Abstract
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. This builds upon earlier work on co-circularity, or the transport of tangents along the osculating circle. 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.
Research supported by AFOSR; L. Iverson computed the co-circular compatibilities and S. Alibhai implemented the stereo computations.
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Zucker, S.W. (2000). Computing in Cortical Columns: curve inference and stereo correspondence. In: Lee, SW., Bülthoff, H.H., Poggio, T. (eds) Biologically Motivated Computer Vision. BMCV 2000. Lecture Notes in Computer Science, vol 1811. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45482-9_19
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DOI: https://doi.org/10.1007/3-540-45482-9_19
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