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

2015 ◽  
Vol 2015 ◽  
pp. 1-16 ◽  
Author(s):  
Xuehui Yin ◽  
Shangbo Zhou
Keyword(s):  
Fractional Order ◽  
Anisotropic Diffusion ◽  
Noise Removal ◽  
Experimental Results ◽  
New Techniques ◽  
Proposed Model ◽  
Staircase Effect ◽  
The Difference ◽  
Curvature Driven ◽  
Difference Curvature

The traditional integer-order partial differential equations and gradient regularization based image denoising techniques often suffer from staircase effect, speckle artifacts, and the loss of image contrast and texture details. To address these issues, in this paper, a difference curvature driven fractional anisotropic diffusion for image noise removal is presented, which uses two new techniques, fractional calculus and difference curvature, to describe the intensity variations in images. The fractional-order derivatives information of an image can deal well with the textures of the image and achieve a good tradeoff between eliminating speckle artifacts and restraining staircase effect. The difference curvature constructed by the second order derivatives along the direction of gradient of an image and perpendicular to the gradient can effectively distinguish between ramps and edges. Fourier transform technique is also proposed to compute the fractional-order derivative. Experimental results demonstrate that the proposed denoising model can avoid speckle artifacts and staircase effect and preserve important features such as curvy edges, straight edges, ramps, corners, and textures. They are obviously superior to those of traditional integral based methods. The experimental results also reveal that our proposed model yields a good visual effect and better values of MSSIM and PSNR.

Difference Curvature Driven Anisotropic Diffusion for Image Denoising Using Laplacian Kernel

2013 ◽  
Vol 347-350 ◽  
pp. 2412-2417
Author(s):  
Yi Yan Wang ◽  
Zhuo Er Wang
Keyword(s):  
Differential Equation ◽  
Anisotropic Diffusion ◽  
Noise Removal ◽  
The Other ◽  
Local Analysis ◽  
Preliminary Step ◽  
Staircase Effect ◽  
High Level ◽  
Curvature Driven ◽  
Difference Curvature

Image noise removal forms a significant preliminary step in many machine vision tasks, such as object detection and pattern recognition. The original anisotropic diffusion denoising methods based on partial differential equation often suffer the staircase effect and the loss of edge details when the image contains a high level of noise. Because its controlling function is based on gradient, which is sensitive to noise. To alleviate this drawback, a novel anisotropic diffusion algorithm is proposed. Firstly, we present a new controlling function based on Laplacian kernel, then making use of the local analysis of an image, we propose a difference curvature driven to describe the intensity variations in images. Experimental results on several natural and medical images show that the new method has better performance in the staircase alleviation and details preserving than the other anisotropic diffusions.

scholarly journals Fractional-Order Fusion Model for Low-Light Image Enhancement

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 574 ◽  
Author(s):  
Qiang Dai ◽  
Yi-Fei Pu ◽  
Ziaur Rahman ◽  
Muhammad Aamir
Keyword(s):  
Image Enhancement ◽  
Fractional Order ◽  
Input Image ◽  
Experimental Results ◽  
Fusion Model ◽  
Low Light ◽  
Visual Appearance ◽  
Light Image ◽  
Proposed Model ◽  
Detail Enhancement

In this paper, a novel fractional-order fusion model (FFM) is presented for low-light image enhancement. Existing image enhancement methods don’t adequately extract contents from low-light areas, suppress noise, and preserve naturalness. To solve these problems, the main contributions of this paper are using fractional-order mask and the fusion framework to enhance the low-light image. Firstly, the fractional mask is utilized to extract illumination from the input image. Secondly, image exposure adjusts to visible the dark regions. Finally, the fusion approach adopts the extracting of more hidden contents from dim areas. Depending on the experimental results, the fractional-order differential is much better for preserving the visual appearance as compared to traditional integer-order methods. The FFM works well for images having complex or normal low-light conditions. It also shows a trade-off among contrast improvement, detail enhancement, and preservation of the natural feel of the image. Experimental results reveal that the proposed model achieves promising results, and extracts more invisible contents in dark areas. The qualitative and quantitative comparison of several recent and advance state-of-the-art algorithms shows that the proposed model is robust and efficient.

scholarly journals Modified Perona-Malik Equation and Computer Simulation for Image Denoising

2014 ◽  
Vol 8 (1) ◽  
pp. 37-41
Author(s):  
Zheng Jian Feng ◽  
Huang Chengwei ◽  
Zhang Ji
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Computer Simulation ◽  
Image Denoising ◽  
Digital Image ◽  
Gaussian Noise ◽  
Anisotropic Diffusion ◽  
Difficult Problem ◽  
Experimental Results ◽  
Proposed Model

The edges and textures of a digital image may be destroyed by traditional denoising methods, which is a difficult problem in image denoising. In this paper, anisotropic diffusion algorithm based on Partial differential equation is studied. First, image denoising algorithms based on Perona-Malik model are studied. Second, a modified Perona-Malik model is proposed. In the proposed model, the gradient statistic and edge thresholds are embedded into the Perona-Malik equation. Finally, the effects of this model and some other models are compared and analyzed. The experimental results show that the proposed modified Perona-Malik model outperforms the original Perona-Malik model in removing Gaussian noise, and the edges and textures of the image are well preserved.

