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Integral invariants for shape matching.

Siddharth Manay1, Daniel Cremers, Byung-Woo Hong

  • 1Electronics Engineering Technologies Division, Lawrence Livermore National Laboratory, PO Box 508, L-290 Livermore, CA 94551-0508, USA. smanay.ece98@gtalumni.org

IEEE Transactions on Pattern Analysis and Machine Intelligence
|September 22, 2006
PubMed
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This study introduces integral invariants for shape analysis, offering a robust method for shape matching that is insensitive to noise and occlusions. This approach enables accurate shape comparison and retrieval even with deformed or incomplete shapes.

Area of Science:

  • Computer Vision
  • Image Analysis
  • Computational Geometry

Background:

  • Traditional shape analysis methods often rely on differential invariants, which are sensitive to noise and require pre-smoothing.
  • Existing techniques struggle with shape matching under occlusions, deformations, and missing parts.

Purpose of the Study:

  • To develop a novel class of integral invariants for analyzing shapes represented as closed planar contours.
  • To establish a robust and noise-insensitive framework for shape matching and retrieval.
  • To define an efficient distance measure between shapes based on these integral invariants.

Main Methods:

  • Formulation of Euclidean-group-invariant functionals using integral operations on closed planar contours.
  • Development of a multi-scale shape analysis capability.

Related Experiment Videos

  • Definition of a shape distance measure derived from integral invariants, enabling optimal point correspondence and boundary warping.

    • Main Results:

    • Integral invariants demonstrate robustness against noise, eliminating the need for input shape pre-smoothing.
    • The proposed distance measure facilitates efficient shape matching, successfully handling subpart deformations, missing parts, and noise.
    • Quantitative analysis confirms the framework's effectiveness in shape retrieval from a database, achieving high matching scores.

    Conclusions:

    • Integral invariants provide a powerful and noise-resilient alternative to differential invariants for shape analysis and matching.
    • The developed framework offers a computationally efficient and accurate method for comparing and retrieving shapes in the presence of significant variations.
    • This approach advances the field of shape analysis, particularly for applications requiring robust matching under challenging real-world conditions.