On the reprojection of 3D and 2D scenes without explicit model selection

It is known that recovering projection matrices from planar configurations is ambiguous, thus, posing the problem of model selection - is the scene planar (2D) or non-planar (3D)? For a 2D scene one would recover a homography matrix, whereas for a 3D scene one would recover the fundamental matrix or trifocal tensor. The task of model selection is especially problematic when the scene is neither 2D nor 3D - for example a “thin” volume in space. In this paper we show that for certain tasks, such as reprojection, there is no need to select a model. The ambiguity that arises from a 2D scene is orthogonal to the reprojection process, thus if one desires to use multilinear matching constraints for transferring points along a sequence of views it is possible to do so under any situation of 2D, 3D or “thin” volumes.