Minimal Paths and Deformable Models for Image Analysis. Chemins Minimaux et Modèles Déformables en Analyse d’Images

Minimal Paths and Deformable Models for Image Analysis

Chemins Minimaux et Modèles Déformables en Analyse d’Images

Laurent D. Cohen

CEREMADE, UMR CNRS 7534, Université Paris-Dauphine, 75775 Paris cedex 16, France

Corresponding Author Email: 
cohen@ceremade.dauphine.fr
Page: 
225-241
|
Received: 
N/A
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Accepted: 
N/A
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Published: 
30 September 2003
| Citation

OPEN ACCESS

Abstract: 

We present an overview of part of our work on minimal paths. Introduced first in order to find the global minimum of active contours' energy using Fast Marching [18], we have then used minimal paths for finding multiple contours for contour completion from points, curves or regions in 2D or 3D images. Some variations allow to decrease computation time, make easier initialization and centering a path in a tubular structure. Fast Marching is also an efficient way to solve balloon model evolution using level sets. We show applications like for road and vessel segmentation and for virtual endoscopy.

Résumé

Nous présentons une synthèse d'une partie de nos travaux sur les chemins minimaux. Introduits au départ pour trouver le minimum global de l'énergie pour les contours actifs à l'aide du Fast Marching [18], nous les avons utilisés par la suite pour la recherche de contours multiples pour compléter des points, des courbes ou des régions dans des images 2D et 3D. Plusieurs variantes permettent d'améliorer le temps de calcul, de simplifier l'initialisation ou de centrer le chemin dans une structure tubulaire. Le Fast Marching est aussi un moyen efficace de résoudre l'évolution d'un modèle de contour actif ballon par « level sets ». Nous montrons des applications notamment pour la segmentation de routes et vaisseaux et pour l'endoscopie virtuelle. 

Keywords: 

Minimal paths, active contours, deformable models, fast marching, Eikonal Equation, level sets, weighted distance, reconstruction, energy minimization, Perceptual grouping, salient curve detection, 2D and 3D medical images, aerial images. 

Mots clés 

Chemins minimaux, contours actifs, modèles déformables, fast marching, Equation Eikonale, Ensembles de niveaux, distance pondérée, minimisation d'énergie, Groupement perceptuel, imagerie médicale 2D et 3D, Imagerie aérienne.

1. Introduction
2. Chemins Minimaux
3. Chemins Minimaux Multiples 2D Entre Points pk
4. Chemins Minimaux Multiples entre Régions Rk
5. Structures Tubulaires 2D et 3D
6. Segmentation par Fast Marching
7. Chemins Minimaux 3D Centrés et Endoscopie Virtuelle
Conclusion
Remerciements
  References

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