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Edge detection and image restoration with anisotropic topological gradient

Stanislas Larnier, Jerome Fehrenbach
2010 2010 IEEE International Conference on Acoustics, Speech and Signal Processing  
Edge detection and image restoration with anisotropic topological gradient. ABSTRACT Topological asymptotic analysis provides tools to detect edges and their orientation.  ...  The purpose of this article is to show the possibilities of anisotropic topological gradient in image restoration.  ...  The diffusion tensor used to restore an image is anisotropic on the edges, with a small diffusion coefficient on primary edges and a larger one on the secondary edges.  ... 
doi:10.1109/icassp.2010.5495448 dblp:conf/icassp/LarnierF10 fatcat:mcsxpx75zbcehnudb47e3y7vo4

An Overview of the Topological Gradient Approach in Image Processing: Advantages and Inconveniences

Lamia Jaafar Belaid
2010 Journal of Applied Mathematics  
This paper aims at reviewing this methodology through various applications in image processing; in particular image restoration with edge detection, classification and segmentation problems for both grey  ...  The numerical experiments show the efficiency of the topological gradient approach for modelling and solving different image analysis problems.  ...  method, c zoom of the restored Lena image using topological gradient approach with the isotropic algorithm, and d zoom of the restored Lena image using topological gradient approach with the anisotropic  ... 
doi:10.1155/2010/761783 fatcat:ijqgx37c3rehzgqvmyb74zqvy4

The Topological Gradient Method: From Optimal Design to Image Processing

Stanislas Larnier, Jérôme Fehrenbach, Mohamed Masmoudi
2012 Milan Journal of Mathematics  
The aim of this article is to review and extend the applications of the topological gradient to major image processing problems.  ...  Edge detection is of extreme importance, as edges convey essential information in a picture. A second natural application is then the image reconstruction.  ...  Gunturk, Keigo Hirakawa, Gabriel Peyre and Zhou Wang for their codes.  ... 
doi:10.1007/s00032-012-0196-5 fatcat:bfhrtorbjnhofknjndjdldk7uq

Image Processing by Topological Asymptotic Expansion

Didier Auroux, Mohamed Masmoudi
2008 Journal of Mathematical Imaging and Vision  
A second natural application is then the image restoration or enhancement. The identification of the main edges of the image allows us to preserve them, and smooth the image outside the edges.  ...  If the conductivity outside edges goes to infinity, the regularized image is piecewise constant and provides a natural solution to the segmentation problem.  ...  Application to Image Restoration In this section, we use the topological gradient as a tool for detecting edges for image restoration.  ... 
doi:10.1007/s10851-008-0121-2 fatcat:amnuyixenvcabk4p4k3l36oogq

Numerical Analysis of the Topological Gradient Method for Fourth Order Models and Applications to the Detection of Fine Structures in Imaging

Audric Drogoul
2014 SIAM Journal of Imaging Sciences  
We show that as for edge detection [16] , the topological gradient is not only a filament detector but it also allows to restore images containing filaments.  ...  First used in mechanics of structures [1], this method has been then applied in imaging for edge detection and image restoration [11, 16] .  ...  We will see in section 5 that the topological gradient is not only a detector but it also allows to restore images.  ... 
doi:10.1137/140967374 fatcat:dzg3ngn465ecjetp6ick6rfise

Image processing by topological asymptotic analysis

Didier Auroux, Mohamed Masmoudi
2008 Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing  
Finally, we present a coupled approach combining the topological gradient and the minimal path technique in order to improve the edge detection, and to avoid non-connex contours.  ...  Finally, we present a hybrid scheme for contour detection and completion based on topological gradient and fast marching algorithms.  ...  The main idea is to use the topological gradient for detecting the edges of the noisy image in order to preserve them during the restoration process.  ... 
doi:10.1109/icassp.2008.4517725 dblp:conf/icassp/AurouxM08 fatcat:uczgwizmrzdd7gqgpkd2en454m

Image processing by topological asymptotic analysis

Didier Auroux, Mohamed Masmoudi, H. Ammari
2009 ESAIM: Proceedings and Surveys  
Finally, we present a coupled approach combining the topological gradient and the minimal path technique in order to improve the edge detection, and to avoid non-connex contours.  ...  Finally, we present a hybrid scheme for contour detection and completion based on topological gradient and fast marching algorithms.  ...  The main idea is to use the topological gradient for detecting the edges of the noisy image in order to preserve them during the restoration process.  ... 
doi:10.1051/proc/2009003 fatcat:dd6lyyyihfbxhm2np6j73kygfy

Sparse Finite Element Level-Sets for Anisotropic Boundary Detection in 3D Images [chapter]

