Image Segmentation Using Active Contours: Calculus of Variations or Shape Gradients? - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue SIAM Journal on Applied Mathematics Année : 2003

Image Segmentation Using Active Contours: Calculus of Variations or Shape Gradients?

Résumé

We consider the problem of segmenting an image through the minimization of an energy criterion involving region and boundary functionals. We show that one can go from one class to the otherb y solving Poisson's orHelmholtz's equation with well-chosen boundary conditions. Using this equivalence, we study the case of a large class of region functionals by standard methods of the calculus of variations and derive the corresponding Euler-Lagrange equations. We revisit this problem using the notion of a shape derivative and show that the same equations can be elegantly derived without going through the unnatural step of converting the region integrals into boundary integrals. We also define a larger class of region functionals based on the estimation and comparison to a prototype of the probability density distribution of image features and show how the shape derivative tool allows us to easily compute the corresponding Gˆateaux derivatives and Euler-Lagrange equations. Finally we apply this new functional to the problem of regions segmentation in sequences of color images. We briefly describe our numerical scheme and show some experimental results.
Fichier principal
Vignette du fichier
SIAM-03.pdf (251.77 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00964649 , version 1 (24-03-2014)

Identifiants

Citer

Gilles Aubert, Michel Barlaud, Olivier Faugeras, Stéphanie Jehan-Besson. Image Segmentation Using Active Contours: Calculus of Variations or Shape Gradients?. SIAM Journal on Applied Mathematics, 2003, 63 (6), pp.2128-2154. ⟨10.1137/S0036139902408928⟩. ⟨hal-00964649⟩
286 Consultations
800 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More