Geometry of Contour-based Correspondence for Stereo

We consider the problem of computing stereo correspondence for scenes dense in physical structure, such as a bouquet of flowers. Boundaries are then space curves, formally governed by the projective geometry induced by the stereo camera configuration and by the differential structure of the curves in the scene. We propose that the correspondence problem can be solved by relating the differential structure in the left and right image planes to the geometry of curves in space. Based on the Frenet equations, we show that the compatibility between pairs of corresponding points, and tangents and curvatures at those points, is related to the local approximation of a space curve using an osculating helix. A relaxation labeling network demonstrates that the compatibilities can be used to infer the appropriate correspondences in a scene. Examples are shown.