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Shape Representation and Classification Using the Poisson Equation
December 2006 (vol. 28 no. 12)
pp. 1991-2005
Eitan Sharon, IEEE Computer Society
Ronen Basri, IEEE Computer Society
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 and retrieval.

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Index Terms:
Computer vision, shape, Poisson equation, silhouette classification.
Lena Gorelick, Meirav Galun, Eitan Sharon, Ronen Basri, Achi Brandt, "Shape Representation and Classification Using the Poisson Equation," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 28, no. 12, pp. 1991-2005, Dec. 2006, doi:10.1109/TPAMI.2006.253
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