The geometry and matching of curves in multiple views

Abstract

In this paper there are two innovations. First, the geometry of imaged curves is developed in two and three views. A set of results are given for both conics and non-algebraic curves. It is shown that the homography between the images induced by the plane of the curve can be computed from two views given only the epipolar geometry, and that the trifocal tensor can be used to transfer a conic or the curvature from two views to a third. The second innovation is an algorithm for automatically matching individual curves between images. The algorithm uses both photometric information and the multiple view geometric results. For image pairs the homography facilitates the computation of a neighbourhood cross-correlation based matching score for putative curve correspondences. For image triplets cross-correlation matching scores are used in conjunction with curve transfer based on the trifocal geometry to disambiguate matches. Algorithms are developed for both short and wide baselines. The algorithms are robust to deficiencies in the curve segment extraction and partial occlusion. Experimental results are given for image pairs and triplets, for varying motions between views, and for different scene types. The method is applicable to curve matching in stereo and trinocular rigs, and as a starting point for curve matching through monocular image sequences.