Martin Weber, Andrew Blake, Roberto Cipolla
2005 Lecture Notes in Computer Science  
Boundary detection is performed using an anisotropic extension of the isotropic geodesic model. With the sparse representation, the anisotropic model is computationally feasible.  ...  We present experimental results on volumetric data sets including images with a significant amount of noise.  ...  Gradient descent for the anisotropic scheme Surface evolution is defined as the gradient descent of the cost (2) with density (4).  ... 
doi:10.1007/11408031_47 fatcat:xrk55yuaozcadamd7xecnzeyxq

New PDE-based methods for image enhancement using SOM and Bayesian inference in various discretization schemes

D A Karras, G B Mertzios
2009 Measurement science and technology  
it is shown to be efficient in image filtering and restoration applications.  ...  The proposed modifications attempt to capture not only simple edges but also difficult textural edges and incorporate their probability in the anisotropic diffusion model.  ...  edge detection was motivated.  ... 
doi:10.1088/0957-0233/20/10/104012 fatcat:wylbbdb2ybd57c6pnaihc3b4r4

A nonstandard higher-order variational model to speckle noise removal and thin-structure detection [article]

Hamdi Houichet, Anis Theljani, Maher Moakher, Badreddine Rjaibi
2018 arXiv   pre-print
First, we consider a topological gradient approach for a semilinear case in order to detect important object of image.  ...  We compare our model with other classical variational approaches such that the TVL and biharmonic restoration models.  ...  The proposed approach combines the advantages of the topological gradient method for important feature detection and the anisotropic diffusion model based on the p(·)-Kirchhoff operator for the denoising  ... 
arXiv:1706.06190v2 fatcat:3vc3aesxind2hc37ywojnjw55q

From restoration by topological gradient to medical image segmentation via an asymptotic expansion

Didier Auroux
2009 Mathematical and computer modelling  
We first recall the classical variational of the image restoration problem, and its resolution by topological asymptotic analysis in which the identification of the diffusion coefficient can be seen as  ...  In this paper is introduced a technique based on a power series expansion of the solution to the image restoration problem with respect to this small coefficient.  ...  Application to image restoration In this section, we use the topological gradient as a tool for detecting edges for image restoration.  ... 
doi:10.1016/j.mcm.2008.07.002 fatcat:jopucgxsbfgpxk37est7z3hnsq

Application of the Topological Gradient Method to Color Image Restoration

Didier Auroux, Lamia Jaafar Belaid, Badreddine Rjaibi
2010 SIAM Journal of Imaging Sciences  
We derive an asymptotic expansion of this gradient with respect to the insertion of a small crack in the image, and we propose a new algorithm based on the topological gradient for the color image restoration  ...  The aim of this paper is to generalize to color images the topological gradient method for the restoration problem.  ...  The authors would like to thank the referees for their useful comments and suggestions.  ... 
doi:10.1137/080721017 fatcat:phgfczwcubg2vbyvjbyq3m4dh4

A new PDE-based approach for singularity-preserving regularization: application to degraded characters restoration

Fadoua Drira, Frank LeBourgeois, Hubert Emptoz
2011 International Journal on Document Analysis and Recognition  
Existing PDE-approaches do not preserve singularities and edge continuities while smoothing.  ...  The massive digitization of heritage documents have raised new prospects for Research like degraded document image restoration.  ...  Edge preservation: if λ +/− ≫ 0, the smoothing process should be anisotropic and directed along the edge direction Θ − . 2.  ... 
doi:10.1007/s10032-011-0165-5 fatcat:lhlnpmi3cbfuvfluq3wiwqs34q

A topological asymptotic analysis for the regularized grey-level image classification problem

Didier Auroux, Lamia Jaafar Belaid, Mohamed Masmoudi
2007 Mathematical Modelling and Numerical Analysis  
We first present the classical variational approach without and with a regularization term in order to smooth the contours of the classified image.  ...  Then we present the general topological asymptotic analysis, and we finally introduce its application to the grey-level image classification problem.  ...  the optimal design ω ⊂ Ω ant its complementary; • In image processing problems like edge detection, classification, and segmentation, the goal is to split the image in several parts.  ... 
doi:10.1051/m2an:2007027 fatcat:ibhw4smp7zhzngvjwtougsud7y

Deformable Model with Non-euclidean Metrics [chapter]

Benjamin Taton, Jacques-Olivier Lachaud
2002 Lecture Notes in Computer Science  
Highly deformable models extend them with the ability to handle dynamic topological changes, and therefore to extract arbitrary complex shapes.  ...  With this property, a significant precision is achieved in the interesting parts of the image, while a coarse resolution is maintained elsewhere.  ...  Detecting special configurations allows them to detect and handle topological changes.  ... 
doi:10.1007/3-540-47977-5_29 fatcat:simjcvdkyfe4zlyvuo5z3x4nj4
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