The general setting for Shape Analysis

摘要: In shape analysis, the concept of spaces has always been vague, requiring a case-by-case approach for every new type shape. this paper, we give general definition an abstract space shapes in manifold. This notion encompasses studied so far literature, and offers rigorous framework several possible generalizations. We then appropriate setting LDDMM methods which arises naturally as sub-Riemannian structure on space. is deduced from infinitesimal deformations their action. describe properties Hamiltonian geodesic flow, study applications equivariant mappings between spaces.