%0 Conference Paper %B Discrete Geometry for Computer Imagery %D 2011 %T Smale-like decomposition and forman theory for discrete scalar fields %A Čomić,L. %A Mesmoudi,M. %A De Floriani, Leila %X Forman theory, which is a discrete alternative for cell complexes to the well-known Morse theory, is currently finding several applications in areas where the data to be handled are discrete, such as image processing and computer graphics. Here, we show that a discrete scalar field f, defined on the vertices of a triangulated multidimensional domain Σ, and its gradient vector field Grad f through the Smale-like decomposition of f [6], are both the restriction of a Forman function F and its gradient field Grad F that extends f over all the simplexes of Σ. We present an algorithm that gives an explicit construction of such an extension. Hence, the scalar field f inherits the properties of Forman gradient vector fields and functions from field Grad F and function F. %B Discrete Geometry for Computer Imagery %P 477 - 488 %8 2011/// %G eng %R 10.1007/978-3-642-19867-0_40