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Hamiltonian Systems and Optimal Control in Computational Anatomy: 100 Years Since D'Arcy Thompson
Ist Teil von
Annual review of biomedical engineering, 2015-12, Vol.17 (1), p.447-509
Ort / Verlag
United States: Annual Reviews
Erscheinungsjahr
2015
Link zum Volltext
Quelle
Free E-Journal (出版社公開部分のみ）
Beschreibungen/Notizen
The Computational Anatomy project is the morphome-scale study of shape and form, which we model as an orbit under diffeomorphic group action. Metric comparison calculates the geodesic length of the diffeomorphic flow connecting one form to another. Geodesic connection provides a positioning system for coordinatizing the forms and positioning their associated functional information. This article reviews progress since the Euler-Lagrange characterization of the geodesics a decade ago. Geodesic positioning is posed as a series of problems in Hamiltonian control, which emphasize the key reduction from the Eulerian momentum with dimension of the flow of the group, to the parametric coordinates appropriate to the dimension of the submanifolds being positioned. The Hamiltonian viewpoint provides important extensions of the core setting to new, object-informed positioning systems. Several submanifold mapping problems are discussed as they apply to metamorphosis, multiple shape spaces, and longitudinal time series studies of growth and atrophy via shape splines.