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A Surface-Theoretic Approach for Statistical Shape Modeling

  • We present a novel approach for nonlinear statistical shape modeling that is invariant under Euclidean motion and thus alignment-free. By analyzing metric distortion and curvature of shapes as elements of Lie groups in a consistent Riemannian setting, we construct a framework that reliably handles large deformations. Due to the explicit character of Lie group operations, our non-Euclidean method is very efficient allowing for fast and numerically robust processing. This facilitates Riemannian analysis of large shape populations accessible through longitudinal and multi-site imaging studies providing increased statistical power. We evaluate the performance of our model w.r.t. shape-based classification of pathological malformations of the human knee and show that it outperforms the standard Euclidean as well as a recent nonlinear approach especially in presence of sparse training data. To provide insight into the model’s ability of capturing natural biological shape variability, we carry out an analysis of specificity and generalization ability.
Author:Felix AmbellanORCiD, Stefan ZachowORCiD, Christoph von TycowiczORCiD
Document Type:In Proceedings
Parent Title (English):Proc. Medical Image Computing and Computer Assisted Intervention (MICCAI), Part IV
First Page:21
Last Page:29
Series:Lecture Notes in Computer Science
Year of first publication:2019
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