Fractional-Order Anisotropic Diffusion for Defogging of RGB Images

2020 ◽  
Vol 20 (01) ◽  
pp. 2050001 ◽  
Author(s):  
Savita Nandal ◽  
Sanjeev Kumar
Keyword(s):  
Fractional Order ◽  
Efficient Algorithm ◽  
Anisotropic Diffusion ◽  
Point Of View ◽  
Experimental Results ◽  
Coupling Term ◽  
Rgb Images ◽  
Fog Effect

This paper proposes a novel and efficient algorithm for defogging of color (RGB) images. The fog in a scene is mostly due to the attenuation and airlight map, which decrease the quality of the image of the scene. To enhance such images from the visual point of view, a fractional-order anisotropic diffusion algorithm with [Formula: see text]-Laplace norm is proposed for removing the fog effect. In particular, a coupling term is added in order to model the inter-channel correlations. The weights used in the coupling term stop the transmission of diffusion with in the edges, thus balances the inter-channel data in the diffusion procedure. Experimental results validate the better performance of the proposed algorithm over some of the existing anisotropic diffusion-based methods. The proposed method is independent of the measure of fog in the images, thus images with different amount of fog can be enhanced.

scholarly journals Combined total variation of first and fractional orders for Poisson noise removal in digital images

2021 ◽  
pp. 10-19
Author(s):  
Cong Pham ◽  
Thi Thu Tran ◽  
Minh Pham ◽  
Thanh Cong Nguyen
Keyword(s):  
Image Reconstruction ◽  
Image Restoration ◽  
Total Variation ◽  
Fractional Order ◽  
Optimization Problem ◽  
Poisson Noise ◽  
Experimental Results ◽  
First Order ◽  
Proposed Model ◽  
Total Variation Model

Introduction: Many methods have been proposed to handle the image restoration problem with Poisson noise. A popular approach to Poissonian image reconstruction is the one based on Total Variation. This method can provide significantly sharp edges and visually fine images, but it results in piecewise-constant regions in the resulting images. Purpose: Developing an adaptive total variation-based model for the reconstruction of images contaminated by Poisson noise, and an algorithm for solving the optimization problem. Results: We proposed an effective way to restore images degraded by Poisson noise. Using the Bayesian framework, we proposed an adaptive model based on a combination of first-order total variation and fractional order total variation. The first-order total variation model is efficient for suppressing the noise and preserving the keen edges simultaneously. However, the first-order total variation method usually causes artifact problems in the obtained results. To avoid this drawback, we can use high-order total variation models, one of which is the fractional-order total variation-based model for image restoration. In the fractional-order total variation model, the derivatives have an order greater than or equal to one. It leads to the convenience of computation with a compact discrete form. However, methods based on the fractional-order total variation may cause image blurring. Thus, the proposed model incorporates the advantages of two total variation regularization models, having a significant effect on the edge-preserving image restoration. In order to solve the considered optimization problem, the Split Bregman method is used. Experimental results are provided, demonstrating the effectiveness of the proposed method.  Practical relevance: The proposed method allows you to restore Poissonian images preserving their edges. The presented numerical simulation demonstrates the competitive performance of the model proposed for image reconstruction. Discussion: From the experimental results, we can see that the proposed algorithm is effective in suppressing noise and preserving the image edges. However, the weighted parameters in the proposed model were not automatically selected at each iteration of the proposed algorithm. This requires additional research.

scholarly journals Anisotropic Diffusion Based Multiplicative Speckle Noise Removal

Sensors ◽  
2019 ◽  
Vol 19 (14) ◽  
pp. 3164 ◽  
Author(s):  
Mei Gao ◽  
Baosheng Kang ◽  
Xiangchu Feng ◽  
Wei Zhang ◽  
Wenjuan Zhang
Keyword(s):  
Standard Deviation ◽  
Anisotropic Diffusion ◽  
Additive Noise ◽  
Ground Truth ◽  
Speckle Noise ◽  
Noise Removal ◽  
Noisy Image ◽  
Stopping Criteria ◽  
Proposed Model ◽  
Optimal Values

