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A Smale-like decomposition for discrete scalar fields

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3 Author(s)
De Floriani, L. ; Dept. of Comput. & Inf. Sci., Genoa Univ., Italy ; Mesmoudi, M.M. ; Danovaro, E.

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.

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Pattern Recognition, 2002. Proceedings. 16th International Conference on  (Volume:1 )

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