Shape analysis with hyperbolic wasserstein distance

Jie Shi, Wen Zhang, Yalin Wang

Research output: Chapter in Book/Report/Conference proceedingConference contribution

10 Scopus citations

Abstract

Shape space is an active research field in computer vision study. The shape distance defined in a shape space may provide a simple and refined index to represent a unique shape. Wasserstein distance defines a Riemannian metric for the Wasserstein space. It intrinsically measures the similarities between shapes and is robust to image noise. Thus it has the potential for the 3D shape indexing and classification research. While the algorithms for computing Wasserstein distance have been extensively studied, most of them only work for genus-0 surfaces. This paper proposes a novel framework to compute Wasserstein distance between general topological surfaces with hyperbolic metric. The computational algorithms are based on Ricci flow, hyperbolic harmonic map, and hyperbolic power Voronoi diagram and the method is general and robust. We apply our method to study human facial expression, longitudinal brain cortical morphometry with normal aging, and cortical shape classification in Alzheimer's disease (AD). Experimental results demonstrate that our method may be used as an effective shape index, which outperforms some other standard shape measures in our AD versus healthy control classification study.

Original languageEnglish (US)
Title of host publicationProceedings - 29th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2016
PublisherIEEE Computer Society
Pages5051-5061
Number of pages11
ISBN (Electronic)9781467388504
DOIs
StatePublished - Dec 9 2016
Event29th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2016 - Las Vegas, United States
Duration: Jun 26 2016Jul 1 2016

Publication series

NameProceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
Volume2016-December
ISSN (Print)1063-6919

Conference

Conference29th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2016
CountryUnited States
CityLas Vegas
Period6/26/167/1/16

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition

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