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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.
Author: | Christoph von TycowiczORCiD, Felix AmbellanORCiD, Anirban Mukhopadhyay, Stefan ZachowORCiD |
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Document Type: | Article |
Parent Title (English): | Medical Image Analysis |
Volume: | 43 |
Issue: | 1 |
First Page: | 1 |
Last Page: | 9 |
Year of first publication: | 2018 |
Preprint: | urn:nbn:de:0297-zib-61175 |
DOI: | https://doi.org/10.1016/j.media.2017.09.004 |