A Smale-like decomposition for discrete scalar fields

TitleA Smale-like decomposition for discrete scalar fields
Publication TypeConference Papers
Year of Publication2002
AuthorsDe Floriani L, Mesmoudi MM, Danovaro E
Conference NamePattern Recognition, 2002. Proceedings. 16th International Conference on
Date Published2002///
Keywordsdata, decomposition;, differentiable, discrete, domain;, field;, fields;, functions;, gradient, graph-based, methods;, multidimensional, multiresolution, representation;, scalar, Smale-like, structure, Topology, triangulated, vector, visualisation;

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.