Fractional differentiation for edge detection

Benoit, M.; Melchior, Pierre; Oustaloup, Alain; Ceyral, C.

doi:10.1016/s0165-1684(03)00194-4

Cited by 327 publications

(192 citation statements)

References 6 publications

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“…In the recent years, fractional calculus was and still is getting more and more important to various applications [1], [2], [3], [6]. In real image processing applications it is often necessary to perform a robust edge detection also to noisy input data with low SNR respectively.…”

Section: Introductionmentioning

confidence: 99%

“…In real image processing applications it is often necessary to perform a robust edge detection also to noisy input data with low SNR respectively. Most of the edge detection operators are based on integer order differentiation operators [2], which often do not lead to sufficient detection results. For these purposes, a very powerful eCRONE (extended Contour Robuste d'Ordre Non Entier) edge detector, an extended version of the CRONE detector introduced by [2] based on fractional order differentiation and orthogonal averaging with high immunity to noisy input data, is presented.…”

Section: Introductionmentioning

confidence: 99%

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Edge detection based on fractional order differentiation and its application to railway track images

Telke

Beitelschmidt

2015

Proc Appl Math and Mech

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Edge detection is one of the most fundamental necessities in image processing. Usally, edge detection algorithms are based on integer order differentiation operators. In many applications it is essential to perform a robust edge detection also to noisy input image data with low SNR as well. Thereby, integer based differentiation operators are often not leading to sufficient detection results. For this purpose an edge detector based on fractional order differentiation is introduced, which can significantly improve the detection performance to noisy images. Furthermore, a real application scenario of fractional order based edge detection is given within a modular railway track measurement system.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Edge detection based on fractional order differentiation and its application to railway track images

Telke

Beitelschmidt

2015

Proc Appl Math and Mech

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“…These successes motivated researchers to apply fractional derivatives to digital image processing [3,6,7,8,9,10,11]. Zhang et al [3] developed an algorithm based on the Riemann-Liouville definition and applied the resulting model with a fractional derivative index between one and two to enhance the texture and edges of a digital image.…”

Section: Introductionmentioning

confidence: 99%

“…Pesquet-Popescu and Véhel [7] developed stochastic fractal models for image processing. Mathieu et al [8] applied fractional differentiation for edge detection. Gao et al [9] applied a quaternion fractional differential based on the Grünwald-Letnikov definition to a colour image.…”

Section: Introductionmentioning

confidence: 99%

The use of a Riesz fractional differential-based approach for texture enhancement in image processing

Liu

Turner

et al. 2013

ANZIAMJ

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Texture enhancement is an important component of image processing that finds extensive application in science and engineering. The quality of medical images, quantified using the imaging texture, plays a significant role in the routine diagnosis performed by medical practitioners. Most image texture enhancement is performed using classical integral order differential mask operators. Recently, first order fractional differential operators were used to enhance images. Experimentation with these methods led to the conclusion that fractional differential operators not only maintain the low frequency contour Contents C591features in the smooth areas of the image, but they also nonlinearly enhance edges and textures corresponding to high frequency image components. However, whilst these methods perform well in particular cases, they are not routinely useful across all applications. To this end, we apply the second order Riesz fractional differential operator to improve upon existing approaches of texture enhancement. Compared with the classical integral order differential mask operators and other first order fractional differential operators, we find that our new algorithms provide higher signal to noise values and superior image quality. Subject class: 26A33, 92C55

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“…Fractional derivatives have been shown to be effective tools both for regularization [13] (where fractional diffusions are considered) and for edge detection [26] (where one dimensional signals are considered). The models proposed by Guidotti are based on the equations…”

Section: Introductionmentioning

confidence: 99%

Two Enhanced Fourth Order Diffusion Models for Image Denoising

Guidotti

Longo

2011

J Math Imaging Vis

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This paper presents two new higher order diffusion models for removing noise from images. The models employ fractional derivatives and are modifications of an existing fourth order partial differential equation (PDE) model which was developed by You and Kaveh as a generalization of the well-known second order Perona-Malik equation. The modifications serve to cure the ill-posedness of the You-Kaveh model without sacrificing performance. Also proposed in this paper is a simple smoothing technique which can be used in numerical experiments to improve denoising and reduce processing time. Numerical experiments are shown for comparison.

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Fractional differentiation for edge detection

Cited by 327 publications

References 6 publications

Edge detection based on fractional order differentiation and its application to railway track images

Edge detection based on fractional order differentiation and its application to railway track images

The use of a Riesz fractional differential-based approach for texture enhancement in image processing

Two Enhanced Fourth Order Diffusion Models for Image Denoising

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