7590
2020
eng
549
559
4
62
article
0
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Geodesic Analysis in Kendall's Shape Space with Epidemiological Applications
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.
Journal of Mathematical Imaging and Vision
10.1007/s10851-020-00945-w
1906.11950
yes
2020-01-28
Esfandiar Nava-Yazdani
Christoph von Tycowicz
Hans-Christian Hege
T. J. Sullivan
Christoph von Tycowicz
Visual Data Analysis
Hege, Hans-Christian
Tycowicz, Christoph von
Navayazdani, Esfandiar
ECMath-CH15
MathPlus-EF2-3
Visual and Data-centric Computing
Geometric Data Analysis and Processing
6975
eng
reportzib
0
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2018-08-01
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A Shape Trajectories Approach to Longitudinal Statistical Analysis
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.
1438-0064
urn:nbn:de:0297-zib-69759
Esfandiar Nava-Yazdani
Hans-Christian Hege
Hans-Christian Hege
Christoph von Tycowicz
T. J. Sullivan
ZIB-Report
18-42
eng
uncontrolled
shape space, shape trajectories, geodesic regression, longitudinal analysis, osteoarthritis
PROBABILITY AND STATISTICS
DIFFERENTIAL GEOMETRY (For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx)
STATISTICS
Visual Data Analysis
Visual Data Analysis in Science and Engineering
Therapy Planning
Hege, Hans-Christian
Tycowicz, Christoph von
Navayazdani, Esfandiar
ECMath-CH15
Visual and Data-centric Computing
Geometric Data Analysis and Processing
https://opus4.kobv.de/opus4-zib/files/6975/shape_trj.pdf