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// For Open Source Computer Vision Library
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// Copyright (C) 2009, Willow Garage Inc., all rights reserved.
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//M*/
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#ifndef OPENCV_IMGPROC_DETAIL_DISTORTION_MODEL_HPP
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#define OPENCV_IMGPROC_DETAIL_DISTORTION_MODEL_HPP
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//! @cond IGNORED
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namespace cv { namespace detail {
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/**
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Computes the matrix for the projection onto a tilted image sensor
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\param tauX angular parameter rotation around x-axis
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\param tauY angular parameter rotation around y-axis
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\param matTilt if not NULL returns the matrix
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\f[
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\vecthreethree{R_{33}(\tau_x, \tau_y)}{0}{-R_{13}((\tau_x, \tau_y)}
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{0}{R_{33}(\tau_x, \tau_y)}{-R_{23}(\tau_x, \tau_y)}
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{0}{0}{1} R(\tau_x, \tau_y)
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\f]
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where
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\f[
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R(\tau_x, \tau_y) =
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\vecthreethree{\cos(\tau_y)}{0}{-\sin(\tau_y)}{0}{1}{0}{\sin(\tau_y)}{0}{\cos(\tau_y)}
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\vecthreethree{1}{0}{0}{0}{\cos(\tau_x)}{\sin(\tau_x)}{0}{-\sin(\tau_x)}{\cos(\tau_x)} =
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\vecthreethree{\cos(\tau_y)}{\sin(\tau_y)\sin(\tau_x)}{-\sin(\tau_y)\cos(\tau_x)}
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{0}{\cos(\tau_x)}{\sin(\tau_x)}
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{\sin(\tau_y)}{-\cos(\tau_y)\sin(\tau_x)}{\cos(\tau_y)\cos(\tau_x)}.
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\f]
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\param dMatTiltdTauX if not NULL it returns the derivative of matTilt with
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respect to \f$\tau_x\f$.
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\param dMatTiltdTauY if not NULL it returns the derivative of matTilt with
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respect to \f$\tau_y\f$.
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\param invMatTilt if not NULL it returns the inverse of matTilt
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**/
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template <typename FLOAT>
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void computeTiltProjectionMatrix(FLOAT tauX,
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FLOAT tauY,
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Matx<FLOAT, 3, 3>* matTilt = 0,
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Matx<FLOAT, 3, 3>* dMatTiltdTauX = 0,
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Matx<FLOAT, 3, 3>* dMatTiltdTauY = 0,
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Matx<FLOAT, 3, 3>* invMatTilt = 0)
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{
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FLOAT cTauX = cos(tauX);
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FLOAT sTauX = sin(tauX);
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FLOAT cTauY = cos(tauY);
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FLOAT sTauY = sin(tauY);
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Matx<FLOAT, 3, 3> matRotX = Matx<FLOAT, 3, 3>(1,0,0,0,cTauX,sTauX,0,-sTauX,cTauX);
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Matx<FLOAT, 3, 3> matRotY = Matx<FLOAT, 3, 3>(cTauY,0,-sTauY,0,1,0,sTauY,0,cTauY);
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Matx<FLOAT, 3, 3> matRotXY = matRotY * matRotX;
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Matx<FLOAT, 3, 3> matProjZ = Matx<FLOAT, 3, 3>(matRotXY(2,2),0,-matRotXY(0,2),0,matRotXY(2,2),-matRotXY(1,2),0,0,1);
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if (matTilt)
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{
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// Matrix for trapezoidal distortion of tilted image sensor
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*matTilt = matProjZ * matRotXY;
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}
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if (dMatTiltdTauX)
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{
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// Derivative with respect to tauX
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Matx<FLOAT, 3, 3> dMatRotXYdTauX = matRotY * Matx<FLOAT, 3, 3>(0,0,0,0,-sTauX,cTauX,0,-cTauX,-sTauX);
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Matx<FLOAT, 3, 3> dMatProjZdTauX = Matx<FLOAT, 3, 3>(dMatRotXYdTauX(2,2),0,-dMatRotXYdTauX(0,2),
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0,dMatRotXYdTauX(2,2),-dMatRotXYdTauX(1,2),0,0,0);
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*dMatTiltdTauX = (matProjZ * dMatRotXYdTauX) + (dMatProjZdTauX * matRotXY);
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}
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if (dMatTiltdTauY)
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{
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// Derivative with respect to tauY
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Matx<FLOAT, 3, 3> dMatRotXYdTauY = Matx<FLOAT, 3, 3>(-sTauY,0,-cTauY,0,0,0,cTauY,0,-sTauY) * matRotX;
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Matx<FLOAT, 3, 3> dMatProjZdTauY = Matx<FLOAT, 3, 3>(dMatRotXYdTauY(2,2),0,-dMatRotXYdTauY(0,2),
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0,dMatRotXYdTauY(2,2),-dMatRotXYdTauY(1,2),0,0,0);
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*dMatTiltdTauY = (matProjZ * dMatRotXYdTauY) + (dMatProjZdTauY * matRotXY);
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}
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if (invMatTilt)
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{
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FLOAT inv = 1./matRotXY(2,2);
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Matx<FLOAT, 3, 3> invMatProjZ = Matx<FLOAT, 3, 3>(inv,0,inv*matRotXY(0,2),0,inv,inv*matRotXY(1,2),0,0,1);
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*invMatTilt = matRotXY.t()*invMatProjZ;
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}
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}
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}} // namespace detail, cv
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//! @endcond
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#endif // OPENCV_IMGPROC_DETAIL_DISTORTION_MODEL_HPP
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