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Principal Geodesic Analysis for the Study of Nonlinear Statistics of Shape (2004)
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| Venue: | TO APPEAR IEEE TRANSACTIONS ON MEDICAL IMAGING |
| Citations: | 181 - 33 self |
BibTeX
@MISC{Fletcher04principalgeodesic,
author = {P. Thomas Fletcher and Conglin Lu and Stephen M. Pizer and Sarang Joshi},
title = { Principal Geodesic Analysis for the Study of Nonlinear Statistics of Shape},
year = {2004}
}
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Abstract
A primary goal of statistical shape analysis is to describe the variability of a population of geometric objects. A standard technique for computing such descriptions is principal component analysis. However, principal component analysis is limited in that it only works for data lying in a Euclidean vector space. While this is certainly sufficient for geometric models that are parameterized by a set of landmarks or a dense collection of boundary points, it does not handle more complex representations of shape. We have been developing representations of geometry based on the medial axis description or m-rep. While the medial representation provides a rich language for variability in terms of bending, twisting, and widening, the medial parameters are not elements of a Euclidean vector space. They are in fact elements of a nonlinear Riemannian symmetric space. In this paper we develop the method of principal geodesic analysis, a generalization of principal component analysis to the manifold setting. We demonstrate its use in describing the variability of medially-defined anatomical objects. Results of applying this framework on a population of hippocampi in a schizophrenia study are presented.
Keyphrases
principal geodesic analysis nonlinear statistic principal component analysis appear ieee transaction medical imaging euclidean vector space manifold setting complex representation deformable model medial representation nonlinear riemannian symmetric space geometric object boundary point medial geometry statistical shape analysis geometric model dense collection medial axis description index term statistical shape analysis medial parameter standard technique fact element schizophrenia study medially-defined anatomical object primary goal rich language
