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

Computational anatomy (CA) is the mathematical study of anatomy I = is an element of T = I-alpha (o)G, an orbit under groups of diffeomorphisms (i.e., smooth invertible mappings) g is an element of G of anatomical exemplars I-alpha is an element of= T. 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 is an element of G defining the shape or geometry of the anatomical manifolds, and (iii) generation of probability laws of anatomical variation P( (.)) on the images T for inference and disease testing within anatomical models. This paper reviews recent advances in these three areas applied to shape, growth, and atrophy. (C) 2004 Elsevier Inc. All rights reserved.