Robust estimation of the fundamental matrix and stereo correspondences

This paper addresses the problem of robustly estimating correspondences between stereo images, together with the computation of the Fundamental Matrix-F. The fundamental matrix describes the epipolar geometry of a pair of stereo images, and a number of algorithms have been described in the literature to estimate this matrix. However, most of these algorithms assume that a number of correct point correspondences has been established a priori, which is hardly ever the case in practice. In the paper, we focus on the joint estimation of point correspondences and F, in the practical situation where a number of points may correspond to erroneous matches. We compare various methods for the estimation of the fundamental matrix using a robust procedure to select good point correspondences from a larger data set. A new algorithm based on the Least Median of Squares is presented. It compares favourably to various existing ones, both in accuracy and computational eeort. The robust estimation of F and point correspondences is a determinant step for numerous applications like 3D reconstruction and video mosaicing, that are discussed in the paper.