Hyperbolic Wasserstein Distance for Shape Indexing

Jie Shi, Yalin Wang

Research output: Contribution to journalArticle

Abstract

Shape space is an active research topic in computer vision and medical imaging fields. The distance defined in a shape space may provide a simple and refined index to represent a unique shape. This work studies the Wasserstein space and proposes a novel framework to compute the Wasserstein distance between general topological surfaces by integrating hyperbolic Ricci flow, hyperbolic harmonic map, and hyperbolic power Voronoi diagram algorithms. The resulting hyperbolic Wasserstein distance can intrinsically measure the similarity between general topological surfaces. Our proposed algorithms are theoretically rigorous and practically efficient. It has the potential to be a powerful tool for 3D shape indexing research. We tested our algorithm with human face classification and Alzheimer's disease (AD) progression tracking studies. Experimental results demonstrated that our work may provide a succinct and effective shape index.

Original languageEnglish (US)
Article number8637773
Pages (from-to)1362-1376
Number of pages15
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Volume42
Issue number6
DOIs
StatePublished - Jun 1 2020
Externally publishedYes

Keywords

  • hyperbolic conformal geometry
  • shape indexing
  • Shape space
  • Wasserstein distance

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition
  • Computational Theory and Mathematics
  • Artificial Intelligence
  • Applied Mathematics

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