@conference {13272,
	title = {A Smale-like decomposition for discrete scalar fields},
	booktitle = {Pattern Recognition, 2002. Proceedings. 16th International Conference on},
	volume = {1},
	year = {2002},
	month = {2002///},
	pages = {184 - 187 vol.1 - 184 - 187 vol.1},
	abstract = {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.},
	keywords = {data, decomposition;, differentiable, discrete, domain;, field;, fields;, functions;, gradient, graph-based, methods;, multidimensional, multiresolution, representation;, scalar, Smale-like, structure, Topology, triangulated, vector, visualisation;},
	doi = {10.1109/ICPR.2002.1044644},
	author = {De Floriani, Leila and Mesmoudi,M. M. and Danovaro,E.}
}
