Geodesic Analysis in Kendall's Shape Space with Epidemiological Applications

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  • We analytically determine Jacobi fields and parallel transports and compute geodesic regression in Kendall’s shape space. Using the derived expressions, we can fully leverage the geometry via Riemannian optimization and thereby reduce the computational expense by several orders of magnitude over common, nonlinear constrained approaches. The methodology is demonstrated by performing a longitudinal statistical analysis of epidemiological shape data. As an example application we have chosen 3D shapes of knee bones, reconstructed from image data of the Osteoarthritis Initiative (OAI). Comparing subject groups with incident and developing osteoarthritis versus normal controls, we find clear differences in the temporal development of femur shapes. This paves the way for early prediction of incident knee osteoarthritis, using geometry data alone.

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Metadaten
Author:Esfandiar Nava-YazdaniORCiD, Hans-Christian HegeORCiD, T.J. Sullivan, Christoph von TycowiczORCiD
Document Type:Article
Parent Title (English):Journal of Mathematical Imaging and Vision
Fulltext Url:https://arxiv.org/abs/1906.11950
Year of first publication:2020