A Shape Trajectories Approach to Longitudinal Statistical Analysis

Please always quote using this URN: urn:nbn:de:0297-zib-69759
  • For Kendall’s shape space we determine analytically Jacobi fields and parallel transport, and compute geodesic regression. Using the derived expressions, we can fully leverage the geometry via Riemannian optimization and reduce the computational expense by several orders of magnitude. The methodology is demonstrated by performing a longitudinal statistical analysis of epidemiological shape data. As application example we have chosen 3D shapes of knee bones, reconstructed from image data of the Osteoarthritis Initiative. 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 only.

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Author:Esfandiar Nava-Yazdani, Hans-Christian HegeORCiD, Christoph von TycowiczORCiD, Tim Sullivan
Document Type:ZIB-Report
Tag:shape space, shape trajectories, geodesic regression, longitudinal analysis, osteoarthritis
MSC-Classification:53-XX DIFFERENTIAL GEOMETRY (For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx)
62-XX STATISTICS
CCS-Classification:G. Mathematics of Computing / G.3 PROBABILITY AND STATISTICS
Date of first Publication:2018/08/01
Series (Serial Number):ZIB-Report (18-42)
ISSN:1438-0064