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Shape Analysis with Hyperbolic Wasserstein Distance.

Jie Shi1, Wen Zhang1, Yalin Wang1

  • 1School of Computing, Informatics, and Decision Systems Engineering Arizona State University.

Proceedings. IEEE Computer Society Conference on Computer Vision and Pattern Recognition
|April 11, 2017
PubMed
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This study introduces a new method to calculate shape distances for complex surfaces, improving 3D shape analysis and classification, particularly for medical imaging like Alzheimer's disease research.

Area of Science:

  • Computer Vision
  • Differential Geometry
  • Medical Imaging Analysis

Background:

  • Shape space analysis is crucial for understanding object similarities.
  • Wasserstein distance offers robust shape comparison but is limited to simple surfaces.
  • General topological surfaces require advanced methods for accurate shape distance computation.

Purpose of the Study:

  • To develop a novel framework for computing Wasserstein distance between general topological surfaces.
  • To extend shape analysis capabilities beyond genus-0 surfaces.
  • To provide a robust and generalizable method for 3D shape indexing and classification.

Main Methods:

  • Utilized Ricci flow, hyperbolic harmonic maps, and hyperbolic power Voronoi diagrams.
  • Developed computational algorithms for Wasserstein distance on hyperbolic surfaces.

Related Experiment Videos

  • Applied the framework to analyze facial expressions, brain morphometry, and Alzheimer's disease (AD) related cortical shape changes.

    • Main Results:

    • Successfully computed Wasserstein distance for general topological surfaces.
    • Demonstrated the method's robustness and generality across diverse applications.
    • Showcased superior performance in AD versus healthy control classification compared to standard measures.

    Conclusions:

    • The proposed framework effectively computes Wasserstein distance for complex surfaces.
    • This method serves as a powerful shape index for 3D shape analysis and classification.
    • The approach shows significant potential in medical research, particularly for neurodegenerative disease studies.