Shape classification using wasserstein distance for brain morphometry analysis

Zhengyu Su, Wei Zeng, Yalin Wang, Zhong Lin Lu, Xianfeng Gu

Research output: Contribution to journalArticlepeer-review


Brain morphometry study plays a fundamental role in medical imaging analysis and diagnosis. This work proposes a novel framework for brain cortical surface classification using Wasserstein distance, based on uniformization theory and Riemannian optimal mass transport theory. By Poincare uniformization theorem, all shapes can be conformally deformed to one of the three canonical spaces: the unit sphere, the Euclidean plane or the hyperbolic plane. The uniformization map will distort the surface area elements. The area-distortion factor gives a probability measure on the canonical uniformization space. All the probability measures on a Riemannian manifold form the Wasserstein space. Given any 2 probability measures, there is a unique optimal mass transport map between them, the transportation cost defines the Wasserstein distance between them. Wasserstein distance gives a Riemannian metric for the Wasserstein space. It intrinsically measures the dissimilarities between shapes and thus has the potential for shape classification. To the best of our knowledge, this is the first work to introduce the optimal mass transport map to general Riemannian manifolds. The method is based on geodesic power Voronoi diagram. Comparing to the conventional methods, our approach solely depends on Riemannian metrics and is invariant under rigid motions and scalings, thus it intrinsically measures shape distance. Experimental results on classifying brain cortical surfaces with different intelligence quotients demonstrated the efficiency and efficacy of our method.

Original languageEnglish (US)
Article numberA32
Pages (from-to)411-423
Number of pages13
JournalLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
StatePublished - 2015


  • Brain morphometry
  • Optimal mass transport
  • Wasserstein distance

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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