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Differential topology methods for shape description
Author(s) -
Biasotti Silvia,
Giorgi Daniela,
Patané Giuseppe
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700173
Subject(s) - eigenfunction , morse theory , topology (electrical circuits) , differential (mechanical device) , function (biology) , laplace operator , mathematics , field (mathematics) , encode , computer science , pure mathematics , eigenvalues and eigenvectors , mathematical analysis , physics , combinatorics , biochemistry , chemistry , quantum mechanics , evolutionary biology , biology , gene , thermodynamics
Differential topology, and specifically Morse theory, provides a suitable setting for formalizing and solving several problems related to shape analysis. In this field, we discuss how a shape can be analyzed according to the properties of a real function defined on it (e.g., harmonic fields or laplacian eigenfunctions), and how these properties can be stored in compact and informative descriptors. We refer to Reeb graphs, that encode the configuration of level sets and critical points of the function