Pose from essential matrix, the order of transform

Question

From I've understood, the transform order (rotate first or translate first) yield different [R|t].

So I want to know what's the order of the 4 possible poses you got from essential matrix SVD.

I've read a code implementation of Pose From Essential Matrix(Hartley and Zisserman's multiple view geometry (page 259)). And the author seems to interpret it as rotate first then translate, where he retrieve camera position by using p = -R^T * t.

Also, opencv seems to use trasnlate first then rotate rule. Because the t vector I got from calibrating camera is the position of camera.

Or maybe I have been wrong and the order doesn't matter?

Answer 1

You shouldn't use SVD to decompose a transformation into rotation and translation components. Viewed as x' = M*x = T*R*x, the translation is just the fourth column of M, and the rotation is in the upper-left 3x3 submatrix.

If you feed the whole 4x4 matrix into SVD, I'm not sure what you'll get out, but it won't be useful. (If nothing else, U and V will not be affine.)