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Geodesic analysis in Kendall’s shape space with epidemiological applications
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Nava-Yazdani, Esfandiar, Hege, Hans-Christian, Sullivan, T. J. and von Tycowicz, Christoph (2020) Geodesic analysis in Kendall’s shape space with epidemiological applications. Journal of Mathematical Imaging and Vision, 62 (4). pp. 549-559. doi:10.1007/s10851-020-00945-w ISSN 0924-9907.
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WRAP-geodesic-analysis-kendalls-shape-space-epidemiological-applications-Sullivan-2020.pdf - Published Version - Requires a PDF viewer. Available under License Creative Commons Attribution 4.0. Download (815Kb) | Preview |
Official URL: http://dx.doi.org/10.1007/s10851-020-00945-w
Abstract
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. 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.
| Item Type: | Journal Article | ||||||||||||||||||
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| Subjects: | Q Science > QA Mathematics R Medicine > RA Public aspects of medicine R Medicine > RC Internal medicine |
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| Divisions: | Faculty of Science, Engineering and Medicine > Engineering > Engineering Faculty of Science, Engineering and Medicine > Science > Mathematics |
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| Library of Congress Subject Headings (LCSH): | Knee -- Longitudinal studies , Osteoarthritis -- Simulation methods , Shapes, Riemannian manifolds , Geodesics (Mathematics), Knee -- Simulation methods | ||||||||||||||||||
| Journal or Publication Title: | Journal of Mathematical Imaging and Vision | ||||||||||||||||||
| Publisher: | Springer | ||||||||||||||||||
| ISSN: | 0924-9907 | ||||||||||||||||||
| Official Date: | May 2020 | ||||||||||||||||||
| Dates: |
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| Volume: | 62 | ||||||||||||||||||
| Number: | 4 | ||||||||||||||||||
| Page Range: | pp. 549-559 | ||||||||||||||||||
| DOI: | 10.1007/s10851-020-00945-w | ||||||||||||||||||
| Status: | Peer Reviewed | ||||||||||||||||||
| Publication Status: | Published | ||||||||||||||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||||||||||||||
| Date of first compliant deposit: | 13 July 2020 | ||||||||||||||||||
| Date of first compliant Open Access: | 15 July 2020 | ||||||||||||||||||
| RIOXX Funder/Project Grant: |
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| Is Part Of: | 1 |
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