TU Darmstadt / ULB / TUbiblio

An efficient Riemannian statistical shape model using differential coordinates

von Tycowicz, Christoph and Ambellan, Felix and Mukhopadhyay, Anirban and Zachow, Stefan (2018):
An efficient Riemannian statistical shape model using differential coordinates.
In: Medical Image Analysis, pp. 1-9, 43, ISSN 13618415,
DOI: 10.1016/j.media.2017.09.004,
[Online-Edition: https://doi.org/10.1016/j.media.2017.09.004],
[Article]

Abstract

We propose a novel Riemannian framework for statistical analysis of shapes that is able to account for the nonlinearity in shape variation. By adopting a physical perspective, we introduce a differential rep- resentation that puts the local geometric variability into focus. We model these differential coordinates as elements of a Lie group thereby endowing our shape space with a non-Euclidean structure. A key ad- vantage of our framework is that statistics in a manifold shape space becomes numerically tractable im- proving performance by several orders of magnitude over state-of-the-art. We show that our Riemannian model is well suited for the identification of intra-population variability as well as inter-population differ- ences. In particular, we demonstrate the superiority of the proposed model in experiments on specificity and generalization ability. We further derive a statistical shape descriptor that outperforms the standard Euclidean approach in terms of shape-based classification of morphological disorders.

Item Type: Article
Erschienen: 2018
Creators: von Tycowicz, Christoph and Ambellan, Felix and Mukhopadhyay, Anirban and Zachow, Stefan
Title: An efficient Riemannian statistical shape model using differential coordinates
Language: English
Abstract:

We propose a novel Riemannian framework for statistical analysis of shapes that is able to account for the nonlinearity in shape variation. By adopting a physical perspective, we introduce a differential rep- resentation that puts the local geometric variability into focus. We model these differential coordinates as elements of a Lie group thereby endowing our shape space with a non-Euclidean structure. A key ad- vantage of our framework is that statistics in a manifold shape space becomes numerically tractable im- proving performance by several orders of magnitude over state-of-the-art. We show that our Riemannian model is well suited for the identification of intra-population variability as well as inter-population differ- ences. In particular, we demonstrate the superiority of the proposed model in experiments on specificity and generalization ability. We further derive a statistical shape descriptor that outperforms the standard Euclidean approach in terms of shape-based classification of morphological disorders.

Journal or Publication Title: Medical Image Analysis
Volume: 43
Uncontrolled Keywords: Statistical shape models (SSM), Medical diagnosis, Feature classifications
Divisions: 20 Department of Computer Science
20 Department of Computer Science > Interactive Graphics Systems
Date Deposited: 19 Jun 2019 11:08
DOI: 10.1016/j.media.2017.09.004
Official URL: https://doi.org/10.1016/j.media.2017.09.004
Export:
Suche nach Titel in: TUfind oder in Google

Optionen (nur für Redakteure)

View Item View Item