I would like to get opinions and ideas on how to do camera pose estimation, given a transparent object marker.
The object I have is a uniform hexagonal prism with transparent faces, with little dots printed on each face in a regular square grid. Something like the following, made out of transparent glass and with dots all over the faces (not just three). It's not clear from the picture here, but given that the camera is close to the object, I can -relatively- easily tell points on the close face apart from points on the far away face, as they are clearly of different sizes.
I know the size of the object, and the size of the grid.
How can I reconstruct the camera intrinsic and extrinsic parameters by looking at this object? Should I go for a homography based approach or is there a better way? Any code samples of course would be welcome.