A new paradigm for describing the shape of manifolds is presented,with a particular regard to applications in pattern recognition.Given a Morse function f defined on a closed smooth manifoldM, the shape of the pair (M,f) is represented by the evolutionof the homology groups of the lower level sets of M with respect to f. The main tool is classical Morse theory. Analgorithm for treating the case of orientable surfaces is given.
F., Cagliari, Claudia, Landi e Luigi, Grasselli. "Presentations of Morse homology for studying shape of manifolds" Working paper, Dipartimento di Scienze e Metodi dell'Ingegneria, Università di Modena e Reggio Emilia, 2001.
Presentations of Morse homology for studying shape of manifolds
LANDI, Claudia;GRASSELLI, Luigi
2001
Abstract
A new paradigm for describing the shape of manifolds is presented,with a particular regard to applications in pattern recognition.Given a Morse function f defined on a closed smooth manifoldM, the shape of the pair (M,f) is represented by the evolutionof the homology groups of the lower level sets of M with respect to f. The main tool is classical Morse theory. Analgorithm for treating the case of orientable surfaces is given.Pubblicazioni consigliate
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