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| HAL: hal-00372706, version 1 |
| DOI: 10.1007/s11075-008-9174-y |
| Detailed view |  Export this paper |
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| Numerical Algorithms 48, 1-3 (2008) 105-133 |
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| Geodesic Active Contour under Geometrical Conditions: theory and 3D applications |
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| Carole Le Guyader 1, 2, 3Christian Gout 4, 5 |
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| (2008) |
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| In this paper, we propose a new scheme for both detection of boundaries and fitting of geometrical data based on a geometrical partial differential equation, which allows a rigorous mathematical analysis. The model is a geodesic-active-contour-based model, in which we are trying to determine a curve that best approaches the given geometrical conditions (for instance a set of points or curves to approach) while detecting the object under consideration. Formal results concerning existence, uniqueness (viscosity solution) and stability are presented as well. We give the discretization of the method using an additive operator splitting scheme which is very efficient for this kind of problem. We also give 2D and 3D numerical examples on real data sets. |
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| 1: | Laboratoire de Mathématiques de l'INSA Rouen |
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Aucune |
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| 2: | Institut National des Sciences Appliquées de Rennes (INSA Rennes) |
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Institut National des Sciences Appliquées (INSA) - Rennes |
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| 3: | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
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| 4: | Laboratoire de Mathématiques et leurs Applications de Valenciennes, EA 45 (LAMAV) |
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Université de Valenciennes et du Hainaut-Cambresis – CNRS : FRE2956 |
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| 5: | Laboratoire Mathématique de l'INSA (LMI) |
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Université de Rouen – Institut National des Sciences Appliquées (INSA) - Rouen |
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| Subject | : | Mathematics/Numerical Analysis |
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| Geodesic active contours – Level set method – Viscosity solution – Approximation of points |
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| hal-00372706, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00372706 | |
| oai:hal.archives-ouvertes.fr:hal-00372706 | |
| From: Maryse Collin | |
| Submitted on: Thursday, 2 April 2009 09:50:21 | |
| Updated on: Thursday, 2 April 2009 09:50:21 | |
