Shape representation and classification using the Poisson equation

Authors:
Lena Gorelick;Meirav Galun;Eitan Sharon;Ronen Basri;Achi Brandt
Affiliations:
Dept. of Computer Science and Applied Math., The Weizmann Inst. of Science, Rehovot, Israel;Dept. of Computer Science and Applied Math., The Weizmann Inst. of Science, Rehovot, Israel;Brown University, Providence, RI;Dept. of Computer Science and Applied Math., The Weizmann Inst. of Science, Rehovot, Israel;Dept. of Computer Science and Applied Math., The Weizmann Inst. of Science, Rehovot, Israel
Venue:
CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition
Year:
2004

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Abstract

Silhouettes contain rich information about the shape of objects that can be used for recognition and classification. We present a novel approach that allows us to reliably compute many useful properties of a silhouette. Our approach assigns for every internal point of the silhouette a value reflecting the mean time required for a random walk beginning at the point to hit the boundaries. This function can be computed by solving Poisson's equation, with the silhouette contours providing boundary conditions. We show how this function can be used to reliably extract various shape properties including part structure and rough skeleton, local orientation and aspect ratio of different parts, and convex and concave sections of the boundaries. In addition to this we discuss properties of the solution and show how to efficiently compute this solution using multigrid algorithms. We demonstrate the utility of the extracted properties by using them for shape classification.