATIO** Optimize \f$f^{(j)}_y\f$ . Fix the ratio \f$f^{(j)}_x/f^{(j)}_y\f$
|
.
|
- **CALIB_SAME_FOCAL_LENGTH** Enforce \f$f^{(0)}_x=f^{(1)}_x\f$ and \f$f^{(0)}_y=f^{(1)}_y\f$ .
|
- **CALIB_ZERO_TANGENT_DIST** Set tangential distortion coefficients for each camera to
|
zeros and fix there.
|
- **CALIB_FIX_K1,...,CALIB_FIX_K6** Do not change the corresponding radial
|
distortion coefficient during the optimization. If CALIB_USE_INTRINSIC_GUESS is set,
|
the coefficient from the supplied distCoeffs matrix is used. Otherwise, it is set to 0.
|
- **CALIB_RATIONAL_MODEL** Enable coefficients k4, k5, and k6. To provide the backward
|
compatibility, this extra flag should be explicitly specified to make the calibration
|
function use the rational model and return 8 coefficients. If the flag is not set, the
|
function computes and returns only 5 distortion coefficients.
|
- **CALIB_THIN_PRISM_MODEL** Coefficients s1, s2, s3 and s4 are enabled. To provide the
|
backward compatibility, this extra flag should be explicitly specified to make the
|
calibration function use the thin prism model and return 12 coefficients. If the flag is not
|
set, the function computes and returns only 5 distortion coefficients.
|
- **CALIB_FIX_S1_S2_S3_S4** The thin prism distortion coefficients are not changed during
|
the optimization. If CALIB_USE_INTRINSIC_GUESS is set, the coefficient from the
|
supplied distCoeffs matrix is used. Otherwise, it is set to 0.
|
- **CALIB_TILTED_MODEL** Coefficients tauX and tauY are enabled. To provide the
|
backward compatibility, this extra flag should be explicitly specified to make the
|
calibration function use the tilted sensor model and return 14 coefficients. If the flag is not
|
set, the function computes and returns only 5 distortion coefficients.
|
- **CALIB_FIX_TAUX_TAUY** The coefficients of the tilted sensor model are not changed during
|
the optimization. If CALIB_USE_INTRINSIC_GUESS is set, the coefficient from the
|
supplied distCoeffs matrix is used. Otherwise, it is set to 0.
|
@param criteria Termination criteria for the iterative optimization algorithm.
|
|
The function estimates transformation between two cameras making a stereo pair. If you have a stereo
|
camera where the relative position and orientation of two cameras is fixed, and if you computed
|
poses of an object relative to the first camera and to the second camera, (R1, T1) and (R2, T2),
|
respectively (this can be done with solvePnP ), then those poses definitely relate to each other.
|
This means that, given ( \f$R_1\f$,\f$T_1\f$ ), it should be possible to compute ( \f$R_2\f$,\f$T_2\f$ ). You only
|
need to know the position and orientation of the second camera relative to the first camera. This is
|
what the described function does. It computes ( \f$R\f$,\f$T\f$ ) so that:
|
|
\f[R_2=R*R_1\f]
|
\f[T_2=R*T_1 + T,\f]
|
|
Optionally, it computes the essential matrix E:
|
|
\f[E= \vecthreethree{0}{-T_2}{T_1}{T_2}{0}{-T_0}{-T_1}{T_0}{0} *R\f]
|
|
where \f$T_i\f$ are components of the translation vector \f$T\f$ : \f$T=[T_0, T_1, T_2]^T\f$ . And the function
|
can also compute the fundamental matrix F:
|
|
\f[F = cameraMatrix2^{-T} E cameraMatrix1^{-1}\f]
|
|
Besides the stereo-related information, the function can also perform a full calibration of each of
|
two cameras. However, due to the high dimensionality of the parameter space and noise in the input
|
data, the function can diverge from the correct solution. If the intrinsic parameters can be
|
estimated with high accuracy for each of the cameras individually (for example, using
|
calibrateCamera ), you are recommended to do so and then pass CALIB_FIX_INTRINSIC flag to the
|
function along with the computed intrinsic parameters. Otherwise, if all the parameters are
|
estimated at once, it makes sense to restrict some parameters, for example, pass
|
CALIB_SAME_FOCAL_LENGTH and CALIB_ZERO_TANGENT_DIST flags, which is usually a
|
reasonable assumption.
|
|
Similarly to calibrateCamera , the function minimizes the total re-projection error for all the
|
points in all the available views from both cameras. The function returns the final value of the
|
re-projection error.
|
*/
|
CV_EXPORTS_AS(stereoCalibrateExtended) double stereoCalibrate( InputArrayOfArrays objectPoints,
|
InputArrayOfArrays imagePoints1, InputArrayOfArrays imagePoints2,
|
InputOutputArray cameraMatrix1, InputOutputArray distCoeffs1,
|
InputOutputArray cameraMatrix2, InputOutputArray distCoeffs2,
|
Size imageSize, InputOutputArray R,InputOutputArray T, OutputArray E, OutputArray F,
|
OutputArray perViewErrors, int flags = CALIB_FIX_INTRINSIC,
|
TermCriteria criteria = TermCriteria(TermCriteria::COUNT+TermCriteria::EPS, 30, 1e-6) );
|
|
/// @overload
|
CV_EXPORTS_W double stereoCalibrate( InputArrayOfArrays objectPoints,
|
InputArrayOfArrays imagePoints1, InputArrayOfArrays imagePoints2,
|
InputOutputArray cameraMatrix1, InputOutputArray distCoeffs1,
|
InputOutputArray cameraMatrix2, InputOutputArray distCoeffs2,
|
Size imageSize, OutputArray R,OutputArray T, OutputArray E, OutputArray F,
|
int flags = CALIB_FIX_INTRINSIC,
|
TermCriteria criteria = TermCriteria(TermCriteria::COUNT+TermCriteria::EPS, 30, 1e-6) );
|
|
/** @brief Computes rectification transforms for each head of a calibrated stereo camera.
|
|
@param cameraMatrix1 First camera matrix.
|
@param distCoeffs1 First camera distortion parameters.
|
@param cameraMatrix2 Second camera matrix.
|
@param distCoeffs2 Second camera distortion parameters.
|
@param imageSize Size of the image used for stereo calibration.
|
@param R Rotation matrix from the coordinate system of the first camera to the second.
|
@param T Translation vector from the coordinate system of the first camera to the second.
|
@param R1 Output 3x3 rectification transform (rotation matrix) for the first camera.
|
@param R2 Output 3x3 rectification transform (rotation matrix) for the second camera.
|
@param P1 Output 3x4 projection matrix in the new (rectified) coordinate systems for the first
|
camera.
|
@param P2 Output 3x4 projection matrix in the new (rectified) coordinate systems for the second
|
camera.
|
@param Q Output \f$4 \times 4\f$ disparity-to-depth mapping matrix (see reprojectImageTo3D ).
|
@param flags Operation flags that may be zero or CALIB_ZERO_DISPARITY . If the flag is set,
|
the function makes the principal points of each camera have the same pixel coordinates in the
|
rectified views. And if the flag is not set, the function may still shift the images in the
|
horizontal or vertical direction (depending on the orientation of epipolar lines) to maximize the
|
useful image area.
|
@param alpha Free scaling parameter. If it is -1 or absent, the function performs the default
|
scaling. Otherwise, the parameter should be between 0 and 1. alpha=0 means that the rectified
|
images are zoomed and shifted so that only valid pixels are visible (no black areas after
|
rectification). alpha=1 means that the rectified image is decimated and shifted so that all the
|
pixels from the original images from the cameras are retained in the rectified images (no source
|
image pixels are lost). Obviously, any intermediate value yields an intermediate result between
|
those two extreme cases.
|
@param newImageSize New image resolution after rectification. The same size should be passed to
|
initUndistortRectifyMap (see the stereo_calib.cpp sample in OpenCV samples directory). When (0,0)
|
is passed (default), it is set to the original imageSize . Setting it to larger value can help you
|
preserve details in the original image, especially when there is a big radial distortion.
|
@param validPixROI1 Optional output rectangles inside the rectified images where all the pixels
|
are valid. If alpha=0 , the ROIs cover the whole images. Otherwise, they are likely to be smaller
|
(see the picture below).
|
@param validPixROI2 Optional output rectangles inside the rectified images where all the pixels
|
are valid. If alpha=0 , the ROIs cover the whole images. Otherwise, they are likely to be smaller
|
(see the picture below).
|
|
The function computes the rotation matrices for each camera that (virtually) make both camera image
|
planes the same plane. Consequently, this makes all the epipolar lines parallel and thus simplifies
|
the dense stereo correspondence problem. The function takes the matrices computed by stereoCalibrate
|
as input. As output, it provides two rotation matrices and also two projection matrices in the new
|
coordinates. The function distinguishes the following two cases:
|
|
- **Horizontal stereo**: the first and the second camera views are shifted relative to each other
|
mainly along the x axis (with possible small vertical shift). In the rectified images, the
|
corresponding epipolar lines in the left and right cameras are horizontal and have the same
|
y-coordinate. P1 and P2 look like:
|
|
\f[\texttt{P1} = \begin{bmatrix} f & 0 & cx_1 & 0 \\ 0 & f & cy & 0 \\ 0 & 0 & 1 & 0 \end{bmatrix}\f]
|
|
\f[\texttt{P2} = \begin{bmatrix} f & 0 & cx_2 & T_x*f \\ 0 & f & cy & 0 \\ 0 & 0 & 1 & 0 \end{bmatrix} ,\f]
|
|
where \f$T_x\f$ is a horizontal shift between the cameras and \f$cx_1=cx_2\f$ if
|
CALIB_ZERO_DISPARITY is set.
|
|
- **Vertical stereo**: the first and the second camera views are shifted relative to each other
|
mainly in vertical direction (and probably a bit in the horizontal direction too). The epipolar
|
lines in the rectified images are vertical and have the same x-coordinate. P1 and P2 look like:
|
|
\f[\texttt{P1} = \begin{bmatrix} f & 0 & cx & 0 \\ 0 & f & cy_1 & 0 \\ 0 & 0 & 1 & 0 \end{bmatrix}\f]
|
|
\f[\texttt{P2} = \begin{bmatrix} f & 0 & cx & 0 \\ 0 & f & cy_2 & T_y*f \\ 0 & 0 & 1 & 0 \end{bmatrix} ,\f]
|
|
where \f$T_y\f$ is a vertical shift between the cameras and \f$cy_1=cy_2\f$ if CALIB_ZERO_DISPARITY is
|
set.
|
|
As you can see, the first three columns of P1 and P2 will effectively be the new "rectified" camera
|
matrices. The matrices, together with R1 and R2 , can then be passed to initUndistortRectifyMap to
|
initialize the rectification map for each camera.
|
|
See below the screenshot from the stereo_calib.cpp sample. Some red horizontal lines pass through
|
the corresponding image regions. This means that the images are well rectified, which is what most
|
stereo correspondence algorithms rely on. The green rectangles are roi1 and roi2 . You see that
|
their interiors are all valid pixels.
|
|
|
*/
|
CV_EXPORTS_W void stereoRectify( InputArray cameraMatrix1, InputArray distCoeffs1,
|
InputArray cameraMatrix2, InputArray distCoeffs2,
|
Size imageSize, InputArray R, InputArray T,
|
OutputArray R1, OutputArray R2,
|
OutputArray P1, OutputArray P2,
|
OutputArray Q, int flags = CALIB_ZERO_DISPARITY,
|
double alpha = -1, Size newImageSize = Size(),
|
CV_OUT Rect* validPixROI1 = 0, CV_OUT Rect* validPixROI2 = 0 );
|
|
/** @brief Computes a rectification transform for an uncalibrated stereo camera.
|
|
@param points1 Array of feature points in the first image.
