TY - CONF T1 - A Smale-like decomposition for discrete scalar fields T2 - Pattern Recognition, 2002. Proceedings. 16th International Conference on Y1 - 2002 A1 - De Floriani, Leila A1 - Mesmoudi,M. M. A1 - Danovaro,E. KW - data KW - decomposition; KW - differentiable KW - discrete KW - domain; KW - field; KW - fields; KW - functions; KW - gradient KW - graph-based KW - methods; KW - multidimensional KW - multiresolution KW - representation; KW - scalar KW - Smale-like KW - structure KW - Topology KW - triangulated KW - vector KW - visualisation; AB - 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. JA - Pattern Recognition, 2002. Proceedings. 16th International Conference on VL - 1 M3 - 10.1109/ICPR.2002.1044644 ER -