Image Edge Detection Using Fractional Calculus with Feature and Contrast Enhancement

Nandal, Amita; Gamboa-Rosales, Hamurabi; Celaya-Padilla, José M.; Galván-Tejada, Jorge I.; Galván-Tejada, Carlos E.; Ruiz, Francisco Javier Martínez; Guzmán-Valdivia, Cesar H.

doi:10.1007/s00034-018-0751-6

Cited by 49 publications

(22 citation statements)

References 27 publications

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“…Many dramatic changes in this area have been made by taking the fractional differential concepts into account. In recent years, the use of fractional differential operators to improve image quality, image texture enhancement, image noise reduction, and image edge analysis have yielded stunning results [4][5][6][7][8][9][10][11][12]. One of the most important formulas for expanding of fractional differential operators in image processing is to use the following general form:…”

Section: A Short Review Of Some Of the Well-known Methodsmentioning

confidence: 99%

Some new edge detecting techniques based on fractional derivatives with non-local and non-singular kernels

2020

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Computers and electronics play an enormous role in today's society, impacting everything from communication and medicine to science. The development of computer-related technologies has led to the emergence of many new important interdisciplinary fields, including the field of image processing. Image processing tries to find new ways to access and extract information from digital images or videos. Due to this great importance, many researchers have tried to utilize new and powerful tools introduced in pure and applied mathematics to develop new concepts in imaging science. One of these valuable research areas is the contents of fractional differential calculus. In recent years, extensive applications to the new fractional operators have been employed in real-world problems. This article attempts to address a practical aspect of this era of research in the edge detecting of an image. For this purpose, two general structures are first proposed for making new fractional masks. Then the components in these two structures are evaluated using the fractional integral Atangana-Baleanu operator. The performance and effectiveness of these proposed designs are illustrated by several numerical simulations. A comparison of the results with the results of several well-known masks in the literature indicates that the results presented in this article are much more accurate and efficient. This is the main achievement of this article. These fractional masks are all novel and have been introduced for the first time in this contribution. Moreover, in terms of computational cost, the proposed fractional masks require almost the same amount of computations as the existing conventional ones. By observing the numerical simulations presented in the paper, it is easily understood that with proper adjustment for the fractional-order parameter, the accuracy of the obtained results can be significantly improved. Each of the new suggested structures in this article can be regarded as a valid and effective alternative for the well-known existing kernels in identifying the edges of an image.

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Section: A Short Review Of Some Of the Well-known Methodsmentioning

confidence: 99%

Some new edge detecting techniques based on fractional derivatives with non-local and non-singular kernels

2020

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“…Another application is to use the gradient image to enhance the input image through, for example an un-sharp masking scheme [26], [32]- [37]. The third application in this category is contrast enhancement [29], [38]- [40]. The second category is referred to as PDE-based models.…”

Section: Related Work 1) Fractional Derivative Operators In Imagementioning

confidence: 99%

Discrete Laplacian Operator and Its Applications in Signal Processing

2020

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Fractional calculus has increased in popularity in recent years, as the number of its applications in different fields has increased. Compared to the traditional operations in calculus (integration and differentiation) which are uniquely defined, the fractional-order operators have numerous definitions. Furthermore, a consensus on the most suitable definition for a given task is yet to be reached. Fractional operators are defined as continuous operators and their implementation requires a discretization step. In this article, we propose a discrete fractional Laplacian as a matrix operator. The proposed operator is real (non-complex) which makes it computationally efficient. The construction of the proposed fractional Laplacian utilizes the DCT transform avoiding the complexity associated with the discretization step which is typical in the constructions based on signal processing. We demonstrate the utility of the proposed operator on a number of data modeling and image processing tasks. INDEX TERMS Fractional-Laplacian, discrete operator, image-processing, trend-filtering, fractional calculus.

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“…Over the last ten years, new approaches to edge detection have been presented, for example dictionary learning [44], [45] or fuzzy logic [46], [47]. The most promising methods are based on fractional derivatives [3,39,43], [48][49][50]. Generalized form of the Grunwald-Letnikov fractional derivative d α f(x) of order α is [51] 0 0…”

Section: New Trends In Edge Detectionmentioning

confidence: 99%

About Edge Detection in Digital Images

Hagara¹,

Kubinec²

2018

RADIOENGINEERING

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Edge detection is one of the most commonly used procedures in digital image processing. In the last 30-40 years, many methods and algorithms for edge detection have been proposed. This article presents an overview of edge detection methods, the methods are divided according to the applied basic principles. Next, the measures and image database used for edge detectors performance quantification are described. Ordinary users as well as authors proposing new edge detectors often use Matlab function without understanding it in details. Therefore, one section is devoted to some of Matlab function parameters that affect the final result. Finally, the latest trends in edge detection are listed. Picture Lena and two images from Berkeley segmentation data set (BSDS500) are used for edge detection methods comparison.

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Image Edge Detection Using Fractional Calculus with Feature and Contrast Enhancement

Cited by 49 publications

References 27 publications

Some new edge detecting techniques based on fractional derivatives with non-local and non-singular kernels

Some new edge detecting techniques based on fractional derivatives with non-local and non-singular kernels

Discrete Laplacian Operator and Its Applications in Signal Processing

About Edge Detection in Digital Images

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