MORPHOLOGY-BASED REPRESENTATIONS OF DISCRETE SCALAR FIELDS

Mohammed Mostefa Mesmoudi, Leila De Floriani

2007

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 Harvard Style

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 - Volume 1: GRAPP, ISBN 978-972-8865-71-9, pages 137-144. DOI: 10.5220/0002080501370144

in Bibtex Style

@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 - Volume 1: GRAPP,},
year={2007},
pages={137-144},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0002080501370144},
isbn={978-972-8865-71-9},
}


in EndNote Style

TY - CONF
JO - Proceedings of the Second International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP,
TI - MORPHOLOGY-BASED REPRESENTATIONS OF DISCRETE SCALAR FIELDS
SN - 978-972-8865-71-9
AU - Mostefa Mesmoudi M.
AU - De Floriani L.
PY - 2007
SP - 137
EP - 144
DO - 10.5220/0002080501370144