Computational anatomy: an emerging discipline

Authors:
Ulf Grenander and Michael I. Miller

Journal:
Quart. Appl. Math. **56** (1998), 617-694

MSC:
Primary 92C50; Secondary 00A69, 92B05

DOI:
https://doi.org/10.1090/qam/1668732

MathSciNet review:
MR1668732

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: 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 maintained. For *normal anatomy* one deformable template is studied, with corresponding to a *homogeneous space* [3], in that it can be completely generated from one of its elements, . For *disease*, a family of templates are introduced of perhaps varying dimensional transformation classes. The complete anatomy is a collection of homogeneous spaces .

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DOI:
https://doi.org/10.1090/qam/1668732

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American Mathematical Society