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Principal geodesic analysis for the study of nonlinear statistics of shape
TLDR
The method of principal geodesic analysis is developed, a generalization of principal component analysis to the manifold setting and demonstrated its use in describing the variability of medially-defined anatomical objects.
Landmark matching via large deformation diffeomorphisms
TLDR
Conditions for the existence of solutions in the space of diffeomorphisms are established, with a gradient algorithm provided for generating the optimal flow solving the minimum problem.
Principal Geodesic Analysis on Symmetric Spaces: Statistics of Diffusion Tensors
TLDR
This work introduces principal geodesic analysis, a generalization of principal component analysis, to symmetric spaces and applies it to the computation of the variability of diffusion tensor data, and develops methods for producing statistics, namely averages and modes of variation, in this space.
Hippocampal morphometry in schizophrenia by high dimensional brain mapping.
TLDR
The results of this study demonstrate that abnormalities of hippocampal anatomy occur in schizophrenia and support current hypotheses that schizophrenia involves a disturbance of hippocampus-prefrontal connections and show that comparisons of neuroanatomical shapes can be more informative than volume comparisons for identifying individuals with neuropsychiatric diseases, such as schizophrenia.
Functional and structural mapping of human cerebral cortex: solutions are in the surfaces.
TLDR
This report discusses ways to compensate for the convolutions of the human cerebral cortex by using a combination of strategies whose common denominator involves explicit reconstructions of the cortical surface.
Statistics of shape via principal geodesic analysis on Lie groups
TLDR
This paper shows that medial descriptions are in fact elements of a Lie group, and develops methodology based on Lie groups for the statistical analysis of medially-defined anatomical objects.
Volumetric transformation of brain anatomy
TLDR
It is shown that transformations constrained by quadratic regularization methods such as the Laplacian, biharmonic, and linear elasticity models, do not ensure that the transformation maintains topology and, therefore, must only be used for coarse global registration.
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