The DOI matches its Crossref record; 111 of the 111 references it cites were found in a registry or an index.
On the Metrics and Euler-Lagrange Equations of Computational Anatomy
Abstract
▪ Abstract This paper reviews literature, current concepts and approaches in computational anatomy (CA). The model of CA is a Grenander deformable template, an orbit generated from a template under groups of diffeomorphisms. The metric space of all anatomical images is constructed from the geodesic connecting one anatomical structure to another in the orbit. The variational problems specifying these metrics are reviewed along with their associated Euler-Lagrange equations. The Euler equations of motion derived by Arnold for the geodesics in the group of divergence-free volume-preserving diffeomorphisms of incompressible fluids are generalized for the larger group of diffeomorphisms used in CA with nonconstant Jacobians. Metrics that accommodate photometric variation are described extending the anatomical model to incorporate the construction of neoplasm. Metrics on landmarked shapes are reviewed as well as Joshi's diffeomorphism metrics, Bookstein's thin-plate spline approximate-metrics, and Kendall's affine invariant metrics. We conclude by showing recent experimental results from the Toga & Thompson group in growth, the Van Essen group in macaque and human cortex mapping, and the Csernansky group in hippocampus mapping for neuropsychiatric studies in aging and schizophrenia.
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Cites
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A Voxel-Based Morphometric Study of Ageing in 465 Normal Adult Human Brains
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Cited by
A reproducible evaluation of ANTs similarity metric performance in brain image registration
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Deformable medical image registration: a survey
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“The distance between these elements is defined as a geodesic, according to a metric, that connects them and can be used for studies of anatomical variability [70].”
BackgroundA Review of Geometric Transformations for Nonrigid Body Registration
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Self-citationStatistics on diffeomorphisms via tangent space representations
Vaillant, M., Miller, M. I., Younes, L., & Trouvé, A. (2004) · NeuroImage · doi:10.1016/j.neuroimage.2004.07.023 · Cited by 215
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Metadata
- Authors
- Miller, M. I., Trouvé, A., & Younes, L.
- Venue
- Annual Review of Biomedical Engineering
- Publisher
- Annual Reviews
- Published
- 2002-08
- Volume
- 4
- Issue
- 1
- Pages
- 375-405
- ISSN
- 1523-9829 (ISSN-L)
- 1545-4274
- OpenAlex
- W2115245436
- Cited by
- 438
- References
- 111
- FWCI
- 4.00
- Type
- journal article
- Language
- en
- Open access
- closed
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