|
@param points2 The corresponding points in the second image. The same formats as in
|
findFundamentalMat are supported.
|
@param F Input fundamental matrix. It can be computed from the same set of point pairs using
|
findFundamentalMat .
|
@param imgSize Size of the image.
|
@param H1 Output rectification homography matrix for the first image.
|
@param H2 Output rectification homography matrix for the second image.
|
@param threshold Optional threshold used to filter out the outliers. If the parameter is greater
|
than zero, all the point pairs that do not comply with the epipolar geometry (that is, the points
|
for which \f$|\texttt{points2[i]}^T*\texttt{F}*\texttt{points1[i]}|>\texttt{threshold}\f$ ) are
|
rejected prior to computing the homographies. Otherwise, all the points are considered inliers.
|
|
The function computes the rectification transformations without knowing intrinsic parameters of the
|
cameras and their relative position in the space, which explains the suffix "uncalibrated". Another
|
related difference from stereoRectify is that the function outputs not the rectification
|
transformations in the object (3D) space, but the planar perspective transformations encoded by the
|
homography matrices H1 and H2 . The function implements the algorithm @cite Hartley99 .
|
|
@note
|
While the algorithm does not need to know the intrinsic parameters of the cameras, it heavily
|
depends on the epipolar geometry. Therefore, if the camera lenses have a significant distortion,
|
it would be better to correct it before computing the fundamental matrix and calling this
|
function. For example, distortion coefficients can be estimated for each head of stereo camera
|
separately by using calibrateCamera . Then, the images can be corrected using undistort , or
|
just the point coordinates can be corrected with undistortPoints .
|
*/
|
CV_EXPORTS_W bool stereoRectifyUncalibrated( InputArray points1, InputArray points2,
|
InputArray F, Size imgSize,
|
OutputArray H1, OutputArray H2,
|
double threshold = 5 );
|
|
//! computes the rectification transformations for 3-head camera, where all the heads are on the same line.
|
CV_EXPORTS_W float rectify3Collinear( InputArray cameraMatrix1, InputArray distCoeffs1,
|
InputArray cameraMatrix2, InputArray distCoeffs2,
|
InputArray cameraMatrix3, InputArray distCoeffs3,
|
InputArrayOfArrays imgpt1, InputArrayOfArrays imgpt3,
|
Size imageSize, InputArray R12, InputArray T12,
|
InputArray R13, InputArray T13,
|
OutputArray R1, OutputArray R2, OutputArray R3,
|
OutputArray P1, OutputArray P2, OutputArray P3,
|
OutputArray Q, double alpha, Size newImgSize,
|
CV_OUT Rect* roi1, CV_OUT Rect* roi2, int flags );
|
|
/** @brief Returns the new camera matrix based on the free scaling parameter.
|
|
@param cameraMatrix Input camera matrix.
|
@param distCoeffs Input vector of distortion coefficients
|
\f$(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6 [, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\f$ of
|
4, 5, 8, 12 or 14 elements. If the vector is NULL/empty, the zero distortion coefficients are
|
assumed.
|
@param imageSize Original image size.
|
@param alpha Free scaling parameter between 0 (when all the pixels in the undistorted image are
|
valid) and 1 (when all the source image pixels are retained in the undistorted image). See
|
stereoRectify for details.
|
@param newImgSize Image size after rectification. By default, it is set to imageSize .
|
@param validPixROI Optional output rectangle that outlines all-good-pixels region in the
|
undistorted image. See roi1, roi2 description in stereoRectify .
|
@param centerPrincipalPoint Optional flag that indicates whether in the new camera matrix the
|
principal point should be at the image center or not. By default, the principal point is chosen to
|
best fit a subset of the source image (determined by alpha) to the corrected image.
|
@return new_camera_matrix Output new camera matrix.
|
|
The function computes and returns the optimal new camera matrix based on the free scaling parameter.
|
By varying this parameter, you may retrieve only sensible pixels alpha=0 , keep all the original
|
image pixels if there is valuable information in the corners alpha=1 , or get something in between.
|
When alpha\>0 , the undistorted result is likely to have some black pixels corresponding to
|
"virtual" pixels outside of the captured distorted image. The original camera matrix, distortion
|
coefficients, the computed new camera matrix, and newImageSize should be passed to
|
initUndistortRectifyMap to produce the maps for remap .
|
*/
|
CV_EXPORTS_W Mat getOptimalNewCameraMatrix( InputArray cameraMatrix, InputArray distCoeffs,
|
Size imageSize, double alpha, Size newImgSize = Size(),
|
CV_OUT Rect* validPixROI = 0,
|
bool centerPrincipalPoint = false);
|
|
/** @brief Computes Hand-Eye calibration: \f$_{}^{g}\textrm{T}_c\f$
|
|
@param[in] R_gripper2base Rotation part extracted from the homogeneous matrix that transforms a point
|
expressed in the gripper frame to the robot base frame (\f$_{}^{b}\textrm{T}_g\f$).
|
This is a vector (`vector<Mat>`) that contains the rotation matrices for all the transformations
|
from gripper frame to robot base frame.
|
@param[in] t_gripper2base Translation part extracted from the homogeneous matrix that transforms a point
|
expressed in the gripper frame to the robot base frame (\f$_{}^{b}\textrm{T}_g\f$).
|
This is a vector (`vector<Mat>`) that contains the translation vectors for all the transformations
|
from gripper frame to robot base frame.
|
@param[in] R_target2cam Rotation part extracted from the homogeneous matrix that transforms a point
|
expressed in the target frame to the camera frame (\f$_{}^{c}\textrm{T}_t\f$).
|
This is a vector (`vector<Mat>`) that contains the rotation matrices for all the transformations
|
from calibration target frame to camera frame.
|
@param[in] t_target2cam Rotation part extracted from the homogeneous matrix that transforms a point
|
expressed in the target frame to the camera frame (\f$_{}^{c}\textrm{T}_t\f$).
|
This is a vector (`vector<Mat>`) that contains the translation vectors for all the transformations
|
from calibration target frame to camera frame.
|
@param[out] R_cam2gripper Estimated rotation part extracted from the homogeneous matrix that transforms a point
|
expressed in the camera frame to the gripper frame (\f$_{}^{g}\textrm{T}_c\f$).
|
@param[out] t_cam2gripper Estimated translation part extracted from the homogeneous matrix that transforms a point
|
expressed in the camera frame to the gripper frame (\f$_{}^{g}\textrm{T}_c\f$).
|
@param[in] method One of the implemented Hand-Eye calibration method, see cv::HandEyeCalibrationMethod
|
|
The function performs the Hand-Eye calibration using various methods. One approach consists in estimating the
|
rotation then the translation (separable solutions) and the following methods are implemented:
|
- R. Tsai, R. Lenz A New Technique for Fully Autonomous and Efficient 3D Robotics Hand/EyeCalibration \cite Tsai89
|
- F. Park, B. Martin Robot Sensor Calibration: Solving AX = XB on the Euclidean Group \cite Park94
|
- R. Horaud, F. Dornaika Hand-Eye Calibration \cite Horaud95
|
|
Another approach consists in estimating simultaneously the rotation and the translation (simultaneous solutions),
|
with the following implemented method:
|
- N. Andreff, R. Horaud, B. Espiau On-line Hand-Eye Calibration \cite Andreff99
|
- K. Daniilidis Hand-Eye Calibration Using Dual Quaternions \cite Daniilidis98
|
|
The following picture describes the Hand-Eye calibration problem where the transformation between a camera ("eye")
|
mounted on a robot gripper ("hand") has to be estimated.
|
|
|
|
The calibration procedure is the following:
|
- a static calibration pattern is used to estimate the transformation between the target frame
|
and the camera frame
|
- the robot gripper is moved in order to acquire several poses
|
- for each pose, the homogeneous transformation between the gripper frame and the robot base frame is recorded using for
|
instance the robot kinematics
|
\f[
|
\begin{bmatrix}
|
X_b\\
|
Y_b\\
|
Z_b\\
|
1
|
\end{bmatrix}
|
=
|
\begin{bmatrix}
|
_{}^{b}\textrm{R}_g & _{}^{b}\textrm{t}_g \\
|
0_{1 \times 3} & 1
|
\end{bmatrix}
|
\begin{bmatrix}
|
X_g\\
|
Y_g\\
|
Z_g\\
|
1
|
\end{bmatrix}
|
\f]
|
- for each pose, the homogeneous transformation between the calibration target frame and the camera frame is recorded using
|
for instance a pose estimation method (PnP) from 2D-3D point correspondences
|
\f[
|
\begin{bmatrix}
|
X_c\\
|
Y_c\\
|
Z_c\\
|
1
|
\end{bmatrix}
|
=
|
\begin{bmatrix}
|
_{}^{c}\textrm{R}_t & _{}^{c}\textrm{t}_t \\
|
0_{1 \times 3} & 1
|
\end{bmatrix}
|
\begin{bmatrix}
|
X_t\\
|
Y_t\\
|
Z_t\\
|
1
|
\end{bmatrix}
|
\f]
|
|
The Hand-Eye calibration procedure returns the following homogeneous transformation
|
\f[
|
\begin{bmatrix}
|
X_g\\
|
Y_g\\
|
Z_g\\
|
1
|
\end{bmatrix}
|
=
|
\begin{bmatrix}
|
_{}^{g}\textrm{R}_c & _{}^{g}\textrm{t}_c \\
|
0_{1 \times 3} & 1
|
\end{bmatrix}
|
\begin{bmatrix}
|
X_c\\
|
Y_c\\
|
Z_c\\
|
1
|
\end{bmatrix}
|
\f]
|
|
This problem is also known as solving the \f$\mathbf{A}\mathbf{X}=\mathbf{X}\mathbf{B}\f$ equation:
|
\f[
|
\begin{align*}
|
^{b}{\textrm{T}_g}^{(1)} \hspace{0.2em} ^{g}\textrm{T}_c \hspace{0.2em} ^{c}{\textrm{T}_t}^{(1)} &=
|
\hspace{0.1em} ^{b}{\textrm{T}_g}^{(2)} \hspace{0.2em} ^{g}\textrm{T}_c \hspace{0.2em} ^{c}{\textrm{T}_t}^{(2)} \\
|
|
(^{b}{\textrm{T}_g}^{(2)})^{-1} \hspace{0.2em} ^{b}{\textrm{T}_g}^{(1)} \hspace{0.2em} ^{g}\textrm{T}_c &=
|
\hspace{0.1em} ^{g}\textrm{T}_c \hspace{0.2em} ^{c}{\textrm{T}_t}^{(2)} (^{c}{\textrm{T}_t}^{(1)})^{-1} \\
|
|
\textrm{A}_i \textrm{X} &= \textrm{X} \textrm{B}_i \\
|
\end{align*}
|
\f]
|
|
\note
|
Additional information can be found on this [website](http://campar.in.tum.de/Chair/HandEyeCalibration).
|
\note
|
A minimum of 2 motions with non parallel rotation axes are necessary to determine the hand-eye transformation.
|
So at least 3 different poses are required, but it is strongly recommended to use many more poses.
|
|
*/
|
CV_EXPORTS_W void calibrateHandEye( InputArrayOfArrays R_gripper2base, InputArrayOfArrays t_gripper2base,
|
InputArrayOfArrays R_target2cam, InputArrayOfArrays t_target2cam,
|
OutputArray R_cam2gripper, OutputArray t_cam2gripper,
|
HandEyeCalibrationMethod method=CALIB_HAND_EYE_TSAI );
|
|
/** @brief Converts points from Euclidean to homogeneous space.
|
|
@param src Input vector of N-dimensional points.
|
@param dst Output vector of N+1-dimensional points.
|
|
The function converts points from Euclidean to homogeneous space by appending 1's to the tuple of
|
point coordinates. That is, each point (x1, x2, ..., xn) is converted to (x1, x2, ..., xn, 1).
