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Edge detection and image restoration with anisotropic topological gradient
2010
2010 IEEE International Conference on Acoustics, Speech and Signal Processing
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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
2010
Journal of Applied Mathematics
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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
2012
Milan Journal of Mathematics
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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
2008
Journal of Mathematical Imaging and Vision
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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
2014
SIAM Journal of Imaging Sciences
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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
2008
Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing
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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
2009
ESAIM: Proceedings and Surveys
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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]
2005
Lecture Notes in Computer Science
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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
2009
Measurement science and technology
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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]
2018
arXiv
pre-print
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2017 pre-print arXiv:1706.06190v1 fatcat:ewuvouovtvafnifb5iycpnl5sy
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
2009
Mathematical and computer modelling
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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
2010
SIAM Journal of Imaging Sciences
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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
2011
International Journal on Document Analysis and Recognition
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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
2007
Mathematical Modelling and Numerical Analysis
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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]
2002
Lecture Notes in Computer Science
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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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