A Smale-like decomposition for discrete scalar fields

In this paper we address the problem of representing the structure of the topology of a d-dimensional scalar field as a basis for constructing a multiresolution representation of the structure of such afield. To this aim, we define a discrete decomposition of a triangulated d-dimensional domain, on...

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Bibliographic Details
Main Authors: De Floriani, L., Mesmoudi, M.M., Danovaro, E.
Format: Conference Proceeding
Language:English
Subjects:
Biomedical equipment
Computational fluid dynamics
Computational modeling
Geometry
Image analysis
Medical services
Piecewise linear approximation
Solid modeling
Topology
Visualization
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Summary:In this paper we address the problem of representing the structure of the topology of a d-dimensional scalar field as a basis for constructing a multiresolution representation of the structure of such afield. To this aim, we define a discrete decomposition of a triangulated d-dimensional domain, on whose vertices the values of the field are given. We extend a Smale decomposition, defined by Thom (1949) and Smale (1960) for differentiable functions, to the discrete case, to what we call a Smale-like decomposition. We introduce the notion of discrete gradient vector field, which indicates the growth of the scalar field and matches with our decomposition. We sketch an algorithm for building a Smale-like decomposition and a graph-based representation of this decomposition. We present results for the case of two-dimensional fields.
ISSN:1051-4651
2831-7475
DOI:10.1109/ICPR.2002.1044644