Image Structure-Preserving Denoising Based on Difference Curvature Driven Fractional Nonlinear Diffusion

Yin, Xuehui; Zhou, Shangbo

doi:10.1155/2015/930984

Cited by 13 publications

(9 citation statements)

References 36 publications

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“…The proposed algorithm is tested for the various values of fractional-order gradient in the range [8,14] of step size 0.1 and applied on Gaussian noisy boat image with 10% standard deviation. This algorithm is compared with the model [7] and the model [6] for the selection of the fractional-order. The comparison results are shown in the figure 1.…”

Section: ░ 4 Numerical Experimentsmentioning

confidence: 99%

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Fractional-order Diffusion based Image Denoising Model

Sridevi

Gudla

Bindu³

2022

IJEER

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Edge indicating operators such as gradient, mean curvature, and Gauss curvature-based image noise removal algorithms are incapable of classifying edges, ramps, and flat areas adequately. These operators are often affected by the loss of fine textures. In this paper, these problems are addressed and proposed a new coefficient of diffusion for noise removal. This new coefficient consists of two edge indicating operators, namely fractional-order difference curvature and fractional-order gradient. The fractional-order difference curvature is capable of analyzing flat surfaces, edges, ramps, and tiny textures. The fractional-order gradient can able to distinguish texture regions. The selection of the order is more flexible for the fractional order gradient and fractional-order difference curvature. This will result in effective image denoising. Since the discrete Fourier transform is simple to numerically implement, it is taken into consideration for the implementation of fractional-order gradient. The proposed method can give results that are visually appealing and improved quantitative outputs in terms of the Figure of Merit (FoM), Mean Structural Similarity (MSSIM), and Peak Signal to Noise Ratio (PSNR), according to comparative analysis.

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Section: ░ 4 Numerical Experimentsmentioning

confidence: 99%

“…The fractional-order calculus has been widely used in image processing to retain the edges [1][2][3][4][5][6][7]. The "non-local" attribute of the fractional-order differentiation operator allows for improved texture preservation, in contrast to the traditional integer-order differentiation operator.…”

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confidence: 99%

Fractional-order Diffusion based Image Denoising Model

Sridevi

Gudla

Bindu³

2022

IJEER

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“…For this purpose, the fractional-order derivative based Perona-Malik diffusion is used to smooth the original image. This diffusion process can yield a piecewise constant results while preserving edges and suppressing staircase [55], [56]. Specially, the input image is first smoothed by the following fractional-order diffusion equation:…”

Section: A Fractional-order Diffusion Based Edge Indicatormentioning

confidence: 99%

“…where I x and I y represent the first-order derivatives, I xx and I yy denote the second-order derivatives. The partial differential equation defined in (12) can be solved iteratively in the frequency-domain, for details refer to [55], [56].…”

Section: A Fractional-order Diffusion Based Edge Indicatormentioning

confidence: 99%

Fuzzy Active Contour Model Using Fractional-Order Diffusion Based Edge Indicator and Fuzzy Local Fitted Image

Zhang

Wang

2020

IEEE Access

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Local region-based active contour models (ACMs) can effectively segment images corrupted by intensity inhomogeneity, however, they always converge to local minimum and are sensitive to the initial position of contour. In this paper, a novel fuzzy ACM is proposed to tackle these problems. In order to deal with intensity inhomogeneity, the fuzzy local fitted image is first defined and utilized for constructing a local-region based fuzzy energy term, which is minimized in a variational level set framework to accurately segment inhomogeneous images. Second, the fractional-order diffusion based edge indicator is used to scale the local fuzzy energy term to reduce the effect of intensity inhomogeneity. Third, the fuzzy signed pressure force (FSPF) function defined by local image information is used for constructing the weighted area term to further improve the accuracy of the developed model. Finally, the global FSPF is formulated and used as an adaptive force, which can drive the level set function (LSF) to adaptively move up or down according to image intensity information. Therefore, the initial contour can be initialized as a constant function, which eliminates the problem caused by contour initialization. Moreover, the global FSPF makes the proposed model not easy to fall into local minimum. The results of experiments on synthetic and real images validate the accuracy of the proposed model for inhomogeneous image segmentation. INDEX TERMS Active contour model, inhomogeneous image segmentation, fuzzy local fitted image, edge indicator, FSPF function.

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“…Pu Yifei [19] put forward a set of fractional partial differential equations based on fractional total variation and fractional steepest descent approach to address the problem of traditional drawbacks of PM and ROF multi-scale denoising for texture image. Yin Xuehui, et al [20] presented a difference curvature driven fractional anisotropic diffusion for image noise removal, which uses two new techniques, fractional calculus and difference curvature, to describe the intensity variations in images. Ido Zachevsky, et al [21] proposed an algorithm for the denoising of natural images containing NST, using patchbased fractional Brownian motion model and regularization by means of anisotropic diffusion.…”

Section: Introductionmentioning

confidence: 99%

Image Denoising Based on Adaptive Fractional Order Anisotropic Diffusion

Yu¹,

Tan²,

Zhou³

et al. 2016

KSII TIIS

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Recently, the method based on fractional order partial differential equation has been used in image processing. Usually, the optional order of fractional differentiation is determined by a lot of experiments. In this paper, a denoising model is proposed based on adaptive fractional order anisotropic diffusion. In the proposed model, the complexity of the local image texture is reflected by the local variance, and the order of the fractional differentiation is determined adaptively. In the process of the adaptive fractional order model, the discrete Fourier transform is applied to compute the fractional order difference as well as the dynamic evolution process. Experimental results show that the peak signal-to-noise ratio (PSNR) and structural similarity index measurement (SSIM) of the proposed image denoising algorithm is better than that of other some algorithms. The proposed algorithm not only can keep the detailed image information and edge information, but also obtain a good visual effect.

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Image Structure-Preserving Denoising Based on Difference Curvature Driven Fractional Nonlinear Diffusion

Cited by 13 publications

References 36 publications

Fractional-order Diffusion based Image Denoising Model

Fractional-order Diffusion based Image Denoising Model

Fuzzy Active Contour Model Using Fractional-Order Diffusion Based Edge Indicator and Fuzzy Local Fitted Image

Image Denoising Based on Adaptive Fractional Order Anisotropic Diffusion

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