An Efficient Riemannian Statistical Shape Model using Differential Coordinates

  • 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 representation 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 advantage of our framework is that statistics in a manifold shape space becomes numerically tractable improving 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 differences. 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.

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Author:Christoph von Tycowicz, Felix Ambellan, Anirban Mukhopadhyay, Stefan Zachow
Document Type:Article
Parent Title (English):Medical Image Analysis
First Page:1
Last Page:9
Year of first publication:2018

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