Applicability of fractional transforms in image processing - review, technical challenges and future trends

Jindal, Neeru; Singh, Kulbir

doi:10.1007/s11042-018-6594-0

Cited by 11 publications

(5 citation statements)

References 65 publications

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“…Image processing refers to a variety of techniques that maximize the usefulness of the information contained in an image for a particular target context [11]. In [12], image processing techniques were applied to assess the performance of a convolution-based neural network when classifying images in the context of augmented reality applications.…”

Section: Methodsmentioning

confidence: 99%

Fusión de imágenes satelitales usando la transformada de Brovey y enriquecimiento espectral sobre computación heterogénea CPU/GPU

Rodríguez

Parra

Daza

2021

Investigación e Innovación en Ingenierías

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Satellite image fusion provides a context for potential applications in several fields such as agricultural development, hydrology, environmental studies, and natural disaster actions plans. However, when dealing with large-size images, the time required for the fusion process grows significantly. To reduce processing delays, the present study proposes the use of the Brovey transform as an image-fusion technique together with a spectral richness calibration stage. The proposal makes use of a CPU/GPU heterogeneous computing architecture based on mass parallel processing, conducted with CUDA. The fusion process of a 8192-pixel image evinced a speed-up of 532X. Regarding the quality of the resulting image, a per-band average correlation coefficient of 0.9714 (spatial detail) was obtained when comparing the fused and panchromatic images in an (R,G,B) color space.

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Section: Methodsmentioning

confidence: 99%

Fusión de imágenes satelitales usando la transformada de Brovey y enriquecimiento espectral sobre computación heterogénea CPU/GPU

Rodríguez

Parra

Daza

2021

Investigación e Innovación en Ingenierías

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“…It is well known that the Fourier transform is commonly used in image processing. Namias applied the idea of FC to the Fourier transform and introduced the fractional transform [14]. Since then, the fractional transform has been a hot research topic in many fields because of the benefit that it is easy to control the transformation function by varying the parameter of fractional order [14,15].…”

Section: Introductionmentioning

confidence: 99%

“…Namias applied the idea of FC to the Fourier transform and introduced the fractional transform [14]. Since then, the fractional transform has been a hot research topic in many fields because of the benefit that it is easy to control the transformation function by varying the parameter of fractional order [14,15]. Fractional transform is widely used in image registration [16,17], image encryption [18][19][20], image compression, and other image processing applications.…”

Section: Introductionmentioning

confidence: 99%

Frac-Vector: Better Category Representation

Tan

2023

Fractal Fract

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For this paper, we proposed the fractional category representation vector (FV) based on fractional calculus (FC), of which one-hot label is only the special case when the derivative order is 0. FV can be considered as a distributional representation when negative probability is considered. FVs can be used either as a regularization method or as a distributed category representation. They gain significantly in the generalization of classification models and representability in generative adversarial networks with conditions (C-GANs). In image classification, the linear combinations of FVs correspond to the mixture of images and can be used as an independent variable of the loss function. Our experiments showed that FVs can also be used as space sampling, with fewer dimensions and less computational overhead than normal distributions.

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“…In applications, the Caputo derivative and the Riemann-Liouville derivative are the most often used [1,2]. Fractional calculus is used, inter alia, in mathematical modeling of various problems in mechanics, physics, and biology [3][4][5][6], in control theory [7], in image processing [8], as well as in modeling the phenomena of heat transport [9][10][11][12][13][14][15]. Many mathematical models are based on differential equations containing fractional derivatives.…”

Section: Introductionmentioning

confidence: 99%

Inverse Problem for a Two-Dimensional Anomalous Diffusion Equation with a Fractional Derivative of the Riemann–Liouville Type

2021

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The article presents a method for solving the inverse problem of a two-dimensional anomalous diffusion equation with a Riemann–Liouville fractional-order derivative. In the first part of the present study, the authors present a numerical solution of the direct problem. For this purpose, a differential scheme was developed based on the alternating direction implicit method. The presented method was accompanied by examples illustrating its accuracy. The second part of the study concerned the inverse problem of recreating the model parameters, including the orders of the fractional derivative, in the anomalous diffusion equation. Equations of this type can be used to describe, inter alia, the heat conductivity in porous materials. The ant colony optimization algorithm was used to solve this problem. The authors investigated the impact of the distribution of measurement points, the use of different mesh sizes, and the input data errors on the obtained results.

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Applicability of fractional transforms in image processing - review, technical challenges and future trends

Cited by 11 publications

References 65 publications

Fusión de imágenes satelitales usando la transformada de Brovey y enriquecimiento espectral sobre computación heterogénea CPU/GPU

Fusión de imágenes satelitales usando la transformada de Brovey y enriquecimiento espectral sobre computación heterogénea CPU/GPU

Frac-Vector: Better Category Representation

Inverse Problem for a Two-Dimensional Anomalous Diffusion Equation with a Fractional Derivative of the Riemann–Liouville Type

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