A Riemannian Statistical Shape Model using Differential Coordinates

Please always quote using this URN: urn:nbn:de:0297-zib-61175
  • 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-Euclidian structure. A key advantage of our framework is that statistics in a manifold shape space become 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 Euclidian 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:ZIB-Report
MSC-Classification:53-XX DIFFERENTIAL GEOMETRY (For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx) / 53-04 Explicit machine computation and programs (not the theory of computation or programming)
62-XX STATISTICS / 62-04 Explicit machine computation and programs (not the theory of computation or programming)
68-XX COMPUTER SCIENCE (For papers involving machine computations and programs in a specific mathematical area, see Section -04 in that area) / 68Uxx Computing methodologies and applications / 68U05 Computer graphics; computational geometry [See also 65D18]
CCS-Classification:G. Mathematics of Computing / G.3 PROBABILITY AND STATISTICS / Statistical computing
I. Computing Methodologies / I.3 COMPUTER GRAPHICS / I.3.5 Computational Geometry and Object Modeling
Date of first Publication:2016/11/29
Series (Serial Number):ZIB-Report (16-69)

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