A Variational Model for the Joint Recovery of the Fundamental Matrix and the Optical Flow

Traditional estimation methods for the fundamental matrix rely on a sparse set of point correspondences that have been established by matching salient image features between two images. Recovering the fundamental matrix from dense correspondences has not been extensively researched until now. In this paper we propose a new variational model that recovers the fundamental matrix from a pair of uncalibrated stereo images, and simultaneously estimates an optical flow field that is consistent with the corresponding epipolar geometry. The model extends the highly accurate optical flow technique of Brox et al. (2004) by taking the epipolar constraint into account. In experiments we demonstrate that our approach is able to produce excellent estimates for the fundamental matrix and that the optical flow computation is on par with the best techniques to date.