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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 , the background space of 0, 1, 2, 3-dimensional manifolds, the set of diffeomorphic transformations on the background space , the space of idealized medical imagery , and the family of probability measures on . The group of diffeomorphic transformations is chosen to be rich enough so that a large family of shapes may be generated with the topologies of the template …