|
*/
|
CV_EXPORTS_W void convertPointsToHomogeneous( InputArray src, OutputArray dst );
|
|
/** @brief Converts points from homogeneous to Euclidean space.
|
|
@param src Input vector of N-dimensional points.
|
@param dst Output vector of N-1-dimensional points.
|
|
The function converts points homogeneous to Euclidean space using perspective projection. That is,
|
each point (x1, x2, ... x(n-1), xn) is converted to (x1/xn, x2/xn, ..., x(n-1)/xn). When xn=0, the
|
output point coordinates will be (0,0,0,...).
|
*/
|
CV_EXPORTS_W void convertPointsFromHomogeneous( InputArray src, OutputArray dst );
|
|
/** @brief Converts points to/from homogeneous coordinates.
|
|
@param src Input array or vector of 2D, 3D, or 4D points.
|
@param dst Output vector of 2D, 3D, or 4D points.
|
|
The function converts 2D or 3D points from/to homogeneous coordinates by calling either
|
convertPointsToHomogeneous or convertPointsFromHomogeneous.
|
|
@note The function is obsolete. Use one of the previous two functions instead.
|
*/
|
CV_EXPORTS void convertPointsHomogeneous( InputArray src, OutputArray dst );
|
|
/** @brief Calculates a fundamental matrix from the corresponding points in two images.
|
|
@param points1 Array of N points from the first image. The point coordinates should be
|
floating-point (single or double precision).
|
@param points2 Array of the second image points of the same size and format as points1 .
|
@param method Method for computing a fundamental matrix.
|
- **CV_FM_7POINT** for a 7-point algorithm. \f$N = 7\f$
|
- **CV_FM_8POINT** for an 8-point algorithm. \f$N \ge 8\f$
|
- **CV_FM_RANSAC** for the RANSAC algorithm. \f$N \ge 8\f$
|
- **CV_FM_LMEDS** for the LMedS algorithm. \f$N \ge 8\f$
|
@param ransacReprojThreshold Parameter used only for RANSAC. It is the maximum distance from a point to an epipolar
|
line in pixels, beyond which the point is considered an outlier and is not used for computing the
|
final fundamental matrix. It can be set to something like 1-3, depending on the accuracy of the
|
point localization, image resolution, and the image noise.
|
@param confidence Parameter used for the RANSAC and LMedS methods only. It specifies a desirable level
|
of confidence (probability) that the estimated matrix is correct.
|
@param mask
|
|
The epipolar geometry is described by the following equation:
|
|
\f[[p_2; 1]^T F [p_1; 1] = 0\f]
|
|
where \f$F\f$ is a fundamental matrix, \f$p_1\f$ and \f$p_2\f$ are corresponding points in the first and the
|
second images, respectively.
|
|
The function calculates the fundamental matrix using one of four methods listed above and returns
|
the found fundamental matrix. Normally just one matrix is found. But in case of the 7-point
|
algorithm, the function may return up to 3 solutions ( \f$9 \times 3\f$ matrix that stores all 3
|
matrices sequentially).
|
|
The calculated fundamental matrix may be passed further to computeCorrespondEpilines that finds the
|
epipolar lines corresponding to the specified points. It can also be passed to
|
stereoRectifyUncalibrated to compute the rectification transformation. :
|
@code
|
// Example. Estimation of fundamental matrix using the RANSAC algorithm
|
int point_count = 100;
|
vector<Point2f> points1(point_count);
|
vector<Point2f> points2(point_count);
|
|
// initialize the points here ...
|
for( int i = 0; i < point_count; i++ )
|
{
|
points1[i] = ...;
|
points2[i] = ...;
|
}
|
|
Mat fundamental_matrix =
|
findFundamentalMat(points1, points2, FM_RANSAC, 3, 0.99);
|
@endcode
|
*/
|
CV_EXPORTS_W Mat findFundamentalMat( InputArray points1, InputArray points2,
|
int method = FM_RANSAC,
|
double ransacReprojThreshold = 3., double confidence = 0.99,
|
OutputArray mask = noArray() );
|
|
/** @overload */
|
CV_EXPORTS Mat findFundamentalMat( InputArray points1, InputArray points2,
|
OutputArray mask, int method = FM_RANSAC,
|
double ransacReprojThreshold = 3., double confidence = 0.99 );
|
|
/** @brief Calculates an essential matrix from the corresponding points in two images.
|
|
@param points1 Array of N (N \>= 5) 2D points from the first image. The point coordinates should
|
be floating-point (single or double precision).
|
@param points2 Array of the second image points of the same size and format as points1 .
|
@param cameraMatrix Camera matrix \f$K = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\f$ .
|
Note that this function assumes that points1 and points2 are feature points from cameras with the
|
same camera matrix.
|
@param method Method for computing an essential matrix.
|
- **RANSAC** for the RANSAC algorithm.
|
- **LMEDS** for the LMedS algorithm.
|
@param prob Parameter used for the RANSAC or LMedS methods only. It specifies a desirable level of
|
confidence (probability) that the estimated matrix is correct.
|
@param threshold Parameter used for RANSAC. It is the maximum distance from a point to an epipolar
|
line in pixels, beyond which the point is considered an outlier and is not used for computing the
|
final fundamental matrix. It can be set to something like 1-3, depending on the accuracy of the
|
point localization, image resolution, and the image noise.
|
@param mask Output array of N elements, every element of which is set to 0 for outliers and to 1
|
for the other points. The array is computed only in the RANSAC and LMedS methods.
|
|
This function estimates essential matrix based on the five-point algorithm solver in @cite Nister03 .
|
@cite SteweniusCFS is also a related. The epipolar geometry is described by the following equation:
|
|
\f[[p_2; 1]^T K^{-T} E K^{-1} [p_1; 1] = 0\f]
|
|
where \f$E\f$ is an essential matrix, \f$p_1\f$ and \f$p_2\f$ are corresponding points in the first and the
|
second images, respectively. The result of this function may be passed further to
|
decomposeEssentialMat or recoverPose to recover the relative pose between cameras.
|
*/
|
CV_EXPORTS_W Mat findEssentialMat( InputArray points1, InputArray points2,
|
InputArray cameraMatrix, int method = RANSAC,
|
double prob = 0.999, double threshold = 1.0,
|
OutputArray mask = noArray() );
|
|
/** @overload
|
@param points1 Array of N (N \>= 5) 2D points from the first image. The point coordinates should
|
be floating-point (single or double precision).
|
@param points2 Array of the second image points of the same size and format as points1 .
|
@param focal focal length of the camera. Note that this function assumes that points1 and points2
|
are feature points from cameras with same focal length and principal point.
|
@param pp principal point of the camera.
|
@param method Method for computing a fundamental matrix.
|
- **RANSAC** for the RANSAC algorithm.
|
- **LMEDS** for the LMedS algorithm.
|
@param threshold Parameter used for RANSAC. It is the maximum distance from a point to an epipolar
|
line in pixels, beyond which the point is considered an outlier and is not used for computing the
|
final fundamental matrix. It can be set to something like 1-3, depending on the accuracy of the
|
point localization, image resolution, and the image noise.
|
@param prob Parameter used for the RANSAC or LMedS methods only. It specifies a desirable level of
|
confidence (probability) that the estimated matrix is correct.
|
@param mask Output array of N elements, every element of which is set to 0 for outliers and to 1
|
for the other points. The array is computed only in the RANSAC and LMedS methods.
|
|
This function differs from the one above that it computes camera matrix from focal length and
|
principal point:
|
|
\f[K =
|
\begin{bmatrix}
|
f & 0 & x_{pp} \\
|
0 & f & y_{pp} \\
|
0 & 0 & 1
|
\end{bmatrix}\f]
|
*/
|
CV_EXPORTS_W Mat findEssentialMat( InputArray points1, InputArray points2,
|
double focal = 1.0, Point2d pp = Point2d(0, 0),
|
int method = RANSAC, double prob = 0.999,
|
double threshold = 1.0, OutputArray mask = noArray() );
|
|
/** @brief Decompose an essential matrix to possible rotations and translation.
|
|
@param E The input essential matrix.
|
@param R1 One possible rotation matrix.
|
@param R2 Another possible rotation matrix.
|
@param t One possible translation.
|
|
This function decompose an essential matrix E using svd decomposition @cite HartleyZ00 . Generally 4
|
possible poses exists for a given E. They are \f$[R_1, t]\f$, \f$[R_1, -t]\f$, \f$[R_2, t]\f$, \f$[R_2, -t]\f$. By
|
decomposing E, you can only get the direction of the translation, so the function returns unit t.
|
*/
|
CV_EXPORTS_W void decomposeEssentialMat( InputArray E, OutputArray R1, OutputArray R2, OutputArray t );
|
|
/** @brief Recover relative camera rotation and translation from an estimated essential matrix and the
|
corresponding points in two images, using cheirality check. Returns the number of inliers which pass
|
the check.
|
|
@param E The input essential matrix.
|
@param points1 Array of N 2D points from the first image. The point coordinates should be
|
floating-point (single or double precision).
|
@param points2 Array of the second image points of the same size and format as points1 .
|
@param cameraMatrix Camera matrix \f$K = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\f$ .
|
Note that this function assumes that points1 and points2 are feature points from cameras with the
|
same camera matrix.
|
@param R Recovered relative rotation.
|
@param t Recovered relative translation.
|
@param mask Input/output mask for inliers in points1 and points2.
|
: If it is not empty, then it marks inliers in points1 and points2 for then given essential
|
matrix E. Only these inliers will be used to recover pose. In the output mask only inliers
|
which pass the cheirality check.
|
This function decomposes an essential matrix using decomposeEssentialMat and then verifies possible
|
pose hypotheses by doing cheirality check. The cheirality check basically means that the
|
triangulated 3D points should have positive depth. Some details can be found in @cite Nister03 .
|
|
This function can be used to process output E and mask from findEssentialMat. In this scenario,
|
points1 and points2 are the same input for findEssentialMat. :
|
@code
|
// Example. Estimation of fundamental matrix using the RANSAC algorithm
|
int point_count = 100;
|
vector<Point2f> points1(point_count);
|
vector<Point2f> points2(point_count);
|
|
// initialize the points here ...
|
for( int i = 0; i < point_count; i++ )
|
{
|
points1[i] = ...;
|
points2[i] = ...;
|
}
|
|
// cametra matrix with both focal lengths = 1, and principal point = (0, 0)
|
Mat cameraMatrix = Mat::eye(3, 3, CV_64F);
|
|
Mat E, R, t, mask;
|
|
E = findEssentialMat(points1, points2, cameraMatrix, RANSAC, 0.999, 1.0, mask);
|
recoverPose(E, points1, points2, cameraMatrix, R, t, mask);
|
@endcode
|
*/
|
CV_EXPORTS_W int recoverPose( InputArray E, InputArray points1, InputArray points2,
|
InputArray cameraMatrix, OutputArray R, OutputArray t,
|
InputOutputArray mask = noArray() );
|
|
/** @overload
|
@param E The input essential matrix.
|
@param points1 Array of N 2D points from the first image. The point coordinates should be
|
floating-point (single or double precision).
|
@param points2 Array of the second image points of the same size and format as points1 .
|
@param R Recovered relative rotation.
|
@param t Recovered relative translation.
|
@param focal Focal length of the camera. Note that this function assumes that points1 and points2
|
are feature points from cameras with same focal length and principal point.
|
@param pp principal point of the camera.
|
@param mask Input/output mask for inliers in points1 and points2.
|
: If it is not empty, then it marks inliers in points1 and points2 for then given essential
|
matrix E. Only these inliers will be used to recover pose. In the output mask only inliers
|
which pass the cheirality check.
