I want to compute the epipolar lines of a stereo camera. I know both camera intrinsics matrix as well as R and T. I tried to compute the essential matrix as told in Learning Opencv book and wikipedia.
where [t]x is the matrix representation of the cross product with t.
so
I tried to implement this with python and then use the opencv function cv2.computeCorrespondEpilines to compute the epilines.
The problem is that the lines I get don't converge in a point as they should... I guess I must have a problem computing F.
This is the relevant pice of code:
T #Contains translation vector
R #Rotation matrix
S=np.mat([[0,-T[2],T[1]],[T[2],0,-T[1]],[-T[1],T[0],0]])
E=np.mat(R)*S
M1=np.mat(self.getCameraMatrix(cam1))
M1_inv=np.linalg.inv(M1)
M2=np.mat(self.getCameraMatrix(cam2))
M2_inv=np.linalg.inv(M2)
F=(M2_inv.T)*E*M1_inv
The matrices are:
M1=[[ 776.21275864 0. 773.70733324]
[ 0. 776.21275864 627.82872456]
[ 0. 0. 1. ]]
M2=[[ 764.35675708 0. 831.26052677]
[ 0. 764.35675708 611.85363745]
[ 0. 0. 1. ]]
R=[[ 0.9999902 0.00322032 0.00303674]
[-0.00387935 0.30727176 0.9516139 ]
[ 0.0021314 -0.95161636 0.30728124]]
T=[ 0.0001648 0.04149158 -0.02854541]
The ouput F I get it's something like:
F=[[ 4.75910592e-07 6.28777619e-08 -2.78886982e-04]
[ -4.66942275e-08 -7.62837993e-08 -7.34825205e-04]
[ -8.86965149e-04 -6.86717269e-04 1.40633035e+00]]
EDITED: The cross multiplication matrix was wrong, it has to be: S=np.mat([[0,-T2,T1],[T2,0,-T[0]],[-T1,T[0],0]])
The epilines converge now at the epipole.