Epipolar geometry estimation by tensor voting in 8D

Abstract

We present a novel, efficient, initialization free approach to the problem of epipolar geometry estimation, 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 as obtained from two views of a static scene without correspondences, even in the presence of moving objects, our method pulls out inlier matches while rejecting outliers. Unlike most methods which optimize certain objective function, our approach does not involve initialization or any search in the parameter space, and therefore is free of the problem of local optima or poor convergence. Since no search is involved, it is unnecessary to impose simplifying assumption (such as affine camera or local planar homography) to the scene being analyzed for reducing the search complexity. Subject to the general epipolar constraint only, we detect wrong matches by establishing salient "extremalities" via a naval approach, 8D Tensor Voting: the input set of matches is first transformed into a sparse and discrete 8D point set. Dense tensor kernels are then applied to vote for the most salient hyperplane (normal and intercept) that captures all inliers inherent in the input. With this filtered set of matches, the normalized Eight-point Algorithm suffices for the accurate estimation of the fundamental matrix. By using efficient data structure and locality, our method is both time and space efficient despite the higher dimensionality. We demonstrate the general usefulness of our method using example image pairs (i) for aerial image analysis, (ii) with widely different views, and (iii) from non-static 3D scenes (e.g. basketball game in an indoor stadium). Each example contains a considerable amount of wrong matches.