I stumpled upon a problem that is related to the Perspective-n-Point problem (https://en.wikipedia.org/wiki/Perspective-n-Point) in Computer Vision and the Orthogonal Procrustes problem (https://en.wikipedia.org/wiki/Orthogonal_Procrustes_problem). I'm using a spherical camera model that simply projects any 3d point onto the unit sphere. Now I have N correspondences from 3d world points to normalized 3d points on the unit sphere. My goal is to find the transformation/pose (translation and orientation) of the camera/sphere using these correspondences. I hope image 1 makes situation clearer.
If you use a planar camera model you usually would use a Pnp solver but I have a spherical camera model that can see points from all angles.
It might be that I just don't know the name of the problem or solution but I couldn't find anything. Basically, I'm searching for a solution where the ray pointing from the sphere center t to any 3d point p is colinear with the corresponding normalized ray on the unit sphere. So something like this: (p-t) dot (R*r) = 1 I'm sorry, I'm not a mathematician.
Does anyone knows something about this? Kinds regards, Florian