Computational anatomy: shape, growth, and atrophy comparison via diffeomorphisms.
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.
Miller
Michael I
MI
Center for Imaging Science, The Johns Hopkins University, Baltimore, MD 21218, USA. mim@cis.jhu.edu
D000465:Algorithms; D000818:Animals; D001284:Atrophy; D001921:Brain / Q000033:anatomy & histology* / Q000254:growth & development* / Q000473:pathology; D001931:Brain Mapping; D019295:Computational Biology; D006321:Heart / Q000033:anatomy & histology; D006801:Humans; D007091:Image Processing, Computer-Assisted; D008279:Magnetic Resonance Imaging; D051379:Mice; D015233:Models, Statistical