N-dimensional tensor voting and application to epipolar geometry estimation

We address the problem of epipolar geometry estimation efficiently and effe ctively, by formulating it as one of hyperplane inference from a sparse and noisy point set in an 8D space. Given a set of noisy point correspondences in two images of a static scene without correspondences, even in the prese nce of moving objects, our method extracts good matches and rejects outlier s. The methodology is novel and unconventional, since, unlike most other me thods optimizing certain scalar, objective functions, our approach does not involve initialization or any iterative search in the parameter space. The refore, it is free of the problem of local optima or poor convergence. Furt her, since no search is involved, it is unnecessary to impose simplifying a ssumption (such as affine camera or local planar homography) to the scene b eing analyzed for reducing the search complexity. Subject to the general ep ipolar constraint only, we detect wrong matches by a novel computation sche me, 8D Tensor Voting, which is an instance of the more general N-dimensiona l Tensor Voting framework. In essence, the input set of matches is first tr ansformed into a sparse 8D point set. Dense, 8D tensor kernels are then use d to vote for the most salient hyperplane that captures all inliers inheren t in the input. With this filtered set of matches, the normalized Eight-Poi nt Algorithm can be used to estimate the fundamental matrix accurately. By making use of efficient data structure and locality, our method is both tim e and space efficient despite the higher dimensionality. We demonstrate the general usefulness of our method using example image pairs for aerial imag e analysis, with widely different views, and from nonstatic 3D scenes (e.g. , basketball game in an indoor stadium). Each example contains a considerab le number of wrong matches.