|
|
This function differs from the one above that it computes camera matrix from focal length and
|
principal point:
|
|
\f[K =
|
\begin{bmatrix}
|
f & 0 & x_{pp} \\
|
0 & f & y_{pp} \\
|
0 & 0 & 1
|
\end{bmatrix}\f]
|
*/
|
CV_EXPORTS_W int recoverPose( InputArray E, InputArray points1, InputArray points2,
|
OutputArray R, OutputArray t,
|
double focal = 1.0, Point2d pp = Point2d(0, 0),
|
InputOutputArray mask = noArray() );
|
|
/** @overload
|
@param E The input essential matrix.
|
@param points1 Array of N 2D points from the first image. The point coordinates should be
|
floating-point (single or double precision).
|
@param points2 Array of the second image points of the same size and format as points1.
|
@param cameraMatrix Camera matrix \f$K = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\f$ .
|
Note that this function assumes that points1 and points2 are feature points from cameras with the
|
same camera matrix.
|
@param R Recovered relative rotation.
|
@param t Recovered relative translation.
|
@param distanceThresh threshold distance which is used to filter out far away points (i.e. infinite points).
|
@param mask Input/output mask for inliers in points1 and points2.
|
: If it is not empty, then it marks inliers in points1 and points2 for then given essential
|
matrix E. Only these inliers will be used to recover pose. In the output mask only inliers
|
which pass the cheirality check.
|
@param triangulatedPoints 3d points which were reconstructed by triangulation.
|
*/
|
|
CV_EXPORTS_W int recoverPose( InputArray E, InputArray points1, InputArray points2,
|
InputArray cameraMatrix, OutputArray R, OutputArray t, double distanceThresh, InputOutputArray mask = noArray(),
|
OutputArray triangulatedPoints = noArray());
|
|
/** @brief For points in an image of a stereo pair, computes the corresponding epilines in the other image.
|
|
@param points Input points. \f$N \times 1\f$ or \f$1 \times N\f$ matrix of type CV_32FC2 or
|
vector\<Point2f\> .
|
@param whichImage Index of the image (1 or 2) that contains the points .
|
@param F Fundamental matrix that can be estimated using findFundamentalMat or stereoRectify .
|
@param lines Output vector of the epipolar lines corresponding to the points in the other image.
|
Each line \f$ax + by + c=0\f$ is encoded by 3 numbers \f$(a, b, c)\f$ .
|
|
For every point in one of the two images of a stereo pair, the function finds the equation of the
|
corresponding epipolar line in the other image.
|
|
From the fundamental matrix definition (see findFundamentalMat ), line \f$l^{(2)}_i\f$ in the second
|
image for the point \f$p^{(1)}_i\f$ in the first image (when whichImage=1 ) is computed as:
|
|
\f[l^{(2)}_i = F p^{(1)}_i\f]
|
|
And vice versa, when whichImage=2, \f$l^{(1)}_i\f$ is computed from \f$p^{(2)}_i\f$ as:
|
|
\f[l^{(1)}_i = F^T p^{(2)}_i\f]
|
|
Line coefficients are defined up to a scale. They are normalized so that \f$a_i^2+b_i^2=1\f$ .
|
*/
|
CV_EXPORTS_W void computeCorrespondEpilines( InputArray points, int whichImage,
|
InputArray F, OutputArray lines );
|
|
/** @brief Reconstructs points by triangulation.
|
|
@param projMatr1 3x4 projection matrix of the first camera.
|
@param projMatr2 3x4 projection matrix of the second camera.
|
@param projPoints1 2xN array of feature points in the first image. In case of c++ version it can
|
be also a vector of feature points or two-channel matrix of size 1xN or Nx1.
|
@param projPoints2 2xN array of corresponding points in the second image. In case of c++ version
|
it can be also a vector of feature points or two-channel matrix of size 1xN or Nx1.
|
@param points4D 4xN array of reconstructed points in homogeneous coordinates.
|
|
The function reconstructs 3-dimensional points (in homogeneous coordinates) by using their
|
observations with a stereo camera. Projections matrices can be obtained from stereoRectify.
|
|
@note
|
Keep in mind that all input data should be of float type in order for this function to work.
|
|
@sa
|
reprojectImageTo3D
|
*/
|
CV_EXPORTS_W void triangulatePoints( InputArray projMatr1, InputArray projMatr2,
|
InputArray projPoints1, InputArray projPoints2,
|
OutputArray points4D );
|
|
/** @brief Refines coordinates of corresponding points.
|
|
@param F 3x3 fundamental matrix.
|
@param points1 1xN array containing the first set of points.
|
@param points2 1xN array containing the second set of points.
|
@param newPoints1 The optimized points1.
|
@param newPoints2 The optimized points2.
|
|
The function implements the Optimal Triangulation Method (see Multiple View Geometry for details).
|
For each given point correspondence points1[i] \<-\> points2[i], and a fundamental matrix F, it
|
computes the corrected correspondences newPoints1[i] \<-\> newPoints2[i] that minimize the geometric
|
error \f$d(points1[i], newPoints1[i])^2 + d(points2[i],newPoints2[i])^2\f$ (where \f$d(a,b)\f$ is the
|
geometric distance between points \f$a\f$ and \f$b\f$ ) subject to the epipolar constraint
|
\f$newPoints2^T * F * newPoints1 = 0\f$ .
|
*/
|
CV_EXPORTS_W void correctMatches( InputArray F, InputArray points1, InputArray points2,
|
OutputArray newPoints1, OutputArray newPoints2 );
|
|
/** @brief Filters off small noise blobs (speckles) in the disparity map
|
|
@param img The input 16-bit signed disparity image
|
@param newVal The disparity value used to paint-off the speckles
|
@param maxSpeckleSize The maximum speckle size to consider it a speckle. Larger blobs are not
|
affected by the algorithm
|
@param maxDiff Maximum difference between neighbor disparity pixels to put them into the same
|
blob. Note that since StereoBM, StereoSGBM and may be other algorithms return a fixed-point
|
disparity map, where disparity values are multiplied by 16, this scale factor should be taken into
|
account when specifying this parameter value.
|
@param buf The optional temporary buffer to avoid memory allocation within the function.
|
*/
|
CV_EXPORTS_W void filterSpeckles( InputOutputArray img, double newVal,
|
int maxSpeckleSize, double maxDiff,
|
InputOutputArray buf = noArray() );
|
|
//! computes valid disparity ROI from the valid ROIs of the rectified images (that are returned by cv::stereoRectify())
|
CV_EXPORTS_W Rect getValidDisparityROI( Rect roi1, Rect roi2,
|
int minDisparity, int numberOfDisparities,
|
int SADWindowSize );
|
|
//! validates disparity using the left-right check. The matrix "cost" should be computed by the stereo correspondence algorithm
|
CV_EXPORTS_W void validateDisparity( InputOutputArray disparity, InputArray cost,
|
int minDisparity, int numberOfDisparities,
|
int disp12MaxDisp = 1 );
|
|
/** @brief Reprojects a disparity image to 3D space.
|
|
@param disparity Input single-channel 8-bit unsigned, 16-bit signed, 32-bit signed or 32-bit
|
floating-point disparity image.
|
The values of 8-bit / 16-bit signed formats are assumed to have no fractional bits.
|
If the disparity is 16-bit signed format as computed by
|
StereoBM/StereoSGBM/StereoBinaryBM/StereoBinarySGBM and may be other algorithms,
|
it should be divided by 16 (and scaled to float) before being used here.
|
@param _3dImage Output 3-channel floating-point image of the same size as disparity . Each
|
element of _3dImage(x,y) contains 3D coordinates of the point (x,y) computed from the disparity
|
map.
|
@param Q \f$4 \times 4\f$ perspective transformation matrix that can be obtained with stereoRectify.
|
@param handleMissingValues Indicates, whether the function should handle missing values (i.e.
|
points where the disparity was not computed). If handleMissingValues=true, then pixels with the
|
minimal disparity that corresponds to the outliers (see StereoMatcher::compute ) are transformed
|
to 3D points with a very large Z value (currently set to 10000).
|
@param ddepth The optional output array depth. If it is -1, the output image will have CV_32F
|
depth. ddepth can also be set to CV_16S, CV_32S or CV_32F.
|
|
The function transforms a single-channel disparity map to a 3-channel image representing a 3D
|
surface. That is, for each pixel (x,y) and the corresponding disparity d=disparity(x,y) , it
|
computes:
|
|
\f[\begin{array}{l} [X \; Y \; Z \; W]^T = \texttt{Q} *[x \; y \; \texttt{disparity} (x,y) \; 1]^T \\ \texttt{\_3dImage} (x,y) = (X/W, \; Y/W, \; Z/W) \end{array}\f]
|
|
The matrix Q can be an arbitrary \f$4 \times 4\f$ matrix (for example, the one computed by
|
stereoRectify). To reproject a sparse set of points {(x,y,d),...} to 3D space, use
|
perspectiveTransform .
|
*/
|
CV_EXPORTS_W void reprojectImageTo3D( InputArray disparity,
|
OutputArray _3dImage, InputArray Q,
|
bool handleMissingValues = false,
|
int ddepth = -1 );
|
|
/** @brief Calculates the Sampson Distance between two points.
|
|
The function cv::sampsonDistance calculates and returns the first order approximation of the geometric error as:
|
\f[
|
sd( \texttt{pt1} , \texttt{pt2} )=
|
\frac{(\texttt{pt2}^t \cdot \texttt{F} \cdot \texttt{pt1})^2}
|
{((\texttt{F} \cdot \texttt{pt1})(0))^2 +
|
((\texttt{F} \cdot \texttt{pt1})(1))^2 +
|
((\texttt{F}^t \cdot \texttt{pt2})(0))^2 +
|
((\texttt{F}^t \cdot \texttt{pt2})(1))^2}
|
\f]
|
The fundamental matrix may be calculated using the cv::findFundamentalMat function. See @cite HartleyZ00 11.4.3 for details.
|
@param pt1 first homogeneous 2d point
|
@param pt2 second homogeneous 2d point
|
@param F fundamental matrix
|
@return The computed Sampson distance.
|
*/
|
CV_EXPORTS_W double sampsonDistance(InputArray pt1, InputArray pt2, InputArray F);
|
|
/** @brief Computes an optimal affine transformation between two 3D point sets.
|
|
It computes
|
\f[
|
\begin{bmatrix}
|
x\\
|
y\\
|
z\\
|
\end{bmatrix}
|
=
|
\begin{bmatrix}
|
a_{11} & a_{12} & a_{13}\\
|
a_{21} & a_{22} & a_{23}\\
|
a_{31} & a_{32} & a_{33}\\
|
\end{bmatrix}
|
\begin{bmatrix}
|
X\\
|
Y\\
|
Z\\
|
\end{bmatrix}
|
+
|
\begin{bmatrix}
|
b_1\\
|
b_2\\
|
b_3\\
|
\end{bmatrix}
|
\f]
|
|
@param src First input 3D point set containing \f$(X,Y,Z)\f$.
|
@param dst Second input 3D point set containing \f$(x,y,z)\f$.
|
@param out Output 3D affine transformation matrix \f$3 \times 4\f$ of the form
|
\f[
|
\begin{bmatrix}
|
a_{11} & a_{12} & a_{13} & b_1\\
|
a_{21} & a_{22} & a_{23} & b_2\\
|
a_{31} & a_{32} & a_{33} & b_3\\
|
\end{bmatrix}
|
\f]
|
@param inliers Output vector indicating which points are inliers (1-inlier, 0-outlier).
|
@param ransacThreshold Maximum reprojection error in the RANSAC algorithm to consider a point as
|
an inlier.
|
@param confidence Confidence level, between 0 and 1, for the estimated transformation. Anything
|
between 0.95 and 0.99 is usually good enough. Values too close to 1 can slow down the estimation
|
significantly. Values lower than 0.8-0.9 can result in an incorrectly estimated transformation.
|
|
The function estimates an optimal 3D affine transformation between two 3D point sets using the
|
RANSAC algorithm.
