The DOI matches its Crossref record; 108 of the 108 references it cites were found in a registry or an index.
Computational anatomy: an emerging discipline
Open accessAbstract
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 ( Ω , H , I , P ) , the background space Ω = ˙ U α M α of 0, 1, 2, 3-dimensional manifolds, the set of diffeomorphic transformations on the background space H : Ω ↔ Ω , the space of idealized medical imagery I , and P 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 ( Ω , H , I ) corresponding to a homogeneous space [3], in that it can be completely generated from one of its elements, I = H I t e m p , I t e m p ∈ I . For disease, a family of templates U α I t e m p α are introduced of perhaps varying dimensional transformation classes. The complete anatomy is a collection of homogeneous spaces I t o t a l = U α ( I α , H α ) .
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Self-citation
Metadata
- Authors
- Grenander, U., & Miller, M. I.
- Venue
- Quarterly of Applied Mathematics
- Publisher
- American Mathematical Society (AMS)
- Published
- 1998-12
- Volume
- 56
- Issue
- 4
- Pages
- 617-694
- ISSN
- 0033-569X (ISSN-L)
- 1552-4485
- OpenAlex
- W1503893179
- Cited by
- 623
- References
- 108
- FWCI
- 16.00
- Type
- journal article
- Language
- en
- Open access
- bronze
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
