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| 1 | Camila Xu | -- | 3186 | 2022-11-03 01:40:08 |
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Computational anatomy (CA) is a discipline within medical imaging focusing on the study of anatomical shape and form at the visible or gross anatomical scale of morphology. The field is broadly defined and includes foundations in anatomy, applied mathematics and pure mathematics, including medical imaging, neuroscience, physics, probability, and statistics. It focuses on the anatomical structures being imaged, rather than the medical imaging devices. The central focus of the sub-field of computational anatomy within medical imaging is mapping information across anatomical coordinate systems most often dense information measured within a magnetic resonance image (MRI). The introduction of flows into CA, which are akin to the equations of motion used in fluid dynamics, exploit the notion that dense coordinates in image analysis follow the Lagrangian and Eulerian equations of motion. In models based on Lagrangian and Eulerian flows of diffeomorphisms, the constraint is associated to topological properties, such as open sets being preserved, coordinates not crossing implying uniqueness and existence of the inverse mapping, and connected sets remaining connected. The use of diffeomorphic methods grew quickly to dominate the field of mapping methods post Christensen's original paper, with fast and symmetric methods becoming available.
References
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- U. Grenander and M. I. Miller (2007-02-08). Pattern Theory: From Representation to Inference. Oxford University Press. ISBN 9780199297061.
- M. I. Miller and S. Mori and X. Tang and D. Tward and Y. Zhang (2015-02-14). Bayesian Multiple Atlas Deformable Templates. Brain Mapping: An Encyclopedic Reference. Academic Press. ISBN 9780123973160. https://books.google.com/books?id=ysucBAAAQBAJ.
- Srivastava, S.; Miller, M. I.; Grenander, U. (1997-01-01). Byrnes, Christopher I.. ed. Ergodic Algorithms on Special Euclidean Groups for ATR. Systems & Control: Foundations & Applications. Birkhäuser Boston. pp. 327–350. doi:10.1007/978-1-4612-4120-1_18. ISBN 978-1-4612-8662-2. https://dx.doi.org/10.1007%2F978-1-4612-4120-1_18
- P. Dupuis, U. Grenander, M.I. Miller, Existence of Solutions on Flows of Diffeomorphisms, Quarterly of Applied Math, 1997.
- Trouvé, A. (1995). "Action de groupe de dimension infinie et reconnaissance de formes" (in fr). Comptes Rendus de l'Académie des Sciences, Série I 321 (8): 1031–1034.
- Tang, Xiaoying; Oishi, Kenichi; Faria, Andreia V.; Hillis, Argye E.; Albert, Marilyn S.; Mori, Susumu; Miller, Michael I. (2013-06-18). "Bayesian Parameter Estimation and Segmentation in the Multi-Atlas Random Orbit Model". PLOS ONE 8 (6): e65591. doi:10.1371/journal.pone.0065591. PMID 23824159. Bibcode: 2013PLoSO...865591T. http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=3688886
