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Computing Minimal Distances on Polyhedral Surfaces
September 1989 (vol. 11 no. 9)
pp. 1001-1005

The authors implement an algorithm that finds minimal (geodesic) distances on a three-dimensional polyhedral surface. The algorithm is intrinsically parallel, in as much as it deals with all nodes simultaneously, and is simple to implement. Although exponential in complexity, it can be used with a companion gradient-descent surface-flattening algorithm that produces an optimal flattening of a polyhedral surface. Together, these two algorithms have made it possible to obtain accurate flattening of biological surfaces consisting of several thousand triangular faces (monkey visual cortex) by providing a characterization of the distance geometry of these surfaces. The authors propose this approach as a pragmatic solution to characterizing the surface geometry of the complex polyhedral surfaces which are encountered in the cortex of vertebrates.

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Index Terms:
3D polyhedral surfaces; shortest path; computational geometry; picture processing; pattern recognition; minimal distances; flattening; biological surfaces; distance geometry; surface geometry; biological techniques and instruments; biology computing; computational geometry; computerised pattern recognition; computerised picture processing
E. Wolfson, E.L. Schwartz, "Computing Minimal Distances on Polyhedral Surfaces," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 11, no. 9, pp. 1001-1005, Sept. 1989, doi:10.1109/34.35505
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