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Nonlinear Regression on Manifolds for Shape Analysis using Intrinsic Bézier Splines

  • Intrinsic and parametric regression models are of high interest for the statistical analysis of manifold-valued data such as images and shapes. The standard linear ansatz has been generalized to geodesic regression on manifolds making it possible to analyze dependencies of random variables that spread along generalized straight lines. Nevertheless, in some scenarios, the evolution of the data cannot be modeled adequately by a geodesic. We present a framework for nonlinear regression on manifolds by considering Riemannian splines, whose segments are Bézier curves, as trajectories. Unlike variational formulations that require time-discretization, we take a constructive approach that provides efficient and exact evaluation by virtue of the generalized de Casteljau algorithm. We validate our method in experiments on the reconstruction of periodic motion of the mitral valve as well as the analysis of femoral shape changes during the course of osteoarthritis, endorsing Bézier spline regression as an effective and flexible tool for manifold-valued regression.

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Author:Martin HanikORCiD, Hans-Christian HegeORCiDGND, Anja HennemuthORCiD, Christoph von TycowiczORCiD
Document Type:In Proceedings
Parent Title (English):Proc. Medical Image Computing and Computer Assisted Intervention (MICCAI)
First Page:617
Last Page:626
Publisher:Springer International Publishing
Place of publication:Cham
Year of first publication:2020
Page Number:10
ArXiv Id:http://arxiv.org/abs/2007.05275
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