Authors:
Mohammed Mostefa Mesmoudi
1
and
Leila De Floriani
2
Affiliations:
1
Mostaganem University, Algeria
;
2
University of Genova, Italy
Keyword(s):
Gradient vector field, Morse theory, Geometric modeling, Smale decomposition, Forman theory.
Related
Ontology
Subjects/Areas/Topics:
Applications
;
Computer Vision, Visualization and Computer Graphics
;
Fundamental Methods and Algorithms
;
Geometric Computing
;
Geometry and Modeling
;
Image-Based Modeling
;
Modeling and Algorithms
;
Multi-Resolution Modeling
;
Pattern Recognition
;
Software Engineering
;
Surface Modeling
Abstract:
Forman introduced in (Forman, 1998) a theory for cell complexes that is a discrete version of the well known Morse theory. Forman theory finds several applications in digital geometry and image processing where the data to be processed are discrete, see for instance (Lewiner et al., 2002a), (Lewiner et al., 2002b). In (DeFloriani et al., 2002b), we have introduced a Smale-like decomposition of a scalar field f defined on a triangulated domain M based on a discrete gradient field that simulates well the behavior of the gradient field in the differentiable case. Here, we extend our discrete gradient vector field so that the extended form coincides with a Forman gradient field. The extended gradient field does not change the Smale-like decomposition components and, thus, inherits properties of both smooth Morse and discrete Forman functions.