|
*/
|
CV_EXPORTS_W int estimateAffine3D(InputArray src, InputArray dst,
|
OutputArray out, OutputArray inliers,
|
double ransacThreshold = 3, double confidence = 0.99);
|
|
/** @brief Computes an optimal affine transformation between two 2D point sets.
|
|
It computes
|
\f[
|
\begin{bmatrix}
|
x\\
|
y\\
|
\end{bmatrix}
|
=
|
\begin{bmatrix}
|
a_{11} & a_{12}\\
|
a_{21} & a_{22}\\
|
\end{bmatrix}
|
\begin{bmatrix}
|
X\\
|
Y\\
|
\end{bmatrix}
|
+
|
\begin{bmatrix}
|
b_1\\
|
b_2\\
|
\end{bmatrix}
|
\f]
|
|
@param from First input 2D point set containing \f$(X,Y)\f$.
|
@param to Second input 2D point set containing \f$(x,y)\f$.
|
@param inliers Output vector indicating which points are inliers (1-inlier, 0-outlier).
|
@param method Robust method used to compute transformation. The following methods are possible:
|
- cv::RANSAC - RANSAC-based robust method
|
- cv::LMEDS - Least-Median robust method
|
RANSAC is the default method.
|
@param ransacReprojThreshold Maximum reprojection error in the RANSAC algorithm to consider
|
a point as an inlier. Applies only to RANSAC.
|
@param maxIters The maximum number of robust method iterations.
|
@param confidence Confidence level, between 0 and 1, for the estimated transformation. Anything
|
between 0.95 and 0.99 is usually good enough. Values too close to 1 can slow down the estimation
|
significantly. Values lower than 0.8-0.9 can result in an incorrectly estimated transformation.
|
@param refineIters Maximum number of iterations of refining algorithm (Levenberg-Marquardt).
|
Passing 0 will disable refining, so the output matrix will be output of robust method.
|
|
@return Output 2D affine transformation matrix \f$2 \times 3\f$ or empty matrix if transformation
|
could not be estimated. The returned matrix has the following form:
|
\f[
|
\begin{bmatrix}
|
a_{11} & a_{12} & b_1\\
|
a_{21} & a_{22} & b_2\\
|
\end{bmatrix}
|
\f]
|
|
The function estimates an optimal 2D affine transformation between two 2D point sets using the
|
selected robust algorithm.
|
|
The computed transformation is then refined further (using only inliers) with the
|
Levenberg-Marquardt method to reduce the re-projection error even more.
|
|
@note
|
The RANSAC method can handle practically any ratio of outliers but needs a threshold to
|
distinguish inliers from outliers. The method LMeDS does not need any threshold but it works
|
correctly only when there are more than 50% of inliers.
|
|
@sa estimateAffinePartial2D, getAffineTransform
|
*/
|
CV_EXPORTS_W cv::Mat estimateAffine2D(InputArray from, InputArray to, OutputArray inliers = noArray(),
|
int method = RANSAC, double ransacReprojThreshold = 3,
|
size_t maxIters = 2000, double confidence = 0.99,
|
size_t refineIters = 10);
|
|
/** @brief Computes an optimal limited affine transformation with 4 degrees of freedom between
|
two 2D point sets.
|
|
@param from First input 2D point set.
|
@param to Second input 2D point set.
|
@param inliers Output vector indicating which points are inliers.
|
@param method Robust method used to compute transformation. The following methods are possible:
|
- cv::RANSAC - RANSAC-based robust method
|
- cv::LMEDS - Least-Median robust method
|
RANSAC is the default method.
|
@param ransacReprojThreshold Maximum reprojection error in the RANSAC algorithm to consider
|
a point as an inlier. Applies only to RANSAC.
|
@param maxIters The maximum number of robust method iterations.
|
@param confidence Confidence level, between 0 and 1, for the estimated transformation. Anything
|
between 0.95 and 0.99 is usually good enough. Values too close to 1 can slow down the estimation
|
significantly. Values lower than 0.8-0.9 can result in an incorrectly estimated transformation.
|
@param refineIters Maximum number of iterations of refining algorithm (Levenberg-Marquardt).
|
Passing 0 will disable refining, so the output matrix will be output of robust method.
|
|
@return Output 2D affine transformation (4 degrees of freedom) matrix \f$2 \times 3\f$ or
|
empty matrix if transformation could not be estimated.
|
|
The function estimates an optimal 2D affine transformation with 4 degrees of freedom limited to
|
combinations of translation, rotation, and uniform scaling. Uses the selected algorithm for robust
|
estimation.
|
|
The computed transformation is then refined further (using only inliers) with the
|
Levenberg-Marquardt method to reduce the re-projection error even more.
|
|
Estimated transformation matrix is:
|
\f[ \begin{bmatrix} \cos(\theta) \cdot s & -\sin(\theta) \cdot s & t_x \\
|
\sin(\theta) \cdot s & \cos(\theta) \cdot s & t_y
|
\end{bmatrix} \f]
|
Where \f$ \theta \f$ is the rotation angle, \f$ s \f$ the scaling factor and \f$ t_x, t_y \f$ are
|
translations in \f$ x, y \f$ axes respectively.
|
|
@note
|
The RANSAC method can handle practically any ratio of outliers but need a threshold to
|
distinguish inliers from outliers. The method LMeDS does not need any threshold but it works
|
correctly only when there are more than 50% of inliers.
|
|
@sa estimateAffine2D, getAffineTransform
|
*/
|
CV_EXPORTS_W cv::Mat estimateAffinePartial2D(InputArray from, InputArray to, OutputArray inliers = noArray(),
|
int method = RANSAC, double ransacReprojThreshold = 3,
|
size_t maxIters = 2000, double confidence = 0.99,
|
size_t refineIters = 10);
|
|
/** @example samples/cpp/tutorial_code/features2D/Homography/decompose_homography.cpp
|
An example program with homography decomposition.
|
|
Check @ref tutorial_homography "the corresponding tutorial" for more details.
|
*/
|
|
/** @brief Decompose a homography matrix to rotation(s), translation(s) and plane normal(s).
|
|
@param H The input homography matrix between two images.
|
@param K The input intrinsic camera calibration matrix.
|
@param rotations Array of rotation matrices.
|
@param translations Array of translation matrices.
|
@param normals Array of plane normal matrices.
|
|
This function extracts relative camera motion between two views observing a planar object from the
|
homography H induced by the plane. The intrinsic camera matrix K must also be provided. The function
|
may return up to four mathematical solution sets. At least two of the solutions may further be
|
invalidated if point correspondences are available by applying positive depth constraint (all points
|
must be in front of the camera). The decomposition method is described in detail in @cite Malis .
|
*/
|
CV_EXPORTS_W int decomposeHomographyMat(InputArray H,
|
InputArray K,
|
OutputArrayOfArrays rotations,
|
OutputArrayOfArrays translations,
|
OutputArrayOfArrays normals);
|
|
/** @brief Filters homography decompositions based on additional information.
|
|
@param rotations Vector of rotation matrices.
|
@param normals Vector of plane normal matrices.
|
@param beforePoints Vector of (rectified) visible reference points before the homography is applied
|
@param afterPoints Vector of (rectified) visible reference points after the homography is applied
|
@param possibleSolutions Vector of int indices representing the viable solution set after filtering
|
@param pointsMask optional Mat/Vector of 8u type representing the mask for the inliers as given by the findHomography function
|
|
This function is intended to filter the output of the decomposeHomographyMat based on additional
|
information as described in @cite Malis . The summary of the method: the decomposeHomographyMat function
|
returns 2 unique solutions and their "opposites" for a total of 4 solutions. If we have access to the
|
sets of points visible in the camera frame before and after the homography transformation is applied,
|
we can determine which are the true potential solutions and which are the opposites by verifying which
|
homographies are consistent with all visible reference points being in front of the camera. The inputs
|
are left unchanged; the filtered solution set is returned as indices into the existing one.
|
|
*/
|
CV_EXPORTS_W void filterHomographyDecompByVisibleRefpoints(InputArrayOfArrays rotations,
|
InputArrayOfArrays normals,
|
InputArray beforePoints,
|
InputArray afterPoints,
|
OutputArray possibleSolutions,
|
InputArray pointsMask = noArray());
|
|
/** @brief The base class for stereo correspondence algorithms.
|
*/
|
class CV_EXPORTS_W StereoMatcher : public Algorithm
|
{
|
public:
|
enum { DISP_SHIFT = 4,
|
DISP_SCALE = (1 << DISP_SHIFT)
|
};
|
|
/** @brief Computes disparity map for the specified stereo pair
|
|
@param left Left 8-bit single-channel image.
|
@param right Right image of the same size and the same type as the left one.
|
@param disparity Output disparity map. It has the same size as the input images. Some algorithms,
|
like StereoBM or StereoSGBM compute 16-bit fixed-point disparity map (where each disparity value
|
has 4 fractional bits), whereas other algorithms output 32-bit floating-point disparity map.
|
*/
|
CV_WRAP virtual void compute( InputArray left, InputArray right,
|
OutputArray disparity ) = 0;
|
|
CV_WRAP virtual int getMinDisparity() const = 0;
|
CV_WRAP virtual void setMinDisparity(int minDisparity) = 0;
|
|
CV_WRAP virtual int getNumDisparities() const = 0;
|
CV_WRAP virtual void setNumDisparities(int numDisparities) = 0;
|
|
CV_WRAP virtual int getBlockSize() const = 0;
|
CV_WRAP virtual void setBlockSize(int blockSize) = 0;
|
|
CV_WRAP virtual int getSpeckleWindowSize() const = 0;
|
CV_WRAP virtual void setSpeckleWindowSize(int speckleWindowSize) = 0;
|
|
CV_WRAP virtual int getSpeckleRange() const = 0;
|
CV_WRAP virtual void setSpeckleRange(int speckleRange) = 0;
|
|
CV_WRAP virtual int getDisp12MaxDiff() const = 0;
|
CV_WRAP virtual void setDisp12MaxDiff(int disp12MaxDiff) = 0;
|
};
|
|
|
/** @brief Class for computing stereo correspondence using the block matching algorithm, introduced and
|
contributed to OpenCV by K. Konolige.
|
*/
|
class CV_EXPORTS_W StereoBM : public StereoMatcher
|
{
|
public:
|
enum { PREFILTER_NORMALIZED_RESPONSE = 0,
|
PREFILTER_XSOBEL = 1
|
};
|
|
CV_WRAP virtual int getPreFilterType() const = 0;
|
CV_WRAP virtual void setPreFilterType(int preFilterType) = 0;
|
|
CV_WRAP virtual int getPreFilterSize() const = 0;
|
CV_WRAP virtual void setPreFilterSize(int preFilterSize) = 0;
|
|
CV_WRAP virtual int getPreFilterCap() const = 0;
|
CV_WRAP virtual void setPreFilterCap(int preFilterCap) = 0;
|
|
CV_WRAP virtual int getTextureThreshold() const = 0;
|
CV_WRAP virtual void setTextureThreshold(int textureThreshold) = 0;
|
|
CV_WRAP virtual int getUniquenessRatio() const = 0;
|
CV_WRAP virtual void setUniquenessRatio(int uniquenessRatio) = 0;
|
|
CV_WRAP virtual int getSmallerBlockSize() const = 0;
|
CV_WRAP virtual void setSmallerBlockSize(int blockSize) = 0;
|
|
CV_WRAP virtual Rect getROI1() const = 0;
|
CV_WRAP virtual void setROI1(Rect roi1) = 0;
|
|
CV_WRAP virtual Rect getROI2() const = 0;
|
CV_WRAP virtual void setROI2(Rect roi2) = 0;
|
|
/** @brief Creates StereoBM object
|
|
@param numDisparities the disparity search range. For each pixel algorithm will find the best
|
disparity from 0 (default minimum disparity) to numDisparities. The search range can then be
|
shifted by changing the minimum disparity.
