Principal geodesic analysis for the study of nonlinear statistics of shape

@article{Fletcher2004PrincipalGA,
  title={Principal geodesic analysis for the study of nonlinear statistics of shape},
  author={P. Thomas Fletcher and Conglin Lu and Stephen M. Pizer and Sarang C. Joshi},
  journal={IEEE Transactions on Medical Imaging},
  year={2004},
  volume={23},
  pages={995-1005}
}
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… 
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