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Related Experiment Videos

Analysis of planar shapes using geodesic paths on shape spaces.

Eric Klassen1, Anuj Srivastava, Washington Mio

  • 1Department of Mathematics, Florida State University, Tallahassee, FL 32306, USA. klassen@math.fsu.edu

IEEE Transactions on Pattern Analysis and Machine Intelligence
|September 21, 2004
PubMed
Summary

We introduce a novel differential geometric approach for analyzing planar, closed curve shapes. This method quantizes shape differences using geodesic lengths in infinite-dimensional spaces, enabling applications like shape interpolation and clustering.

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Area of Science:

  • Differential Geometry
  • Computer Vision
  • Shape Analysis

Background:

  • Analyzing planar, closed curves is crucial in various scientific fields.
  • Existing methods may lack robustness or comprehensive shape representation.

Purpose of the Study:

  • To propose a novel differential geometric framework for shape analysis.
  • To represent shapes in infinite-dimensional spaces and quantify differences using geodesic lengths.

Main Methods:

  • Representing shapes using direction and curvature functions.
  • Utilizing a Fourier basis for shape space tangents.
  • Employing a gradient-based shooting method to find geodesics.

Main Results:

  • Demonstrated applications using the Surrey fish database.

Related Experiment Videos

  • Successful shape interpolation, extrapolation, and clustering.
  • Enabled statistical analysis and Bayesian shape extraction from low-quality images.

    • Conclusions:

    • The proposed differential geometric approach offers a powerful method for shape analysis.
    • This framework facilitates diverse applications, from data interpolation to image analysis.