COMPUTATIONAL ANATOMY: AN EMERGING DISCIPLINE

Abstract

This paper studies mathematical methods in the emerging new discipline of Computational Anatomy. Herein we formalize the Brown/Washington University model of anatomyfollowing 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 ( � H � I � P), the background space = [ M of 0 � 1 � 2 � 3;dimensional manifolds, the set of di eomorphic transformations on the background space H: $ , the space of idealized medical imagery I, and P the family of probability measures on H. The group of di eomorphic 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 ( � H � I) corresponding to a homogeneous space [3], in that it can be completely generated from one of its elements, I = HItemp�Itemp 2I. For disease, a family of templates [ Itemp are introduced of perhaps varying dimensional transformation classes. The complete anatomy is is a collection of homogeneous spaces Itotal = [ (I � H). There are three principal components to computational anatomy studied herein