I am having trouble recovering rotation and translation from an essential matrix. I am constructing this matrix using the following equation:
E = R left[tright]_x
which is the equation listed on Wikipedia. With my calculated Essential matrix I am able to show the following relation holds:
left( hat x right) E x = 0
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, t], [t, 0, -t], [-t, t, 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]]