|
@param blockSize the linear size of the blocks compared by the algorithm. The size should be odd
|
(as the block is centered at the current pixel). Larger block size implies smoother, though less
|
accurate disparity map. Smaller block size gives more detailed disparity map, but there is higher
|
chance for algorithm to find a wrong correspondence.
|
|
The function create StereoBM object. You can then call StereoBM::compute() to compute disparity for
|
a specific stereo pair.
|
*/
|
CV_WRAP static Ptr<StereoBM> create(int numDisparities = 0, int blockSize = 21);
|
};
|
|
/** @brief The class implements the modified H. Hirschmuller algorithm @cite HH08 that differs from the original
|
one as follows:
|
|
- By default, the algorithm is single-pass, which means that you consider only 5 directions
|
instead of 8. Set mode=StereoSGBM::MODE_HH in createStereoSGBM to run the full variant of the
|
algorithm but beware that it may consume a lot of memory.
|
- The algorithm matches blocks, not individual pixels. Though, setting blockSize=1 reduces the
|
blocks to single pixels.
|
- Mutual information cost function is not implemented. Instead, a simpler Birchfield-Tomasi
|
sub-pixel metric from @cite BT98 is used. Though, the color images are supported as well.
|
- Some pre- and post- processing steps from K. Konolige algorithm StereoBM are included, for
|
example: pre-filtering (StereoBM::PREFILTER_XSOBEL type) and post-filtering (uniqueness
|
check, quadratic interpolation and speckle filtering).
|
|
@note
|
- (Python) An example illustrating the use of the StereoSGBM matching algorithm can be found
|
at opencv_source_code/samples/python/stereo_match.py
|
*/
|
class CV_EXPORTS_W StereoSGBM : public StereoMatcher
|
{
|
public:
|
enum
|
{
|
MODE_SGBM = 0,
|
MODE_HH = 1,
|
MODE_SGBM_3WAY = 2,
|
MODE_HH4 = 3
|
};
|
|
CV_WRAP virtual int getPreFilterCap() const = 0;
|
CV_WRAP virtual void setPreFilterCap(int preFilterCap) = 0;
|
|
CV_WRAP virtual int getUniquenessRatio() const = 0;
|
CV_WRAP virtual void setUniquenessRatio(int uniquenessRatio) = 0;
|
|
CV_WRAP virtual int getP1() const = 0;
|
CV_WRAP virtual void setP1(int P1) = 0;
|
|
CV_WRAP virtual int getP2() const = 0;
|
CV_WRAP virtual void setP2(int P2) = 0;
|
|
CV_WRAP virtual int getMode() const = 0;
|
CV_WRAP virtual void setMode(int mode) = 0;
|
|
/** @brief Creates StereoSGBM object
|
|
@param minDisparity Minimum possible disparity value. Normally, it is zero but sometimes
|
rectification algorithms can shift images, so this parameter needs to be adjusted accordingly.
|
@param numDisparities Maximum disparity minus minimum disparity. The value is always greater than
|
zero. In the current implementation, this parameter must be divisible by 16.
|
@param blockSize Matched block size. It must be an odd number \>=1 . Normally, it should be
|
somewhere in the 3..11 range.
|
@param P1 The first parameter controlling the disparity smoothness. See below.
|
@param P2 The second parameter controlling the disparity smoothness. The larger the values are,
|
the smoother the disparity is. P1 is the penalty on the disparity change by plus or minus 1
|
between neighbor pixels. P2 is the penalty on the disparity change by more than 1 between neighbor
|
pixels. The algorithm requires P2 \> P1 . See stereo_match.cpp sample where some reasonably good
|
P1 and P2 values are shown (like 8\*number_of_image_channels\*SADWindowSize\*SADWindowSize and
|
32\*number_of_image_channels\*SADWindowSize\*SADWindowSize , respectively).
|
@param disp12MaxDiff Maximum allowed difference (in integer pixel units) in the left-right
|
disparity check. Set it to a non-positive value to disable the check.
|
@param preFilterCap Truncation value for the prefiltered image pixels. The algorithm first
|
computes x-derivative at each pixel and clips its value by [-preFilterCap, preFilterCap] interval.
|
The result values are passed to the Birchfield-Tomasi pixel cost function.
|
@param uniquenessRatio Margin in percentage by which the best (minimum) computed cost function
|
value should "win" the second best value to consider the found match correct. Normally, a value
|
within the 5-15 range is good enough.
|
@param speckleWindowSize Maximum size of smooth disparity regions to consider their noise speckles
|
and invalidate. Set it to 0 to disable speckle filtering. Otherwise, set it somewhere in the
|
50-200 range.
|
@param speckleRange Maximum disparity variation within each connected component. If you do speckle
|
filtering, set the parameter to a positive value, it will be implicitly multiplied by 16.
|
Normally, 1 or 2 is good enough.
|
@param mode Set it to StereoSGBM::MODE_HH to run the full-scale two-pass dynamic programming
|
algorithm. It will consume O(W\*H\*numDisparities) bytes, which is large for 640x480 stereo and
|
huge for HD-size pictures. By default, it is set to false .
|
|
The first constructor initializes StereoSGBM with all the default parameters. So, you only have to
|
set StereoSGBM::numDisparities at minimum. The second constructor enables you to set each parameter
|
to a custom value.
|
*/
|
CV_WRAP static Ptr<StereoSGBM> create(int minDisparity = 0, int numDisparities = 16, int blockSize = 3,
|
int P1 = 0, int P2 = 0, int disp12MaxDiff = 0,
|
int preFilterCap = 0, int uniquenessRatio = 0,
|
int speckleWindowSize = 0, int speckleRange = 0,
|
int mode = StereoSGBM::MODE_SGBM);
|
};
|
|
|
//! cv::undistort mode
|
enum UndistortTypes
|
{
|
PROJ_SPHERICAL_ORTHO = 0,
|
PROJ_SPHERICAL_EQRECT = 1
|
};
|
|
/** @brief Transforms an image to compensate for lens distortion.
|
|
The function transforms an image to compensate radial and tangential lens distortion.
|
|
The function is simply a combination of #initUndistortRectifyMap (with unity R ) and #remap
|
(with bilinear interpolation). See the former function for details of the transformation being
|
performed.
|
|
Those pixels in the destination image, for which there is no correspondent pixels in the source
|
image, are filled with zeros (black color).
|
|
A particular subset of the source image that will be visible in the corrected image can be regulated
|
by newCameraMatrix. You can use #getOptimalNewCameraMatrix to compute the appropriate
|
newCameraMatrix depending on your requirements.
|
|
The camera matrix and the distortion parameters can be determined using #calibrateCamera. If
|
the resolution of images is different from the resolution used at the calibration stage, \f$f_x,
|
f_y, c_x\f$ and \f$c_y\f$ need to be scaled accordingly, while the distortion coefficients remain
|
the same.
|
|
@param src Input (distorted) image.
|
@param dst Output (corrected) image that has the same size and type as src .
|
@param cameraMatrix Input camera matrix \f$A = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\f$ .
|
@param distCoeffs Input vector of distortion coefficients
|
\f$(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6[, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\f$
|
of 4, 5, 8, 12 or 14 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed.
|
@param newCameraMatrix Camera matrix of the distorted image. By default, it is the same as
|
cameraMatrix but you may additionally scale and shift the result by using a different matrix.
|
*/
|
CV_EXPORTS_W void undistort( InputArray src, OutputArray dst,
|
InputArray cameraMatrix,
|
InputArray distCoeffs,
|
InputArray newCameraMatrix = noArray() );
|
|
/** @brief Computes the undistortion and rectification transformation map.
|
|
The function computes the joint undistortion and rectification transformation and represents the
|
result in the form of maps for remap. The undistorted image looks like original, as if it is
|
captured with a camera using the camera matrix =newCameraMatrix and zero distortion. In case of a
|
monocular camera, newCameraMatrix is usually equal to cameraMatrix, or it can be computed by
|
#getOptimalNewCameraMatrix for a better control over scaling. In case of a stereo camera,
|
newCameraMatrix is normally set to P1 or P2 computed by #stereoRectify .
|
|
Also, this new camera is oriented differently in the coordinate space, according to R. That, for
|
example, helps to align two heads of a stereo camera so that the epipolar lines on both images
|
become horizontal and have the same y- coordinate (in case of a horizontally aligned stereo camera).
|
|
The function actually builds the maps for the inverse mapping algorithm that is used by remap. That
|
is, for each pixel \f$(u, v)\f$ in the destination (corrected and rectified) image, the function
|
computes the corresponding coordinates in the source image (that is, in the original image from
|
camera). The following process is applied:
|
\f[
|
\begin{array}{l}
|
x \leftarrow (u - {c'}_x)/{f'}_x \\
|
y \leftarrow (v - {c'}_y)/{f'}_y \\
|
{[X\,Y\,W]} ^T \leftarrow R^{-1}*[x \, y \, 1]^T \\
|
x' \leftarrow X/W \\
|
y' \leftarrow Y/W \\
|
r^2 \leftarrow x'^2 + y'^2 \\
|
x'' \leftarrow x' \frac{1 + k_1 r^2 + k_2 r^4 + k_3 r^6}{1 + k_4 r^2 + k_5 r^4 + k_6 r^6}
|
+ 2p_1 x' y' + p_2(r^2 + 2 x'^2) + s_1 r^2 + s_2 r^4\\
|
y'' \leftarrow y' \frac{1 + k_1 r^2 + k_2 r^4 + k_3 r^6}{1 + k_4 r^2 + k_5 r^4 + k_6 r^6}
|
+ p_1 (r^2 + 2 y'^2) + 2 p_2 x' y' + s_3 r^2 + s_4 r^4 \\
|
s\vecthree{x'''}{y'''}{1} =
|
\vecthreethree{R_{33}(\tau_x, \tau_y)}{0}{-R_{13}((\tau_x, \tau_y)}
|
{0}{R_{33}(\tau_x, \tau_y)}{-R_{23}(\tau_x, \tau_y)}
|
{0}{0}{1} R(\tau_x, \tau_y) \vecthree{x''}{y''}{1}\\
|
map_x(u,v) \leftarrow x''' f_x + c_x \\
|
map_y(u,v) \leftarrow y''' f_y + c_y
|
\end{array}
|
\f]
|
where \f$(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6[, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\f$
|
are the distortion coefficients.
|
|
In case of a stereo camera, this function is called twice: once for each camera head, after
|
stereoRectify, which in its turn is called after #stereoCalibrate. But if the stereo camera
|
was not calibrated, it is still possible to compute the rectification transformations directly from
|
the fundamental matrix using #stereoRectifyUncalibrated. For each camera, the function computes
|
homography H as the rectification transformation in a pixel domain, not a rotation matrix R in 3D
|
space. R can be computed from H as
|
\f[\texttt{R} = \texttt{cameraMatrix} ^{-1} \cdot \texttt{H} \cdot \texttt{cameraMatrix}\f]
|
where cameraMatrix can be chosen arbitrarily.
|
|
@param cameraMatrix Input camera matrix \f$A=\vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\f$ .
|
@param distCoeffs Input vector of distortion coefficients
|
\f$(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6[, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\f$
|
of 4, 5, 8, 12 or 14 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed.
|
@param R Optional rectification transformation in the object space (3x3 matrix). R1 or R2 ,
|
computed by #stereoRectify can be passed here. If the matrix is empty, the identity transformation
|
is assumed. In cvInitUndistortMap R assumed to be an identity matrix.
|
@param newCameraMatrix New camera matrix \f$A'=\vecthreethree{f_x'}{0}{c_x'}{0}{f_y'}{c_y'}{0}{0}{1}\f$.
|
@param size Undistorted image size.