Multiplicative speckle noise removal is a challenging task in image processing. Motivated by the performance of anisotropic diffusion in additive noise removal and the structure of the standard deviation of a compressed speckle noisy image, we address this problem with anisotropic diffusion theories. Firstly, an anisotropic diffusion model based on image statistics, including information on the gradient of the image, gray levels, and noise standard deviation of the image, is proposed. Although the proposed model can effectively remove multiplicative speckle noise, it does not consider the noise at the edge during the denoising process. Hence, we decompose the divergence term in order to make the diffusion at the edge occur along the boundaries rather than perpendicular to the boundaries, and improve the model to meet our requirements. Secondly, the iteration stopping criteria based on kurtosis and correlation in view of the lack of ground truth in real image experiments, is proposed. The optimal values of the parameters in the model are obtained by learning. To improve the denoising effect, post-processing is performed. Finally, the simulation results show that the proposed model can effectively remove the speckle noise and retain minute details of the images for the real ultrasound and RGB color images.

Power Transmission Efficiencies and Friction Coefficients at Teeth of Novikov-Wildhaber and Involute Gears

1985 ◽  
Vol 107 (1) ◽  
pp. 74-81 ◽  
Author(s):  
A. Ishibashi ◽  
H. Yoshino
Keyword(s):  
Power Transmission ◽  
Gear Ratio ◽  
Experimental Results ◽  
New Techniques ◽  
Friction Coefficients ◽  
Cylindrical Gears ◽  
High Speeds ◽  
Involute Gears ◽  
Low Speeds ◽  
The Difference

New equations have been derived to calculate the power transmission efficiencies, at the meshing teeth, of two kinds of representative cylindrical gears, Novikov-Wildhaber and involute gears. The efficiencies could be calculated from the equations and the friction coefficients obtained by simple experiments with test rollers. In order to show clearly the difference in the power transmission efficiencies of the two kinds of gears, the authors designed and made two interesting gear pairs with a small number of pinion teeth (Z1 = 3) and with a high gear ratio (Z2/Z1 = 9) by applying new techniques developed by them. The effects of gear speed, tooth load, type of lubricant, etc. upon the power transmission efficiencies were clarified using two interesting techniques to measure the efficiency. The experimental results indicated that the efficiency of the Novikov-Wildhaber gears was appreciably higher at high speeds, while it was lower than the involute gears at the start of rotation and also at low speeds.

Anisotropic Diffusion Model Based on a New Diffusion Coefficient and Fractional Order Differential for Image Denoising

2016 ◽  
Vol 16 (01) ◽  
pp. 1650003 ◽  
Author(s):  
Jianjun Yuan ◽  
Lipei Liu
Keyword(s):  
Diffusion Coefficient ◽  
Image Denoising ◽  
Diffusion Model ◽  
Fractional Order ◽  
Anisotropic Diffusion ◽  
Model Based ◽  
Proposed Model

This paper presents an improved anisotropic diffusion model which is based on a new diffusion coefficient and fractional order differential for image denoising. In the proposed model, the new diffusion coefficient can protect edges and fine characteristics from being over-smoothed. The fractional order differential is applied to weaken the staircasing effect, preserve fine characteristics. Additionally, the automatic set method of diffusion coefficient threshold is developed. Comparative experiments show that the proposed model succeeds in denoising and preserving fine characteristics.

Fractional-order difference curvature-driven fractional anisotropic diffusion equation for image super-resolution

2019 ◽  
Vol 10 (01) ◽  
pp. 1941012 ◽  
Author(s):  
Xuehui Yin ◽  
Shunli Chen ◽  
Liping Wang ◽  
Shangbo Zhou
Keyword(s):  
Diffusion Equation ◽  
Fractional Order ◽  
Anisotropic Diffusion ◽  
Super Resolution ◽  
Gauss Curvature ◽  
Order Difference ◽  
Image Super Resolution ◽  
Edge Indicator ◽  
Anisotropic Diffusion Equation ◽  
Difference Curvature

Image super-resolution methods-based existing edge indicating operators — namely Gauss curvature, mean curvature and gradient — cannot effectively identify the edges, ramps and flat regions and suffer from the loss of fine textures. To address these issues, this paper presents a fractional anisotropic diffusion equation based on a new edge indicator, named fractional-order difference curvature, which can characterize the intensity variations in images. We introduce the frequency-domain definition for fractional-order derivative by the Fourier transform, which is easy to implement numerically. The new edge indicator is better than the existing edge indicating operators in distinguishing between ramps and edges and can better handle the fine textures. Comparative results for natural images validate that the proposed method can yield a visually pleasing result and better values of MSSIM and PSNR.

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