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Neuroimage. 2004;23 Suppl 1:S19-33.

Computational anatomy: shape, growth, and atrophy comparison via diffeomorphisms.

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1
Center for Imaging Science, The Johns Hopkins University, Baltimore, MD 21218, USA. mim@cis.jhu.edu

Abstract

Computational anatomy (CA) is the mathematical study of anatomy I in I = I(alpha) o G, an orbit under groups of diffeomorphisms (i.e., smooth invertible mappings) g in G of anatomical exemplars I(alpha) in I. The observable images are the output of medical imaging devices. There are three components that CA examines: (i) constructions of the anatomical submanifolds, (ii) comparison of the anatomical manifolds via estimation of the underlying diffeomorphisms g in G defining the shape or geometry of the anatomical manifolds, and (iii) generation of probability laws of anatomical variation P(.) on the images I for inference and disease testing within anatomical models. This paper reviews recent advances in these three areas applied to shape, growth, and atrophy.

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