Change coord system of 2x3 transformation matrix estimated in opencv coord system to a coord system equivalent of doing y'=height-y

transform_matrix_change_base.cpp

/**
 * Changes the coordinate system of the transformation matrix from regular image 
 * coords (opencv-like) to a different coords system like this:
 * 
 *     .-------> x          ^ y
 *     |             V      |
 * 	   |            --->    | 
 * 	   |                    |
 *     v y                  .-------> x  
 *  
 * This is, y_{S2}=h-y_{S1}, where h is the height of the image.
 * 
 * Change of base matrix is V = {{1,0,0},{0,-1,h},{0,0,1}}
 * Inverse of V is exactly V.
 * 
 * T_{S2} = V * T_{S1} * V
 * 
 * Where V:S1->S2 and S1 is the OpenCV coords space and S2 the new coord space.
 * 
 * @param tmat_s1 transformation matrix transform input in S1 coords
 * @param tmat_s2 transformation matrix transform output in S2 coords
 * @param h height of the image
 */
void transform_matrix_change_base(cv::Matx23f tmat_s1, cv::Matx23f &tmat_s2, int h)
{	
	tmat_s2(0,0) = tmat_s1(0,0);
	tmat_s2(0,1) = -tmat_s1(0,1);
	tmat_s2(0,2) = tmat_s1(0,2)+h*tmat_s1(0,1);
	tmat_s2(1,0) = -tmat_s1(1,0);
	tmat_s2(1,1) = tmat_s1(1,1);
	tmat_s2(1,2) = -tmat_s1(1,2)+h*(1-tmat_s1(1,1));
	
	return;
}