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A Hierarchical Geodesic Model for Longitudinal Analysis on Manifolds

Please always quote using this URN: urn:nbn:de:0297-zib-85187
  • 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 employ the approach for longitudinal analysis of 2D rat skulls shapes as well as 3D shapes derived from an imaging study on osteoarthritis. Particularly, we perform hypothesis test and estimate the mean trends.

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Author:Esfandiar Nava-YazdaniORCiD, Hans-Christian HegeORCiDGND, Christoph von TycowiczORCiD
Document Type:ZIB-Report
Tag:Hierarchical; Longitudinal
MSC-Classification:49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX]
53-XX DIFFERENTIAL GEOMETRY (For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx)
Date of first Publication:2021/12/07
Series (Serial Number):ZIB-Report (21-39)
sumbitted to: Journal of Mathematical Imaging and Vision
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