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Shape representation and classification using the poisson equation.

Lena Gorelick1, Meirav Galun, Eitan Sharon

  • 1Department of Computer Science and Applied Mathematics, The Weizmann Institute of Science, Rehovot, Israel. lena.gorelick@weizmann.ac.il

IEEE Transactions on Pattern Analysis and Machine Intelligence
|November 17, 2006
PubMed
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This study introduces a novel method using random walks and Poisson

Area of Science:

  • Computer Vision
  • Computational Geometry
  • Image Analysis

Background:

  • Extracting meaningful shape properties from 2D silhouettes is crucial for various computer vision tasks.
  • Existing methods often struggle with reliability and robustness in capturing complex shape features.

Purpose of the Study:

  • To develop a novel computational approach for reliably extracting diverse properties from object silhouettes.
  • To demonstrate the utility of these extracted properties in shape analysis and retrieval applications.

Main Methods:

  • Assigning a mean hitting time value to internal silhouette points using random walks.
  • Solving Poisson's equation with silhouette contours as boundary conditions.
  • Utilizing multigrid algorithms for efficient computation of the solution.

Related Experiment Videos

Main Results:

  • Reliable computation of silhouette properties: part structure, skeleton, local orientation, aspect ratio, and boundary convexity/concavity.
  • Demonstrated efficiency of the multigrid approach for solving Poisson's equation.

Conclusions:

  • The proposed random walk-based method effectively extracts key shape descriptors from silhouettes.
  • Extracted properties significantly improve performance in shape classification and retrieval tasks.