Cortical Morphometry Analysis Based on Worst Transportation Theory

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

doi:10.1007/978-3-030-78191-0_13

Cortical Morphometry Analysis Based on Worst Transportation Theory

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

Engineering, Ira A. Fulton Schools of (IAFSE)

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

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 language	English (US)
Title of host publication	Information Processing in Medical Imaging - 27th International Conference, IPMI 2021, Proceedings
Editors	Aasa Feragen, Stefan Sommer, Julia Schnabel, Mads Nielsen
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	163-176
Number of pages	14
ISBN (Print)	9783030781903
DOIs	https://doi.org/10.1007/978-3-030-78191-0_13
State	Published - 2021
Event	27th International Conference on Information Processing in Medical Imaging, IPMI 2021 - Virtual, Online Duration: Jun 28 2021 → Jun 30 2021

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	12729 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	27th International Conference on Information Processing in Medical Imaging, IPMI 2021
City	Virtual, Online
Period	6/28/21 → 6/30/21

Keywords

Alzheimer’s disease
Shape analysis
Worst transportation

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-030-78191-0_13

Cite this

Zhang, M., An, D., Lei, N., Wu, J., Zhao, T., Xu, X., Wang, Y., & Gu, X. (2021). Cortical Morphometry Analysis Based on Worst Transportation Theory. In A. Feragen, S. Sommer, J. Schnabel, & M. Nielsen (Eds.), Information Processing in Medical Imaging - 27th International Conference, IPMI 2021, Proceedings (pp. 163-176). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12729 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-030-78191-0_13

Cortical Morphometry Analysis Based on Worst Transportation Theory. / Zhang, Min; An, Dongsheng; Lei, Na et al.
Information Processing in Medical Imaging - 27th International Conference, IPMI 2021, Proceedings. ed. / Aasa Feragen; Stefan Sommer; Julia Schnabel; Mads Nielsen. Springer Science and Business Media Deutschland GmbH, 2021. p. 163-176 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12729 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Zhang, M, An, D, Lei, N, Wu, J, Zhao, T, Xu, X, Wang, Y & Gu, X 2021, Cortical Morphometry Analysis Based on Worst Transportation Theory. in A Feragen, S Sommer, J Schnabel & M Nielsen (eds), Information Processing in Medical Imaging - 27th International Conference, IPMI 2021, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 12729 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 163-176, 27th International Conference on Information Processing in Medical Imaging, IPMI 2021, Virtual, Online, 6/28/21. https://doi.org/10.1007/978-3-030-78191-0_13

Zhang M, An D, Lei N, Wu J, Zhao T, Xu X et al. Cortical Morphometry Analysis Based on Worst Transportation Theory. In Feragen A, Sommer S, Schnabel J, Nielsen M, editors, Information Processing in Medical Imaging - 27th International Conference, IPMI 2021, Proceedings. Springer Science and Business Media Deutschland GmbH. 2021. p. 163-176. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-78191-0_13

Zhang, Min ; An, Dongsheng ; Lei, Na et al. / Cortical Morphometry Analysis Based on Worst Transportation Theory. Information Processing in Medical Imaging - 27th International Conference, IPMI 2021, Proceedings. editor / Aasa Feragen ; Stefan Sommer ; Julia Schnabel ; Mads Nielsen. Springer Science and Business Media Deutschland GmbH, 2021. pp. 163-176 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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AU - Wang, Yalin

AU - Gu, Xianfeng

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AB - 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.

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Cortical Morphometry Analysis Based on Worst Transportation Theory

Abstract

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