# Pose from Fundamental matrix and vice versa

I have computed the Fundamental Matrix between two cameras using opencv's findFundamentalMat. Then I plot the epipolar lines in the image. And I get something like:

Now, I tried to get the pose from that fundamental matrix, computing first the essential matrix and then using Hartley & Zissserman approach.

K2=np.mat(self.calibration.getCameraMatrix(1))
K1=np.mat(self.calibration.getCameraMatrix(0))
E=K2.T*np.mat(F)*K1


w,u,vt = cv2.SVDecomp(np.mat(E))
if np.linalg.det(u) < 0:
u *= -1.0
if np.linalg.det(vt) < 0:
vt *= -1.0
#Find R and T from Hartley & Zisserman
W=np.mat([[0,-1,0],[1,0,0],[0,0,1]],dtype=float)
R = np.mat(u) * W * np.mat(vt)
t = u[:,2] #u3 normalized.


In order to check everything until here was correct, I recompute E and F and plot the epipolar lines again.

S=np.mat([[0,-T[2],T[1]],[T[2],0,-T[0]],[-T[1],T[0],0]])
E=S*np.mat(R)
F=np.linalg.inv(K2).T*np.mat(E)*np.linalg.inv(K1)


But surprise, the lines have moved and they don't go through the points anymore. Have I done something wrong?

It looks similar to this question http://answers.opencv.org/question/18565/pose-estimation-produces-wrong-translation-vector/

The matrices I get are:

Original F=[[ -1.62627683e-07  -1.38840952e-05   8.03246936e-03]
[  5.83844799e-06  -1.37528349e-06  -3.26617731e-03]
[ -1.15902181e-02   1.23440336e-02   1.00000000e+00]]

E=[[-0.09648757 -8.23748182 -0.6192747 ]
[ 3.46397143 -0.81596046  0.29628779]
[-6.32856235 -0.03006961 -0.65380443]]

R=[[  9.99558381e-01  -2.72074658e-02   1.19497464e-02]
[  3.50795548e-04   4.12906861e-01   9.10773189e-01]
[ -2.97139627e-02  -9.10366782e-01   4.12734058e-01]]

T=[[-8.82445166e-02]
[8.73204425e-01]
[4.79298380e-01]]

Recomputed E=
[[-0.0261145  -0.99284189 -0.07613091]
[ 0.47646462 -0.09337537  0.04214901]
[-0.87284976 -0.01267909 -0.09080531]]

Recomputed F=
[[ -4.40154169e-08  -1.67341327e-06   9.85070691e-04]
[  8.03070680e-07  -1.57382143e-07  -4.67389530e-04]
[ -1.57927152e-03   1.47100268e-03   2.56606003e-01]]

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