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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.

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Paper citation in several formats:
Mostefa Mesmoudi, M. and De Floriani, L. (2007). MORPHOLOGY-BASED REPRESENTATIONS OF DISCRETE SCALAR FIELDS. In Proceedings of the Second International Conference on Computer Graphics Theory and Applications (VISIGRAPP 2007) - Volume 2: GRAPP; ISBN 978-972-8865-71-9; ISSN 2184-4321, SciTePress, pages 137-144. DOI: 10.5220/0002080501370144

@conference{grapp07,
author={Mohammed {Mostefa Mesmoudi}. and Leila {De Floriani}.},
title={MORPHOLOGY-BASED REPRESENTATIONS OF DISCRETE SCALAR FIELDS},
booktitle={Proceedings of the Second International Conference on Computer Graphics Theory and Applications (VISIGRAPP 2007) - Volume 2: GRAPP},
year={2007},
pages={137-144},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0002080501370144},
isbn={978-972-8865-71-9},
issn={2184-4321},
}

TY - CONF

JO - Proceedings of the Second International Conference on Computer Graphics Theory and Applications (VISIGRAPP 2007) - Volume 2: GRAPP
TI - MORPHOLOGY-BASED REPRESENTATIONS OF DISCRETE SCALAR FIELDS
SN - 978-972-8865-71-9
IS - 2184-4321
AU - Mostefa Mesmoudi, M.
AU - De Floriani, L.
PY - 2007
SP - 137
EP - 144
DO - 10.5220/0002080501370144
PB - SciTePress