trouble recovering rotation and translation from essential matrix


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[t\right]_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]]