Curves , Compatibility and Correspondence : A Differential - Geometric Approach to the Stereo Correspondence Problem

In stereoscopic images, the behavior of a curve in space is related to the appearance of the curve in the Ieft and right image planes. Formally, this relationship is governeci by the projective geometry induced by the stereo camera configuration and by the differentiai structure of the curve in the scene. In this thesis, 1 propose that the correspondence problemmatching corresponding points in the image planescan 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, 1 introduce the principle of differential invariance and show how this principle resolves a naturai ambiguity in selecting the osculating helix. A relaxation labeling network demonstrates that the cornpatibiiities can be used to infer the appropriate correspondences in a scene. Finally, parallels between the proposed solution and binocular processes in primate vision are discussed.