A Geodesic Mixed Effects Model in Kendall's Shape Space

Please always quote using this URN: urn:nbn:de:0297-zib-74621
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  • In many applications, geodesic hierarchical models are adequate for the study of temporal observations. We employ such a model derived for manifold-valued data to Kendall's shape space. In particular, instead of the Sasaki metric, we adapt a functional-based metric, which increases the computational efficiency and does not require the implementation of the curvature tensor. We propose the corresponding variational time discretization of geodesics and apply the approach for the estimation of group trends and statistical testing of 3D shapes derived from an open access longitudinal imaging study on osteoarthritis.

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Author:Esfandiar Nava-YazdaniORCiD, Hans-Christian HegeORCiD, Christoph von TycowiczORCiD
Document Type:In Proceedings
Parent Title (English):Proc. 7th MICCAI workshop on Mathematical Foundations of Computational Anatomy (MFCA)
Series:Lecture Notes in Computer Science
Tag:Kendall; Shape Space
MSC-Classification:53-XX DIFFERENTIAL GEOMETRY (For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx)
65-XX NUMERICAL ANALYSIS
Year of first publication:2019
Series (Serial Number):ZIB-Report (19-49)
ISSN:1438-0064
DOI:https://doi.org/10.12752/7462