Computational anatomy (CA) is the mathematical study of anatomy I ∈ I = Iα○ G, an orbit under groups of diffeomorphisms (i.e., smooth invertible mappings) g ∈ G of anatomical exemplars Iα∈ 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 ∈ 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. © 2004 Elsevier Inc. All rights reserved.
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