On the Direct Estimation of the Fundamental Matrix

The fundamental matrix is a central construct in the analysis of images captured from a pair of cameras and many feature-based methods have been proposed for its computation. In this paper, we propose a direct method for estimating the fundamental matrix where the motion between the frames is small (e.g. between successive frames of a video). To achieve this, a warping function is presented for the fundamental matrix by using the brightness constancy constraint in conjunction with geometric constraints. Using this warping function, an iterative hierarchical algorithm is described to recover accurate estimates of the fundamental matrix. We present results of experimentation to evaluate the performance of the proposed approach and demonstrate improved accuracy in the computation of the fundamental matrix.