Image Selective Smoothing and Edge Detection by Nonlinear Diffusion. II

Álvarez, Luis; Lions, Pierre-Louis; Morel, Jean‐Michel

doi:10.1137/0729052

Cited by 1,395 publications

(650 citation statements)

References 21 publications

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“…And it is known that PeronaMallik diffusion is an adaptive diffusion process to the different scale, although this scheme cannot deal with texture-rich image for its sensibility to variation of gradient. Shock filters [16] suffer the same shortcoming. We use the complex diffusion [17] to do smoothing inside homogeneous region while enhancing edge.…”

Section: Complex Diffusion and Generalized Gradientmentioning

confidence: 99%

A Geometric Contour Framework with Vector Field Support

Liu

2006

Computer Vision – ACCV 2006

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Abstract. In this paper, we propose a new geometric contour framework with support of specified vector field. First we define three criteria for selection of vector field in geometric model. According to the criteria, EdgeFlow, a powerful segmentation tool, is selected to generate desirable initial vector field. In order to overcome the drawbacks of conventional geometric models, multi-source external forces, such as from texture and multi-spectra, are integrated to provide the ability for segmenting the texture-rich and complex scene images. Instead of common smoothing pre-processing to denoise and suppress possible spurious edges, the more advanced complex diffusion filters are adopted in our algorithm, which result in the piecewise filtered image to help detect those sharp transition regions. We test our model on the Berkeley Segmentation Database, and the experimental results are promising.

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Section: Complex Diffusion and Generalized Gradientmentioning

confidence: 99%

A Geometric Contour Framework with Vector Field Support

Liu

2006

Computer Vision – ACCV 2006

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“…With the objective of eliminating unnecessary parameters, where in many cases they are co-related we propose in this paper an equation to eliminate noise and detect borders in an image where only two inter related parameters exist, and which depend on the image. The model studied here has as its main characteristic the elimination of the parameters used in our previous work([2]), we were inspired by the works of Rudin, Osher and Fatemi( [9]) eAlvares, Lions and Morel ( [1]). The enhancement of the initial image I is performed by the following differential equation:…”

Section: Non Linear Space Scalementioning

confidence: 99%

“…Evans [5]. As this equation is not able to preserve the edges localization, Alvares, Lions and Morel proposed in [1] the following non linear parabolic equation for noise removal (1+ks 2 ) with k as a parameter. In the formula of most of the models based on PDE there exist parameters of which in some cases are determined by specific procedures and in others, for example [3], the parameters are taken from that which produces the best results.…”

Section: Differential Equation With Automatic Selection Of Parametersmentioning

confidence: 99%

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Edge detection and noise removal by use of a partial differential equation with automatic selection of parameters

Barcelos¹,

Boaventura²,

Silva³

2005

Mat. apl. comput.

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Abstract. This work deals with noise removal by the use of an edge preserving method whose parameters are automatically estimated, for any application, by simply providing information about the standard deviation noise level we wish to eliminate. The desired noiseless image u(x), in a Partial Differential Equation based model, can be viewed as the solution of an evolutionary differential equation u t (x) = F (u xx , u x , u, x, t) which means that the true solution will be reached when t → ∞. In practical applications we should stop the time ''t'' at some moment during this evolutionary process. This work presents a sufficient condition, related to time t and to the standard deviation σ of the noise we desire to remove, which gives a constant T such that u(x, T ) is a good approximation of u(x).The approach here focused on edge preservation during the noise elimination process as its main characteristic. The balance between edge points and interior points is carried out by a function g which depends on the initial noisy image u(x, t 0 ), the standard deviation of the noise we want to eliminate and a constant k. The k parameter estimation is also presented in this work therefore making, the proposed model automatic. The model's feasibility and the choice of the optimal time scale is evident through out the various experimental results.#606/04.

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“…These PDE-based models have been extensively studied to answer fundamental questions in image restoration and have allowed researchers and practitioners not only to introduce new mathematical models but also to improve traditional algorithms [1,4,9,22,30] .…”

Section: Introductionmentioning

confidence: 99%

Equalized Net Diffusion (END) for the Preservation of Fine Structures in PDE-based Image Restoration

Cha

Kim

2013

The Journal of Korean Institute of Communications and Informati

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The article is concerned with a mathematical modeling which can improve performances of PDE-based restoration models. Most PDE-based restoration models tend to lose fine structures due to certain degrees of nonphysical dissipation. Sources of such an undesirable dissipation are analyzed for total variation-based restoration models. Based on the analysis, the so-called equalized net diffusion (END) modeling is suggested in order for PDE-based restoration models to significantly reduce nonphysical dissipation. It has been numerically verified that the END-incorporated models can preserve and recover fine structures satisfactorily, outperforming the basic models for both quality and efficiency. Various numerical examples are shown to demonstrate effectiveness of the END modeling.Key Words : Fine structures, nonphysical dissipation, total variation (TV) model, non-convex (NC) model, equalized net diffusion (END). [2,13,19,20,21,24,27] .There have been various partial differential equation (PDE)-based restoration models such as the Perona-Malik model [25] , the total variation (TV) model [18,26] , and color restoration models [3,10,15,17,28] . These PDE-based models have been extensively studied to answer fundamental questions in image restoration and have allowed researchers and practitioners not only to introduce new mathematical models but also to improve traditional algorithms [1,4,9,22,30] .However, most PDE-based restoration models and their numerical realizations show a common drawback: loss of fine structures. Such an undesirable loss is due to an excessive numerical dissipation introduced particularly on regions where the image content changes rapidly such as on edges and textures. Thus the reduction of nonphysical dissipation becomes an interesting problem in image restoration, requiring challenges and innovative ideas. Although advanced models have been recently suggested for the preservation of fine structures [19,23] , more effective strategies have yet to be developed. In this article, we will first analyze sources of nonphysical dissipation for popular PDE-based restoration models. Based on the analysis, we will study the so-called equalized net diffusion (END) modeling for PDE-based restoration models, first introduced in [14] . Here we will study mathematical 논문 / Equalized Net Diffusion (END) for the Preservation of Fine Structures in PDE-based Image Restoration 999properties of the END in detail and suggest a heuristic method for parameter choices. It has been numerically verified that with the new parameters, the END modeling can reduce nonphysical dissipation significantly and more effectively for most of natural images we have tested.The article is organized as follows. In the next section, we review TV-based models along with recent studies for the reduction of nonphysical dissipation. Section III analyzes sources of nonphysical dissipation for PDE-based models: nonphysical dissipation occurs more excessively at pixels where the diffusion term evaluates larger in modulus. In Section IV...

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Image Selective Smoothing and Edge Detection by Nonlinear Diffusion. II

Cited by 1,395 publications

References 21 publications

A Geometric Contour Framework with Vector Field Support

A Geometric Contour Framework with Vector Field Support

Edge detection and noise removal by use of a partial differential equation with automatic selection of parameters

Equalized Net Diffusion (END) for the Preservation of Fine Structures in PDE-based Image Restoration

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