%0 Conference Paper
%B Pattern Recognition, 2002. Proceedings. 16th International Conference on
%D 2002
%T A Smale-like decomposition for discrete scalar fields
%A De Floriani, Leila
%A Mesmoudi,M. M.
%A Danovaro,E.
%K data
%K decomposition;
%K differentiable
%K discrete
%K domain;
%K field;
%K fields;
%K functions;
%K gradient
%K graph-based
%K methods;
%K multidimensional
%K multiresolution
%K representation;
%K scalar
%K Smale-like
%K structure
%K Topology
%K triangulated
%K vector
%K visualisation;
%X 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.
%B Pattern Recognition, 2002. Proceedings. 16th International Conference on
%V 1
%P 184 - 187 vol.1 - 184 - 187 vol.1
%8 2002///
%G eng
%R 10.1109/ICPR.2002.1044644