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Edge detection is a highly researched topic in the field of image processing, with numerous methods proposed by previous scholars. Among these, ant colony algorithms have emerged as a promising approach for detecting image edges. These algorithms have demonstrated high efficacy in accurately identifying edges within images. For this paper, due to the long-term memory, nonlocality, and weak singularity of fractional calculus, fractional-order ant colony algorithm combined with fractional differential mask and coefficient of variation (FACAFCV) for image edge detection is proposed. If we set the order of the fractional-order ant colony algorithm and fractional differential mask to v = 0 , the edge detection method we propose becomes an integer-order edge detection method. We conduct experiments on images that are corrupted by multiplicative noise, as well as on an edge detection dataset. Our experimental results demonstrate that our method is able to detect image edges, while also mitigating the impact of multiplicative noise. These results indicate that our method has the potential to be a valuable tool for edge detection in practical applications. [ABSTRACT FROM AUTHOR]

The traditional integer-order computation-based denoising approaches often blur the edges and textural details of an image. To solve this problem, from the viewpoint of system evolution, and based on the features of fractional calculus, we propose to implement a texture image denoising approach based on fractional developmental mathematics (FDM) which applies a novel mathematical method, fractional calculus, to image denoising. First, we synopsize the necessary theoretical background of fractional calculus. Second, we derive the necessary mathematical models for implementation of a texture image denoising approach based on FDM. We derive fractional Green's formula, fractional Gauss' formula, and fractional Stokes' formula, and fractional Euler-Lagrange equation. Then, a texture image denoising approach based on FDM is proposed. Third, we implement comparative experiments. We firstly derive the numerical implementation of FDM. Then, we study the capability of preserving the edges and textural details of FDM by comparative experiments. The comparative experimental results show that the capability of preserving the edges and textural details of the FDM-based denoising algorithm is obviously superior to that of traditional integer-order computation-based algorithms, especially for texture detail rich images. [ABSTRACT FROM AUTHOR]

Traditional integer-order partial differential equation based image denoising approach can easily lead edge and complex texture detail blur, thus its denoising effect for texture image is always not well. To solve the problem, we propose to implement a fractional partial differential equation (FPDE) based denoising model for texture image by applying a novel mathematical method-fractional calculus to image processing from the view of system evolution. Previous studies show that fractional calculus has some unique properties that it can nonlinearly enhance complex texture detail in digital image processing, which is obvious different with integer-order differential calculus. The goal of the modeling is to overcome the problems of the existed denoising approaches by utilizing the aforementioned properties of fractional differential calculus. Using classic definition and property of fractional differential calculus, we extend integer-order steepest descent approach to fractional field to implement fractional steepest descent approach. Then, based on the earlier fractional formulas, a FPDE based multiscale denoising model for texture image is proposed and further analyze optimal parameters value for FPDE based denoising model. The experimental results prove that the ability for preserving high-frequency edge and complex texture information of the proposed fractional denoising model are obviously superior to traditional integral based algorithms, as for texture detail rich images. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Images are an important medium to represent meaningful information. It may be difficult for computer vision techniques and humans to extract valuable information from images with low illumination. Currently, the enhancement of low-quality images is a challenging task in the domain of image processing and computer graphics. Although there are many algorithms for image enhancement, the existing techniques often produce defective results with respect to the portions of the image with intense or normal illumination, and such techniques also inevitably degrade certain visual artifacts of the image. The model use for image enhancement must perform the following tasks: preserving details, improving contrast, color correction, and noise suppression. In this paper, we have proposed a framework based on a camera response and weighted least squares strategies. First, the image exposure is adjusted using brightness transformation to obtain the correct model for the camera response, and an illumination estimation approach is used to extract a ratio map. Then, the proposed model adjusts every pixel according to the calculated exposure map and Retinex theory. Additionally, a dehazing algorithm is used to remove haze and improve the contrast of the image. The color constancy parameters set the true color for images of low to average quality. Finally, a details enhancement approach preserves the naturalness and extracts more details to enhance the visual quality of the image. The experimental evidence and a comparison with several, recent state-of-the-art algorithms demonstrated that our designed framework is effective and can efficiently enhance low-light images. [ABSTRACT FROM AUTHOR]