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 -