KLT-based linear scaling for the estimation of the fundamental matrix

The Epipolar Geometry describes the relation between two stereo images and the 3D scene. This geometry is encoded in a 3x3 singular matrix called the Fundamental Matrix. ne Fundamental Matrix can be estimated from point correspondences in stereo images. Accurate techniques for the estimation of the Fundamental Matrix are based on optimization models constrained to complex non-linear algebraic conditions. More computationally efficient methods are based on regularization, scaling and preconditioning of simple linear systems derived from the classic eight points algorithm. In this paper a new scaling approach addressing the numerical stability of the eight-points algorithm is proposed. The technique exploits well know properties of the Karhunen-Loeve Transform to improve the condition number and numerical properties of the linear system. The performance of the proposed method is compared with the diagonal scaling introduced by Izquierdo and Guerra as well as the isotropic and the non-isotropic scaling proposed by Hartley.