A Geodesic Mixed Effects Model in Kendall’s Shape Space

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...

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Bibliographic Details
Published inMultimodal Brain Image Analysis and Mathematical Foundations of Computational Anatomy pp. 209 - 218
Main Authors Nava-Yazdani, Esfandiar, Hege, Hans-Christian, von Tycowicz, Christoph
Format Book Chapter
LanguageEnglish
Published Cham Springer International Publishing
SeriesLecture Notes in Computer Science
Subjects
Geodesic regression
Kendall’s shape space
Longitudinal modeling
Parallel transport
Riemannian metric
Shape trajectory
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Summary: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.
ISBN:9783030332259
303033225X
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-030-33226-6_22