Edge-forming methods for color image zooming

Cha, Young-Joon; Kim, Seongjai

doi:10.1109/tip.2006.875182

Cited by 42 publications

(26 citation statements)

References 23 publications

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“…As numerically verified in Section VI below, the NC model can preserve fine structures better than the ITV model. A variant of the NC model has been successfully applied as an edge-forming method for image zooming of arbitrary magnification factors [6,7] . Remark.…”

Section: Total Variation (Tv)-based Modelsmentioning

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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Section: Total Variation (Tv)-based Modelsmentioning

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 ABO model has been applied as an effective edge-forming method for image zooming which incorporates large and non-integer magnification factors [17,18,19] .…”

Section: A General Denoising Modelmentioning

confidence: 99%

“…Theorem 4.1. Consider the general denoising model (2) with the numerical algorithm (10), (11) and (12) incorporated with the MONTE algorithm described in (16) and (17). Let    supx ,    sups   , and the following condition is satisfied.…”

Section: ⅳ Stability Of the Montementioning

confidence: 99%

The Method of Nonflat Time Evolution (Monte) in Pde-Based Image Restoration

Cha¹,

Kim²

2012

The Journal of Korean Institute of Communications and Informati

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This article is concerned with effective numerical techniques for partial differential equation (PDE)-based image restoration. Numerical realizations of most PDE-based denoising models show a common drawback: loss of fine structures. In order to overcome the drawback, the article introduces a new time-stepping procedure, called the method of nonflat time evolution (MONTE), in which the timestep size is determined based on local image characteristics such as the curvature or the diffusion magnitude. The MONTE provides PDE-based restoration models with an effective mechanism for the equalization of the net diffusion over a wide range of image frequency components. It can be easily applied to diverse evolutionary PDE-based restoration models and their spatial and temporal discretizations. It has been numerically verified that the MONTE results in a significant reduction in numerical dissipation and preserves fine structures such as edges and textures satisfactorily, while it removes the noise with an improved efficiency. Various numerical results are shown to confirm the claim.

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“…Recently, as the field of IP requires higher levels of reliability and efficiency, various powerful tools of partial differential equations (PDEs) and functional analysis have been successfully applied to image restoration [1,10,14,21,27,31,33,35,41] and color processing [6,15,22,24,37]. In particular, a considerable amount of research has been carried out for the theoretical and computational understanding of the total variation (TV) model [35] and its variants [1,10,11,14,21,23,27,28,38].…”

Section: Introductionmentioning

confidence: 99%