|
@param m1type Type of the first output map that can be CV_32FC1, CV_32FC2 or CV_16SC2, see #convertMaps
|
@param map1 The first output map.
|
@param map2 The second output map.
|
*/
|
CV_EXPORTS_W
|
void initUndistortRectifyMap(InputArray cameraMatrix, InputArray distCoeffs,
|
InputArray R, InputArray newCameraMatrix,
|
Size size, int m1type, OutputArray map1, OutputArray map2);
|
|
//! initializes maps for #remap for wide-angle
|
CV_EXPORTS
|
float initWideAngleProjMap(InputArray cameraMatrix, InputArray distCoeffs,
|
Size imageSize, int destImageWidth,
|
int m1type, OutputArray map1, OutputArray map2,
|
enum UndistortTypes projType = PROJ_SPHERICAL_EQRECT, double alpha = 0);
|
static inline
|
float initWideAngleProjMap(InputArray cameraMatrix, InputArray distCoeffs,
|
Size imageSize, int destImageWidth,
|
int m1type, OutputArray map1, OutputArray map2,
|
int projType, double alpha = 0)
|
{
|
return initWideAngleProjMap(cameraMatrix, distCoeffs, imageSize, destImageWidth,
|
m1type, map1, map2, (UndistortTypes)projType, alpha);
|
}
|
|
/** @brief Returns the default new camera matrix.
|
|
The function returns the camera matrix that is either an exact copy of the input cameraMatrix (when
|
centerPrinicipalPoint=false ), or the modified one (when centerPrincipalPoint=true).
|
|
In the latter case, the new camera matrix will be:
|
|
\f[\begin{bmatrix} f_x && 0 && ( \texttt{imgSize.width} -1)*0.5 \\ 0 && f_y && ( \texttt{imgSize.height} -1)*0.5 \\ 0 && 0 && 1 \end{bmatrix} ,\f]
|
|
where \f$f_x\f$ and \f$f_y\f$ are \f$(0,0)\f$ and \f$(1,1)\f$ elements of cameraMatrix, respectively.
|
|
By default, the undistortion functions in OpenCV (see #initUndistortRectifyMap, #undistort) do not
|
move the principal point. However, when you work with stereo, it is important to move the principal
|
points in both views to the same y-coordinate (which is required by most of stereo correspondence
|
algorithms), and may be to the same x-coordinate too. So, you can form the new camera matrix for
|
each view where the principal points are located at the center.
|
|
@param cameraMatrix Input camera matrix.
|
@param imgsize Camera view image size in pixels.
|
@param centerPrincipalPoint Location of the principal point in the new camera matrix. The
|
parameter indicates whether this location should be at the image center or not.
|
*/
|
CV_EXPORTS_W
|
Mat getDefaultNewCameraMatrix(InputArray cameraMatrix, Size imgsize = Size(),
|
bool centerPrincipalPoint = false);
|
|
/** @brief Computes the ideal point coordinates from the observed point coordinates.
|
|
The function is similar to #undistort and #initUndistortRectifyMap but it operates on a
|
sparse set of points instead of a raster image. Also the function performs a reverse transformation
|
to projectPoints. In case of a 3D object, it does not reconstruct its 3D coordinates, but for a
|
planar object, it does, up to a translation vector, if the proper R is specified.
|
|
For each observed point coordinate \f$(u, v)\f$ the function computes:
|
\f[
|
\begin{array}{l}
|
x^{"} \leftarrow (u - c_x)/f_x \\
|
y^{"} \leftarrow (v - c_y)/f_y \\
|
(x',y') = undistort(x^{"},y^{"}, \texttt{distCoeffs}) \\
|
{[X\,Y\,W]} ^T \leftarrow R*[x' \, y' \, 1]^T \\
|
x \leftarrow X/W \\
|
y \leftarrow Y/W \\
|
\text{only performed if P is specified:} \\
|
u' \leftarrow x {f'}_x + {c'}_x \\
|
v' \leftarrow y {f'}_y + {c'}_y
|
\end{array}
|
\f]
|
|
where *undistort* is an approximate iterative algorithm that estimates the normalized original
|
point coordinates out of the normalized distorted point coordinates ("normalized" means that the
|
coordinates do not depend on the camera matrix).
|
|
The function can be used for both a stereo camera head or a monocular camera (when R is empty).
|
@param src Observed point coordinates, 2xN/Nx2 1-channel or 1xN/Nx1 2-channel (CV_32FC2 or CV_64FC2) (or
|
vector\<Point2f\> ).
|
@param dst Output ideal point coordinates (1xN/Nx1 2-channel or vector\<Point2f\> ) after undistortion and reverse perspective
|
transformation. If matrix P is identity or omitted, dst will contain normalized point coordinates.
|
@param cameraMatrix Camera matrix \f$\vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\f$ .
|
@param distCoeffs Input vector of distortion coefficients
|
\f$(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6[, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\f$
|
of 4, 5, 8, 12 or 14 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed.
|
@param R Rectification transformation in the object space (3x3 matrix). R1 or R2 computed by
|
#stereoRectify can be passed here. If the matrix is empty, the identity transformation is used.
|
@param P New camera matrix (3x3) or new projection matrix (3x4) \f$\begin{bmatrix} {f'}_x & 0 & {c'}_x & t_x \\ 0 & {f'}_y & {c'}_y & t_y \\ 0 & 0 & 1 & t_z \end{bmatrix}\f$. P1 or P2 computed by
|
#stereoRectify can be passed here. If the matrix is empty, the identity new camera matrix is used.
|
*/
|
CV_EXPORTS_W
|
void undistortPoints(InputArray src, OutputArray dst,
|
InputArray cameraMatrix, InputArray distCoeffs,
|
InputArray R = noArray(), InputArray P = noArray());
|
/** @overload
|
@note Default version of #undistortPoints does 5 iterations to compute undistorted points.
|
*/
|
CV_EXPORTS_AS(undistortPointsIter)
|
void undistortPoints(InputArray src, OutputArray dst,
|
InputArray cameraMatrix, InputArray distCoeffs,
|
InputArray R, InputArray P, TermCriteria criteria);
|
|
//! @} calib3d
|
|
/** @brief The methods in this namespace use a so-called fisheye camera model.
|
@ingroup calib3d_fisheye
|
*/
|
namespace fisheye
|
{
|
//! @addtogroup calib3d_fisheye
|
//! @{
|
|
enum{
|
CALIB_USE_INTRINSIC_GUESS = 1 << 0,
|
CALIB_RECOMPUTE_EXTRINSIC = 1 << 1,
|
CALIB_CHECK_COND = 1 << 2,
|
CALIB_FIX_SKEW = 1 << 3,
|
CALIB_FIX_K1 = 1 << 4,
|
CALIB_FIX_K2 = 1 << 5,
|
CALIB_FIX_K3 = 1 << 6,
|
CALIB_FIX_K4 = 1 << 7,
|
CALIB_FIX_INTRINSIC = 1 << 8,
|
CALIB_FIX_PRINCIPAL_POINT = 1 << 9
|
};
|
|
/** @brief Projects points using fisheye model
|
|
@param objectPoints Array of object points, 1xN/Nx1 3-channel (or vector\<Point3f\> ), where N is
|
the number of points in the view.
|
@param imagePoints Output array of image points, 2xN/Nx2 1-channel or 1xN/Nx1 2-channel, or
|
vector\<Point2f\>.
|
@param affine
|
@param K Camera matrix \f$K = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{_1}\f$.
|
@param D Input vector of distortion coefficients \f$(k_1, k_2, k_3, k_4)\f$.
|
@param alpha The skew coefficient.
|
@param jacobian Optional output 2Nx15 jacobian matrix of derivatives of image points with respect
|
to components of the focal lengths, coordinates of the principal point, distortion coefficients,
|
rotation vector, translation vector, and the skew. In the old interface different components of
|
the jacobian are returned via different output parameters.
|
|
The function computes projections of 3D points to the image plane given intrinsic and extrinsic
|
camera parameters. Optionally, the function computes Jacobians - matrices of partial derivatives of
|
image points coordinates (as functions of all the input parameters) with respect to the particular
|
parameters, intrinsic and/or extrinsic.
|
*/
|
CV_EXPORTS void projectPoints(InputArray objectPoints, OutputArray imagePoints, const Affine3d& affine,
|
InputArray K, InputArray D, double alpha = 0, OutputArray jacobian = noArray());
|
|
/** @overload */
|
CV_EXPORTS_W void projectPoints(InputArray objectPoints, OutputArray imagePoints, InputArray rvec, InputArray tvec,
|
InputArray K, InputArray D, double alpha = 0, OutputArray jacobian = noArray());
|
|
/** @brief Distorts 2D points using fisheye model.
|
|
@param undistorted Array of object points, 1xN/Nx1 2-channel (or vector\<Point2f\> ), where N is
|
the number of points in the view.
|
@param K Camera matrix \f$K = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{_1}\f$.
|
@param D Input vector of distortion coefficients \f$(k_1, k_2, k_3, k_4)\f$.
|
@param alpha The skew coefficient.
|
@param distorted Output array of image points, 1xN/Nx1 2-channel, or vector\<Point2f\> .
|
|
Note that the function assumes the camera matrix of the undistorted points to be identity.
|
This means if you want to transform back points undistorted with undistortPoints() you have to
|
multiply them with \f$P^{-1}\f$.
|
*/
|
CV_EXPORTS_W void distortPoints(InputArray undistorted, OutputArray distorted, InputArray K, InputArray D, double alpha = 0);
|
|
/** @brief Undistorts 2D points using fisheye model
|
|
@param distorted Array of object points, 1xN/Nx1 2-channel (or vector\<Point2f\> ), where N is the
|
number of points in the view.
|
@param K Camera matrix \f$K = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{_1}\f$.
|
@param D Input vector of distortion coefficients \f$(k_1, k_2, k_3, k_4)\f$.
|
@param R Rectification transformation in the object space: 3x3 1-channel, or vector: 3x1/1x3
|
1-channel or 1x1 3-channel
|
@param P New camera matrix (3x3) or new projection matrix (3x4)
|
@param undistorted Output array of image points, 1xN/Nx1 2-channel, or vector\<Point2f\> .
|
*/
|
CV_EXPORTS_W void undistortPoints(InputArray distorted, OutputArray undistorted,
|
InputArray K, InputArray D, InputArray R = noArray(), InputArray P = noArray());
|
|
/** @brief Computes undistortion and rectification maps for image transform by cv::remap(). If D is empty zero
|
distortion is used, if R or P is empty identity matrixes are used.
|
|
@param K Camera matrix \f$K = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{_1}\f$.
|
@param D Input vector of distortion coefficients \f$(k_1, k_2, k_3, k_4)\f$.
|
@param R Rectification transformation in the object space: 3x3 1-channel, or vector: 3x1/1x3
|
1-channel or 1x1 3-channel
|
@param P New camera matrix (3x3) or new projection matrix (3x4)
|
@param size Undistorted image size.
|
@param m1type Type of the first output map that can be CV_32FC1 or CV_16SC2 . See convertMaps()
|
for details.
|
@param map1 The first output map.
|
@param map2 The second output map.
|
*/
|
CV_EXPORTS_W void initUndistortRectifyMap(InputArray K, InputArray D, InputArray R, InputArray P,
|
const cv::Size& size, int m1type, OutputArray map1, OutputArray map2);
|
|
/** @brief Transforms an image to compensate for fisheye lens distortion.
|
|
@param distorted image with fisheye lens distortion.
|
@param undistorted Output image with compensated fisheye lens distortion.
|
@param K Camera matrix \f$K = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{_1}\f$.
|
@param D Input vector of distortion coefficients \f$(k_1, k_2, k_3, k_4)\f$.
|
@param Knew Camera matrix of the distorted image. By default, it is the identity matrix but you
|
may additionally scale and shift the result by using a different matrix.
