On a Class of Diffeomorphic Matching Problems in One Dimension


We study a class of functional which can be used for matching objects which can be represented as mappings from a fixed interval, I, to some “feature space.” This class of functionals corresponds to “elastic matching” in which a symmetry condition and a “focus invariance” are imposed. We provide sufficient conditions under which an optimal matching can be found between two such mappings, the optimal matching being a homeomorphism of the interval I. The differentiability of this matching is also studied, and an application to plane curve comparison is provided.

DOI: 10.1137/S036301299934864X

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@article{Trouv2000OnAC, title={On a Class of Diffeomorphic Matching Problems in One Dimension}, author={Alain Trouv{\'e} and Laurent Younes}, journal={SIAM J. Control and Optimization}, year={2000}, volume={39}, pages={1112-1135} }