Good Edgels to Track: Beating the Aperture Problem with Epipolar Geometry

An open issue in multiple view geometry and structure from motion, applied to real life scenarios, is the sparsity of the matched key-points and of the reconstructed point cloud. We present an approach that can significantly improve the density of measured displacement vectors in a sparse matching or tracking setting, exploiting the partial information of the motion field provided by linear oriented image patches (edgels). Our approach assumes that the epipolar geometry of an image pair already has been computed, either in an earlier feature-based matching step, or by a robustified differential tracker. We exploit key-points of a lower order, edgels, which cannot provide a unique 2D matching, but can be employed if a constraint on the motion is already given. We present a method to extract edgels, which can be effectively tracked given a known camera motion scenario, and show how a constrained version of the Lucas-Kanade tracking procedure can efficiently exploit epipolar geometry to reduce the classical KLT optimization to a 1D search problem. The potential of the proposed methods is shown by experiments performed on real driving sequences.