An Effective Rigidity Constraint for Improving RANSAC in Homography Estimation

Abstract

A homography is a projective transformation which can relate two images of the same planar surface taken from two different points of view. Hence, it can be used for registering images of scenes that can be assimilated to planes. For this purpose a homography is usually estimated by solving a system of equations involving several couples of points detected at different coordinates in two different images, but located at the same position in the real world. A usual and efficient way of obtaining a set of good point correspondences is to start from a putative set obtained somehow and to sort out the good correspondences (inliers) from the wrong ones (outliers) by using the so-called RANSAC algorithm. This algorithm relies on a statistical approach which necessitates estimating iteratively many homographies from randomly chosen sets of four-correspondences. Unfortunately, homographies obtained in this way do not necessarily reflect a rigid transformation. Depending on the number of outliers, evaluating such degenerated cases in RANSAC drastically slows down the process and can even lead to wrong solutions. In this paper we present the expression of a lightweight rigidity constraint and show that it speeds up the RANSAC process and prevents degenerated homographies.