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Finding Shortest Paths on Surfaces Using Level Sets Propagation
June 1995 (vol. 17 no. 6)
pp. 635-640

Abstract—We present a new algorithm for determining minimal length paths between two regions on a three dimensional surface. The numerical implementation is based on finding equal geodesic distance contours from a given area. These contours are calculated as zero sets of a bivariate function designed to evolve so as to track the equal distance curves on the given surface. The algorithm produces all paths of minimal length between the source and destination areas on the surface given as height values on a rectangular grid.

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Index Terms:
Curve evolution, equal distance contours, geodesic path, numerical algorithms, minimal geodesics.
Ron Kimmel, Arnon Amir, Alfred M. Bruckstein, "Finding Shortest Paths on Surfaces Using Level Sets Propagation," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 17, no. 6, pp. 635-640, June 1995, doi:10.1109/34.387512
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