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Phys Med Biol. 2014 Feb 21;59(4):961-73. doi: 10.1088/0031-9155/59/4/961. Epub 2014 Feb 7.

Global point signature for shape analysis of carpal bones.

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Department of Radiology, University of California-Davis School of Medicine, Sacramento, CA 95817, USA.


We present a method based on spectral theory for the shape analysis of carpal bones of the human wrist. We represent the cortical surface of the carpal bone in a coordinate system based on the eigensystem of the two-dimensional Helmholtz equation. We employ a metric--global point signature (GPS)--that exploits the scale and isometric invariance of eigenfunctions to quantify overall bone shape. We use a fast finite-element-method to compute the GPS metric. We capitalize upon the properties of GPS representation--such as stability, a standard Euclidean (ℓ(2)) metric definition, and invariance to scaling, translation and rotation--to perform shape analysis of the carpal bones of ten women and ten men from a publicly-available database. We demonstrate the utility of the proposed GPS representation to provide a means for comparing shapes of the carpal bones across populations.

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