Ascending and descending Morse complexes, defined by the critical points and integral lines of a scalar field f defined on a manifold domain D, induce a subdivision of D into regions of uniform gradient flow, and thus provide a compact description of the morphology of f on D. We propose a dimension-independent representation for the ascending and descending Morse complexes, and we describe a data structure which assumes a discrete representation of the field as a simplicial mesh, that we call the incidence-based data structure. We present algorithms for building such data structure for 2D and 3D scalar fields, which make use of a watershed approach to compute the cells of the Morse decompositions.

Building Morphological Representations for 2D and 3D Scalar Fields

DE FLORIANI, LEILA;
2010

Abstract

Ascending and descending Morse complexes, defined by the critical points and integral lines of a scalar field f defined on a manifold domain D, induce a subdivision of D into regions of uniform gradient flow, and thus provide a compact description of the morphology of f on D. We propose a dimension-independent representation for the ascending and descending Morse complexes, and we describe a data structure which assumes a discrete representation of the field as a simplicial mesh, that we call the incidence-based data structure. We present algorithms for building such data structure for 2D and 3D scalar fields, which make use of a watershed approach to compute the cells of the Morse decompositions.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11567/257373
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