A one-shot inpainting algorithm based on the topological asymptotic analysis

Auroux, Didier; Masmoudi, Mohamed

doi:10.1590/s0101-82052006000200008

Cited by 26 publications

(28 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [67], Tschumperlé and Deriche propose an efficient secondorder anisotropic diffusion equation that preserves curvature and gives good results. The approach of D. Auroux and M. Masmoudi in [4] uses the PDE techniques that have been developed for the inverse conductivity problem in the context of crack detection. In [2,60] a prior segmentation of the edges outside the inpainting domain is performed.…”

Section: Geometric Methodsmentioning

confidence: 99%

Geometrically Guided Exemplar-Based Inpainting

Cao¹,

Gousseau²,

Masnou³

et al. 2011

SIAM J. Imaging Sci.

101

View full text Add to dashboard Cite

Exemplar-based methods have proven their efficiency for the reconstruction of missing parts in a digital image. Texture as well as local geometry are often very well restored. Some applications, however, require the ability to reconstruct non local geometric features, e.g. long edges. We propose in this paper to endow a particular instance of exemplar-based method with a geometric guide. The guide is obtained by a prior interpolation of a simplified version of the image using straight lines or Euler spirals. We derive from it an additional geometric penalization for the metric associated with the exemplar-based algorithm. We discuss the details of the method and show several examples of reconstruction.

show abstract

Section: Geometric Methodsmentioning

confidence: 99%

Geometrically Guided Exemplar-Based Inpainting

Cao¹,

Gousseau²,

Masnou³

et al. 2011

SIAM J. Imaging Sci.

101

View full text Add to dashboard Cite

show abstract

“…Several numerical results are presented in [15] and show the quality and efficiency of the reconstruction.…”

Section: Remarksmentioning

confidence: 99%

Image processing by topological asymptotic analysis

Auroux

Masmoudi

2008

2008 IEEE International Conference on Acoustics, Speech and Signal Processing

Self Cite

View full text Add to dashboard Cite

Abstract. The aim of this article is to recall the applications of the topological asymptotic expansion to many image processing problems. We briefly review the topological asymptotic analysis. A very natural application of this technique in image processing is the inpainting problem, which can be solved by identifying the optimal localization of the missing edges. A second natural application is then the image restoration or enhancement problem. The identification of the main edges of the image allows us to preserve them, and to smooth the image outside the edges. We present then an application to the regularized and unsupervised classification problem. If the conductivity outside the edges goes to infinity, the regularized image is piecewise constant and provides a natural solution to the segmentation problem. We also mention that all these problems are solved with a O(n. log(n)) complexity. Finally, we present a hybrid scheme for contour detection and completion based on topological gradient and fast marching algorithms. We briefly illustrate all these applications with numerical results.Résumé. Dans cet article, nous présentons l'application du gradient topologiqueà plusieurs problèmes classiques en traitement d'images. Après avoir brièvement introduit l'analyse asymptotique topologique, nous présentons son application naturelle au problème de l'inpainting, qui peutêtre résolu en identifiant la localisation optimale des contours manquants dans l'image. Une deuxième application naturelle est la restauration ou le débruitage d'images. L'identification des principaux contours permet de les préserver au cours du processus de restauration. Nous présentons ensuite une applicationà la classification régularisée et non supervisée. Lorsque la conductivité tend vers l'infini en dehors des contours, l'image régularisée devient constante par morceaux, et fournit une solution naturelle au problème de segmentation d'une image. Nous précisons ensuite la complexité de tous ces algorithmes, en O(n. log(n). Enfin, nous présentons un algorithme hybride pour la détection et fermeture des contours d'une image, basé sur les algorithmes du gradient topologique et des chemins minimaux. Pour chacune des applications, nous illustrons l'algorithme avec quelques résultats numériques.

show abstract

“…A natural application of this idea is the problem of segmentation: since the identification of the main edges of the image allows us to preserve them and smooth the image outside the edges, then if the conductivity c outside edges is large enough, the regularized image is piecewise constant and provides a natural segmentation of the image. However, this efficient technique introduced by some of the authors in Jaafar Belaid et al (2006;2008), Auroux and Masmoudi (2006), Auroux et al (2007), and Auroux (2008), to solve several image processing problems like restoration, classification, segmentation, inpainting and enhancement or denoising, presents a major drawback: the identified edges are not necessarily connected and then the results obtained for the segmentation problem can be degraded, particularly for complex images. So, the main idea of this work is to take advantage of the topological gradient efficiency, to detect the main contours with an interesting computational cost (the topological gradient algorithms require only three system resolutions) and to overcome the drawback of the topological gradient approach by using a method giving closed contours.…”

Section: Introductionmentioning

confidence: 99%

Image Segmentation: A Watershed Transformation Algorithm

Belaid¹,

Mourou²

2011

Image Anal Stereol

View full text Add to dashboard Cite

The goal of this work is to present a new method for image segmentation using mathematical morphology. The approach used is based on the watershed transformation. In order to avoid an oversegmentation, we propose to adapt the topological gradient method. The watershed transformation combined with a fast algorithm based on the topological gradient approach gives good results. The numerical tests obtained illustrate the efficiency of our approach for image segmentation.

show abstract

A one-shot inpainting algorithm based on the topological asymptotic analysis

Cited by 26 publications

References 23 publications

Geometrically Guided Exemplar-Based Inpainting

Geometrically Guided Exemplar-Based Inpainting

Image processing by topological asymptotic analysis

Image Segmentation: A Watershed Transformation Algorithm

Contact Info

Product

Resources

About