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. Key words. calculus of variations, shape representation and recognition, elastic matching, geodesic distance AMS subject classifications. Primary, 49J45; Secondary, 68T10, 53A04 PII. S036301299934864X

• Type: Journal
• Year: 2000
• Where: SIAMCO
• Authors: Alain Trouvé, Laurent Younes
• Keywords: Elastic Matching, Feature Space, Fixed Interval, SIAMCO 2000