Computational anatomy (CA) is the mathematical study of anatomy I a I = I a BG, an orbit under groups of diffeomorphisms (i.e., smooth invertible mappings) g a G of anatomical exemplars Iaa 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 a G defining the shape or geometry of the anatomical manifolds, and (iii) generation of probability laws of anatomical variation P(d) 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.

Morphometric variability of the human brain poses significant challenges for the creation of population-based atlases. The ability to statistically and visually compare and contrast brain image data from multiple individuals is essential to understand normal variability within a particular population as well as differentiate normal from diseased populations. This chapter introduces the application of probabilistic atlases to describe specific subpopulations, measures their variability and characterizes the structural differences between them. Utilizing data from structural MRI, we have built atlases with defined coordinate systems creating a framework to map data from functional, histological and other studies of the same population. These structural atlases provide an indexed and robust framework for the mapping of functions and other attributes. This paper describes the basic approach and a brief description of the underlying mathematical constructs that enable the calculation of probabilistic atlases and examples of their results from several different normal and diseased populations.

journal homepage: www.elsevier.com/locate/ynimg A novel framework for segmentation of deep brain structures based on Markov