期刊
JOURNAL OF MATHEMATICAL IMAGING AND VISION
卷 24, 期 2, 页码 209-228出版社
SPRINGER
DOI: 10.1007/s10851-005-3624-0
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资金
- NCRR NIH HHS [P41 RR015241, U24 RR021382-04, P41 RR015241-078616, U24 RR021382] Funding Source: Medline
- NIMH NIH HHS [P50 MH071616, P50 MH071616-01] Funding Source: Medline
Studying large deformations with a Riemannian approach has been an efficient point of view to generate metrics between deformable objects, and to provide accurate, non ambiguous and smooth matchings between images. In this paper, we study the geodesics of such large deformation diffeomorphisms, and more precisely, introduce a fundamental property that they satisfy, namely the conservation of momentum. This property allows us to generate and store complex deformations with the help of one initial momentum which serves as the initial state of a differential equation in the group of diffeomorphisms. Moreover, it is shown that this momentum can be also used for describing a deformation of given visual structures, like points, contours or images, and that, it has the same dimension as the described object, as a consequence of the normal momentum constraint we introduce.
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