Contour-based correspondence for stereo

In stereoscopic images, the behavior of a curve in space is related to the appearance of the curve in the left and right image planes. Formally, this relationship is governed by the projective geometry induced by the stereo camera configuration and by the differential structure of the curve in the scene. We propose that the correspondence problem-matching corresponding points in the image planes-can be solved by relating the differential structure in the left and right image planes to the geometry of curves in space. Specifically, the compatibility between two pairs of corresponding points and tangents at those points is related to the local approximation of a space curve using an osculating helix. To guarantee robustness against small changes in the camera parameters, we select a specific osculating helix. A relaxation labeling network demonstrates that the compatibilities can be used to infer the appropriate correspondences in a scene. Examples on which standard approaches fail are demonstrated.