Shape Classification Using Wasserstein Distance for Brain Morphometry Analysis

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

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

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)
Pages (from-to)411-423
Number of pages13
JournalInformation processing in medical imaging : proceedings of the ... conference
Volume24
StatePublished - Jan 1 2015

Fingerprint

Brain
Diagnostic Imaging
Intelligence
Costs and Cost Analysis
Power (Psychology)

ASJC Scopus subject areas

  • Medicine(all)

Cite this

Shape Classification Using Wasserstein Distance for Brain Morphometry Analysis. / Su, Zhengyu; Zeng, Wei; Wang, Yalin; Lu, Zhong Lin; Gu, Xianfeng.

In: Information processing in medical imaging : proceedings of the ... conference, Vol. 24, 01.01.2015, p. 411-423.

Research output: Contribution to journalArticle

@article{ffe040e45b4440e5a97610ea4d4e1d37,
title = "Shape Classification Using Wasserstein Distance for Brain Morphometry Analysis",
abstract = "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.",
author = "Zhengyu Su and Wei Zeng and Yalin Wang and Lu, {Zhong Lin} and Xianfeng Gu",
year = "2015",
month = "1",
day = "1",
language = "English (US)",
volume = "24",
pages = "411--423",
journal = "Information processing in medical imaging : proceedings of the ... conference",
issn = "1011-2499",
publisher = "Springer Verlag",

}

TY - JOUR

T1 - Shape Classification Using Wasserstein Distance for Brain Morphometry Analysis

AU - Su, Zhengyu

AU - Zeng, Wei

AU - Wang, Yalin

AU - Lu, Zhong Lin

AU - Gu, Xianfeng

PY - 2015/1/1

Y1 - 2015/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84964697725&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84964697725&partnerID=8YFLogxK

M3 - Article

C2 - 26221691

AN - SCOPUS:84964697725

VL - 24

SP - 411

EP - 423

JO - Information processing in medical imaging : proceedings of the ... conference

JF - Information processing in medical imaging : proceedings of the ... conference

SN - 1011-2499

ER -