New fractional derivatives in the sense of Riemann-Liouville and Caputo approaches

Nchama, Gustavo Asumu Mboro

doi:10.20852/ntmsci.2020.409

Cited by 2 publications

(3 citation statements)

References 17 publications

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“…In [11], G. Asumu suggested new fractional derivatives to theoretically improve the Riemann-Liouville and Caputo fractional derivatives. One of the derivatives is based upon the Riemann-Liouville viewpoint and the other one is on the Caputo approach.…”

Section: Asumu Fractional Differential Maskmentioning

confidence: 99%

Suppression of the Block Effect while Enhancing Dark Images Using Asumu Derivative

Nchama

2023

Mathematical Problems in Engineering

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Image contrast enhancement is one of the most important tasks in the field of image digital processing. With the help of computers and programming languages, many mathematical methods have been implemented to improve the visual quality of an image. However, the majority of these methods have a major drawback: they tend to make the image look blocked. This effect is visually unpleasant and is likely to cause a computer vision system to falsely recognize as edges the boundaries of different blocks that belong to the same smooth area in the original image. To avoid the block effect while enhancing the quality of dark images, we propose a new fractional differential mask based on the Asumu fractional derivative. Experiments with dark natural images show that, even though our method does not have a better performance in statistical quality, it achieves a solution to the problem that was the motivation to write this paper, suppressing efficiently the block effect while improving the visual qualities of dark images.

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Section: Asumu Fractional Differential Maskmentioning

confidence: 99%

Suppression of the Block Effect while Enhancing Dark Images Using Asumu Derivative

Nchama

2023

Mathematical Problems in Engineering

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“…In [23], Nchama suggested new fractional derivatives to improve theoretically the Riemann-Liouville and Caputo fractional derivatives. One of the derivatives is based upon the Riemann-Liouville view point and the other one on the Caputo approach.…”

Section: The Asumu Fractional Derivative Definitionmentioning

confidence: 99%

“…In [23], we can find also the Laplace transform formula of equation ( 4) given by the following theorem:…”

Section: The Asumu Fractional Derivative Definitionmentioning

confidence: 99%

Asumu Fractional Derivative Applied to Edge Detection on SARS-COV2 Images

Nchama

Alfonso

Morales

et al. 2022

Journal of Applied Mathematics

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Edge detection consists of a set of mathematical methods which identifies the points in a digital image where image brightness changes sharply. In the traditional edge detection methods such as the first-order derivative filters, it is easy to lose image information details and the second-order derivative filters are more sensitive to noise. To overcome these problems, the methods based on the fractional differential-order filters have been proposed in the literature. This paper presents the construction and implementation of the Prewitt fractional differential filter in the Asumu definition sense for SARS-COV2 image edge detection. The experiments show that these filters can avoid noise and detect rich edge details. The experimental comparison show that the proposed method outperforms some edge detection methods. In the next paper, we are planning to improve and combine the proposed filters with artificial intelligence algorithm in order to program a training system for SARS-COV2 image classification with the aim of having a supplemental medical diagnostic.

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New fractional derivatives in the sense of Riemann-Liouville and Caputo approaches

Cited by 2 publications

References 17 publications

Suppression of the Block Effect while Enhancing Dark Images Using Asumu Derivative

Suppression of the Block Effect while Enhancing Dark Images Using Asumu Derivative

Asumu Fractional Derivative Applied to Edge Detection on SARS-COV2 Images

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