Estimating the fundamental matrix using second-order cone programming

Abstract

Computing the fundamental matrix is the first step of many computer vision applications including camera calibration, image rectification and structure from motion. A new method for the estimation of the fundamental matrix from point correspondences is presented. The minimization of the geometric error is performed based L- infinity norm minimization framework. A single global minimum exists and it may be found by SOCP (Second-Order Cone Programming), which is a standard technique in convex optimization. In a SOCP a linear function is minimized over the intersection of an affine set and the product of second-order (quadratic) cones. Several efficient primal-dual interior-point methods for SOCP have been developed. Experiments on real images show that this method provides a more accurate estimate of the fundamental matrix and superior to previous approaches, and the method is no need for normalization of the image coordinates. © 2011 Springer-Verlag.