Cortical Morphometry Analysis Based on Worst Transportation Theory

Min Zhang, Dongsheng An, Na Lei, Jianfeng Wu, Tong Zhao, Xiaoyin Xu, Yalin Wang, Xianfeng Gu

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


Biomarkers play an important role in early detection and intervention in Alzheimer’s disease (AD). However, obtaining effective biomarkers for AD is still a big challenge. In this work, we propose to use the worst transportation cost as a univariate biomarker to index cortical morphometry for tracking AD progression. The worst transportation (WT) aims to find the least economical way to transport one measure to the other, which contrasts to the optimal transportation (OT) that finds the most economical way between measures. To compute the WT cost, we generalize the Brenier theorem for the OT map to the WT map, and show that the WT map is the gradient of a concave function satisfying the Monge-Ampere equation. We also develop an efficient algorithm to compute the WT map based on computational geometry. We apply the algorithm to analyze cortical shape difference between dementia due to AD and normal aging individuals. The experimental results reveal the effectiveness of our proposed method which yields better statistical performance than other competiting methods including the OT.

Original languageEnglish (US)
Title of host publicationInformation Processing in Medical Imaging - 27th International Conference, IPMI 2021, Proceedings
EditorsAasa Feragen, Stefan Sommer, Julia Schnabel, Mads Nielsen
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages14
ISBN (Print)9783030781903
StatePublished - 2021
Event27th International Conference on Information Processing in Medical Imaging, IPMI 2021 - Virtual, Online
Duration: Jun 28 2021Jun 30 2021

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12729 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference27th International Conference on Information Processing in Medical Imaging, IPMI 2021
CityVirtual, Online


  • Alzheimer’s disease
  • Shape analysis
  • Worst transportation

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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