#StackBounty: #computer-vision trouble recovering rotation and translation from essential matrix

Bounty: 50

I am having trouble recovering rotation and translation from an essential matrix. I am constructing this matrix using the following equation:
$$begin{equation} E = R left[tright]_x end{equation}$$

which is the equation listed on Wikipedia. With my calculated Essential matrix I am able to show the following relation holds:
$$begin{equation} left( hat x right) E x = 0 end{equation}$$

for the forty or so points I am randomly generating and projecting into coordinate frames. I decompose $$E$$ using SVD then compute the 2 possible translations and the two possible rotations. These solutions differ significantly from the components I’m starting with.

I have pasted a simplified version of the problem I am struggling with below. Is there anything wrong with how I am recovering the these components?

``````import numpy as np

t = np.array([-0.08519122, -0.34015967, -0.93650086])

R = np.array([[ 0.5499506 , 0.28125727, -0.78641508],
[-0.6855271 , 0.68986729, -0.23267083],
[ 0.47708168, 0.66706632, 0.57220241]])

def cross(t):
return np.array([
[0, -t[2], t[1]],
[t[2], 0, -t[0]],
[-t[1], t[0], 0]])

E = R.dot(cross(t))

u, _, vh = np.linalg.svd(E, full_matrices=True)

W = np.array([
[ 0,-1, 0],
[ 1, 0, 0],
[ 0, 0, 1]])

Rs = [u.dot(W.dot(vh.T)), u.dot(W.T.dot(vh.T))]
Ts = [u[:,2], -u[:,2]]
``````

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