%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