Joint feature distributions for image correspondence

We introduce 'Joint Feature Distributions', a general statistical framework for feature based multi-image matching that explicitly models the joint probability distributions of corresponding features across several images. Conditioning on feature positions in some of the images gives well-localized distributions for their correspondents in the others, and hence tight likelihood regions for correspondence search. We apply the framework in the simplest case of Gaussian-like distributions over the direct sum (affine images) and tensor product (projective images) of the image coordinates. This produces probabilistic correspondence models that generalize the geometric multi-image matching constraints, roughly speaking by a form of model-averaging over them. These very simple methods predict accurate correspondence likelihood regions for any scene geometry including planar and near-planar scenes, without ill-conditioning or explicit model selection. Small amounts of distortion and non-rigidity are also tolerated. We develop the theory for any number of affine or projective images, explain its relationship to matching tensors, and give results for an initial implementation.