Computational anatomy: an emerging discipline
This paper studies mathematical methods in the emerging new discipline of Computational Anatomy. Herein we formalize the Brown/Washington University model of anatomy following the global pattern theory introduced in [1, 2], in which anatomies are represented as deformable templates, collections of 0,1,2,3-dimensional manifolds. Typical structure is carried by the template with the variabilities accommodated via the application of random transformations to the background manifolds. The anatomical model is a quadruple (0,W, X,V), the background space f2 = \JaMa of 0,1,2,3-dimensional manifolds, the set of diffeomorphic transformations on the background space W : <-> O, the space of idealized medical imagery X, and V the family of probability measures on H. The group of diffeomorphic transformations H is chosen to be rich enough so that a large family of shapes may be generated with the topologies of the template maintained. For normal anatomy one deformable template is studied, with (f1,H,X) corresponding to a homogeneous space [3], in that it can be completely generated from one of its elements, X = Tiltemp-, hemp £ For disease, a family of templates Ua I"emp are introduced of perhaps varying dimensional transformation classes. The complete anatomy is a collection of homogeneous spaces Xtotai — UQ(^a> ~Ha )There are three principal components to computational anatomy studied herein. (1) Computation of large deformation maps: Given any two elements 1,1' £ X in the same homogeneous anatomy (fl,7i,X), compute diffeomorphisms h from one h anatomy to the other I1I'. This is the principal method by which anatomical Received May 5, 1998.