BLOGS: Balanced local and global search for non-degenerate two view epipolar geometry

This work considers the problem of estimating the epipolar geometry between two cameras without needing a prespecified set of correspondences. It is capable of resolving the epipolar geometry for cases when the views differ significantly in terms of baseline and rotation, resulting in a large number features in one image that have no correspondence in the other image. We do conditional characterization of the probability space of correspondences based on Joint Feature Distributions (JFD). We seek to maximize the probabilistic support of the putative correspondence set over a number of MCMC iterations, guided by proposal distributions based on similarity or JFD. Similarity based guidance provides large movements (global) through correspondence space and JFD based guidance provides small movements (local) around the best known epipolar geometry the algorithm has found so far. We also propose a simple and novel method to rule out, at each iteration, correspondences that lead to degenerate configurations, thus speeding up convergence. We compare our algorithm with LO-RANSAC, NAPSAC, MAPSAC and BEEM, which are the current state of the art competing methods, on a dataset that has significantly more change in baseline, rotation, and scale than those used in the current literature. We quantitatively benchmark the performance using manually specified ground truth corresponding point pairs. We find that our approach can achieve results of similar quality as the current state of art in 10 times lesser number of iterations. We are also able to tolerate upto 90% outlier correspondences.