Joint Feature Distributions for Image Correspondence

We develop a probabilistic framework for feature based multi-image matching that explicitly models the joint distribution of corresponding feature positions across several images. Conditioning this distribution on feature positions in some of the images gives welllocalized distributions for their correspondents in the others, which directly guide the correspondence search. This general framework is explored here in the simplest case of Gaussian distributions over the direct sum (affine images) and the tensor product (perspective images) of the image coordinates. Under these parametrizations, the formalism becomes a probabilistic generalization of the theory of multi-image matching constraints. It gracefully handles the full range of geometric correspondence models, including illconditioned near-planar ones intermediate between between full perspective and plane homographies. Small amounts of distortion and non-rigidity can also be tolerated. We develop the theory for any number of affine or projective images, explain its relationship to matching tensors, and give brief comments on implementation.