|
@param new_size the new size
|
|
The function transforms an image to compensate radial and tangential lens distortion.
|
|
The function is simply a combination of fisheye::initUndistortRectifyMap (with unity R ) and remap
|
(with bilinear interpolation). See the former function for details of the transformation being
|
performed.
|
|
See below the results of undistortImage.
|
- a\) result of undistort of perspective camera model (all possible coefficients (k_1, k_2, k_3,
|
k_4, k_5, k_6) of distortion were optimized under calibration)
|
- b\) result of fisheye::undistortImage of fisheye camera model (all possible coefficients (k_1, k_2,
|
k_3, k_4) of fisheye distortion were optimized under calibration)
|
- c\) original image was captured with fisheye lens
|
|
Pictures a) and b) almost the same. But if we consider points of image located far from the center
|
of image, we can notice that on image a) these points are distorted.
|
|
|
*/
|
CV_EXPORTS_W void undistortImage(InputArray distorted, OutputArray undistorted,
|
InputArray K, InputArray D, InputArray Knew = cv::noArray(), const Size& new_size = Size());
|
|
/** @brief Estimates new camera matrix for undistortion or rectification.
|
|
@param K Camera matrix \f$K = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{_1}\f$.
|
@param image_size Size of the image
|
@param D Input vector of distortion coefficients \f$(k_1, k_2, k_3, k_4)\f$.
|
@param R Rectification transformation in the object space: 3x3 1-channel, or vector: 3x1/1x3
|
1-channel or 1x1 3-channel
|
@param P New camera matrix (3x3) or new projection matrix (3x4)
|
@param balance Sets the new focal length in range between the min focal length and the max focal
|
length. Balance is in range of [0, 1].
|
@param new_size the new size
|
@param fov_scale Divisor for new focal length.
|
*/
|
CV_EXPORTS_W void estimateNewCameraMatrixForUndistortRectify(InputArray K, InputArray D, const Size &image_size, InputArray R,
|
OutputArray P, double balance = 0.0, const Size& new_size = Size(), double fov_scale = 1.0);
|
|
/** @brief Performs camera calibaration
|
|
@param objectPoints vector of vectors of calibration pattern points in the calibration pattern
|
coordinate space.
|
@param imagePoints vector of vectors of the projections of calibration pattern points.
|
imagePoints.size() and objectPoints.size() and imagePoints[i].size() must be equal to
|
objectPoints[i].size() for each i.
|
@param image_size Size of the image used only to initialize the intrinsic camera matrix.
|
@param K Output 3x3 floating-point camera matrix
|
\f$A = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\f$ . If
|
fisheye::CALIB_USE_INTRINSIC_GUESS/ is specified, some or all of fx, fy, cx, cy must be
|
initialized before calling the function.
|
@param D Output vector of distortion coefficients \f$(k_1, k_2, k_3, k_4)\f$.
|
@param rvecs Output vector of rotation vectors (see Rodrigues ) estimated for each pattern view.
|
That is, each k-th rotation vector together with the corresponding k-th translation vector (see
|
the next output parameter description) brings the calibration pattern from the model coordinate
|
space (in which object points are specified) to the world coordinate space, that is, a real
|
position of the calibration pattern in the k-th pattern view (k=0.. *M* -1).
|
@param tvecs Output vector of translation vectors estimated for each pattern view.
|
@param flags Different flags that may be zero or a combination of the following values:
|
- **fisheye::CALIB_USE_INTRINSIC_GUESS** cameraMatrix contains valid initial values of
|
fx, fy, cx, cy that are optimized further. Otherwise, (cx, cy) is initially set to the image
|
center ( imageSize is used), and focal distances are computed in a least-squares fashion.
|
- **fisheye::CALIB_RECOMPUTE_EXTRINSIC** Extrinsic will be recomputed after each iteration
|
of intrinsic optimization.
|
- **fisheye::CALIB_CHECK_COND** The functions will check validity of condition number.
|
- **fisheye::CALIB_FIX_SKEW** Skew coefficient (alpha) is set to zero and stay zero.
|
- **fisheye::CALIB_FIX_K1..fisheye::CALIB_FIX_K4** Selected distortion coefficients
|
are set to zeros and stay zero.
|
- **fisheye::CALIB_FIX_PRINCIPAL_POINT** The principal point is not changed during the global
|
optimization. It stays at the center or at a different location specified when CALIB_USE_INTRINSIC_GUESS is set too.
|
@param criteria Termination criteria for the iterative optimization algorithm.
|
*/
|
CV_EXPORTS_W double calibrate(InputArrayOfArrays objectPoints, InputArrayOfArrays imagePoints, const Size& image_size,
|
InputOutputArray K, InputOutputArray D, OutputArrayOfArrays rvecs, OutputArrayOfArrays tvecs, int flags = 0,
|
TermCriteria criteria = TermCriteria(TermCriteria::COUNT + TermCriteria::EPS, 100, DBL_EPSILON));
|
|
/** @brief Stereo rectification for fisheye camera model
|
|
@param K1 First camera matrix.
|
@param D1 First camera distortion parameters.
|
@param K2 Second camera matrix.
|
@param D2 Second camera distortion parameters.
|
@param imageSize Size of the image used for stereo calibration.
|
@param R Rotation matrix between the coordinate systems of the first and the second
|
cameras.
|
@param tvec Translation vector between coordinate systems of the cameras.
|
@param R1 Output 3x3 rectification transform (rotation matrix) for the first camera.
|
@param R2 Output 3x3 rectification transform (rotation matrix) for the second camera.
|
@param P1 Output 3x4 projection matrix in the new (rectified) coordinate systems for the first
|
camera.
|
@param P2 Output 3x4 projection matrix in the new (rectified) coordinate systems for the second
|
camera.
|
@param Q Output \f$4 \times 4\f$ disparity-to-depth mapping matrix (see reprojectImageTo3D ).
|
@param flags Operation flags that may be zero or CALIB_ZERO_DISPARITY . If the flag is set,
|
the function makes the principal points of each camera have the same pixel coordinates in the
|
rectified views. And if the flag is not set, the function may still shift the images in the
|
horizontal or vertical direction (depending on the orientation of epipolar lines) to maximize the
|
useful image area.
|
@param newImageSize New image resolution after rectification. The same size should be passed to
|
initUndistortRectifyMap (see the stereo_calib.cpp sample in OpenCV samples directory). When (0,0)
|
is passed (default), it is set to the original imageSize . Setting it to larger value can help you
|
preserve details in the original image, especially when there is a big radial distortion.
|
@param balance Sets the new focal length in range between the min focal length and the max focal
|
length. Balance is in range of [0, 1].
|
@param fov_scale Divisor for new focal length.
|
*/
|
CV_EXPORTS_W void stereoRectify(InputArray K1, InputArray D1, InputArray K2, InputArray D2, const Size &imageSize, InputArray R, InputArray tvec,
|
OutputArray R1, OutputArray R2, OutputArray P1, OutputArray P2, OutputArray Q, int flags, const Size &newImageSize = Size(),
|
double balance = 0.0, double fov_scale = 1.0);
|
|
/** @brief Performs stereo calibration
|
|
@param objectPoints Vector of vectors of the calibration pattern points.
|
@param imagePoints1 Vector of vectors of the projections of the calibration pattern points,
|
observed by the first camera.
|
@param imagePoints2 Vector of vectors of the projections of the calibration pattern points,
|
observed by the second camera.
|
@param K1 Input/output first camera matrix:
|
\f$\vecthreethree{f_x^{(j)}}{0}{c_x^{(j)}}{0}{f_y^{(j)}}{c_y^{(j)}}{0}{0}{1}\f$ , \f$j = 0,\, 1\f$ . If
|
any of fisheye::CALIB_USE_INTRINSIC_GUESS , fisheye::CALIB_FIX_INTRINSIC are specified,
|
some or all of the matrix components must be initialized.
|
@param D1 Input/output vector of distortion coefficients \f$(k_1, k_2, k_3, k_4)\f$ of 4 elements.
|
@param K2 Input/output second camera matrix. The parameter is similar to K1 .
|
@param D2 Input/output lens distortion coefficients for the second camera. The parameter is
|
similar to D1 .
|
@param imageSize Size of the image used only to initialize intrinsic camera matrix.
|
@param R Output rotation matrix between the 1st and the 2nd camera coordinate systems.
|
@param T Output translation vector between the coordinate systems of the cameras.
|
@param flags Different flags that may be zero or a combination of the following values:
|
- **fisheye::CALIB_FIX_INTRINSIC** Fix K1, K2? and D1, D2? so that only R, T matrices
|
are estimated.
|
- **fisheye::CALIB_USE_INTRINSIC_GUESS** K1, K2 contains valid initial values of
|
fx, fy, cx, cy that are optimized further. Otherwise, (cx, cy) is initially set to the image
|
center (imageSize is used), and focal distances are computed in a least-squares fashion.
|
- **fisheye::CALIB_RECOMPUTE_EXTRINSIC** Extrinsic will be recomputed after each iteration
|
of intrinsic optimization.
|
- **fisheye::CALIB_CHECK_COND** The functions will check validity of condition number.
|
- **fisheye::CALIB_FIX_SKEW** Skew coefficient (alpha) is set to zero and stay zero.
|
- **fisheye::CALIB_FIX_K1..4** Selected distortion coefficients are set to zeros and stay
|
zero.
|
@param criteria Termination criteria for the iterative optimization algorithm.
|
*/
|
CV_EXPORTS_W double stereoCalibrate(InputArrayOfArrays objectPoints, InputArrayOfArrays imagePoints1, InputArrayOfArrays imagePoints2,
|
InputOutputArray K1, InputOutputArray D1, InputOutputArray K2, InputOutputArray D2, Size imageSize,
|
OutputArray R, OutputArray T, int flags = fisheye::CALIB_FIX_INTRINSIC,
|
TermCriteria criteria = TermCriteria(TermCriteria::COUNT + TermCriteria::EPS, 100, DBL_EPSILON));
|
|
//! @} calib3d_fisheye
|
} // end namespace fisheye
|
|
} //end namespace cv
|
|
#if 0 //def __cplusplus
|
//////////////////////////////////////////////////////////////////////////////////////////
|
class CV_EXPORTS CvLevMarq
|
{
|
public:
|
CvLevMarq();
|
CvLevMarq( int nparams, int nerrs, CvTermCriteria criteria=
|
cvTermCriteria(CV_TERMCRIT_EPS+CV_TERMCRIT_ITER,30,DBL_EPSILON),
|
bool completeSymmFlag=false );
|
~CvLevMarq();
|
void init( int nparams, int nerrs, CvTermCriteria criteria=
|
cvTermCriteria(CV_TERMCRIT_EPS+CV_TERMCRIT_ITER,30,DBL_EPSILON),
|
bool completeSymmFlag=false );
|
bool update( const CvMat*& param, CvMat*& J, CvMat*& err );
|
bool updateAlt( const CvMat*& param, CvMat*& JtJ, CvMat*& JtErr, double*& errNorm );
|
|
void clear();
|
void step();
|
enum { DONE=0, STARTED=1, CALC_J=2, CHECK_ERR=3 };
|
|
cv::Ptr<CvMat> mask;
|
cv::Ptr<CvMat> prevParam;
|
cv::Ptr<CvMat> param;
|
cv::Ptr<CvMat> J;
|
cv::Ptr<CvMat> err;
|
cv::Ptr<CvMat> JtJ;
|
cv::Ptr<CvMat> JtJN;
|
cv::Ptr<CvMat> JtErr;
|
cv::Ptr<CvMat> JtJV;
|
cv::Ptr<CvMat> JtJW;
|
double prevErrNorm, errNorm;
|
int lambdaLg10;
|
CvTermCriteria criteria;
|
int state;
|
int iters;
|
bool completeSymmFlag;
|
int solveMethod;
|
};
|
#endif
|
|
#endif
|
