A generalization of the Perona-Malik anisotropic diffusion method using restricted dissimilarity functions

López-Molina, Carlos; Baets, Bernard De; Cerrón, Juan; Galar, Mikel; Bustince, Humberto

doi:10.1080/18756891.2013.752658

Cited by 6 publications

(5 citation statements)

References 28 publications

(28 reference statements)

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“…Diffusion, in the context of image processing, involves a physical process that allows intermingling of high‐value and low‐value pixels, without modifying the effective pixel count in the image, until the system equilibrates [28–32]. This is, indeed, a denoising process that suppresses noise and other unwanted artefacts in the image – noisy pixels contain higher values, and diffusion helps to reduce (smooth) them out.…”

Section: Methodsmentioning

confidence: 99%

Diffusion‐steered super‐resolution method based on the Papoulis–Gerchberg algorithm

Maiseli

2016

IET Image Processing

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Section: Methodsmentioning

confidence: 99%

Diffusion‐steered super‐resolution method based on the Papoulis–Gerchberg algorithm

Maiseli

2016

IET Image Processing

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“…In this work, we present a generalization of the Perona and Malik anisotropic diffusion method [38] for color images. A previous generalization was presented in [42] for grayscale images using Restricted Dissimilarity Functions (RDF) [43], following a similar strategy to the one in this work.…”

Section: B Extending the Pmad Model To Color Imagesmentioning

confidence: 99%

“…Specifically, in the quantitative comparison of each pixel with its four-point neighbours. In [42], the scalar differences in Eq. ( 23) were replaced by RDFs.…”

Section: B Extending the Pmad Model To Color Imagesmentioning

confidence: 99%

From Restricted Equivalence Functions on $L^{n}$ to Similarity Measures Between Fuzzy Multisets

Ferrero-Jaurrieta

Takáč

Rodríguez-Martínez

et al. 2023

IEEE Trans. Fuzzy Syst.

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Restricted equivalence functions are well-known functions to compare two numbers in the interval between 0 and 1. Despite the numerous works studying the properties of restricted equivalence functions and their multiple applications as support for different similarity measures, an extension of these functions to an n-dimensional space is absent from the literature. In this paper, we present a novel contribution to the restricted equivalence function theory, allowing to compare multivalued elements. Specifically, we extend the notion of restricted equivalence functions from L to L n and present a new similarity construction on L n . Our proposal is tested in the context of color image anisotropic diffusion as an example of one of its many applications.

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“…Wavelet analysis is a new numerical concept which allows one to represent a function in terms of a set of basis function, called wavelets, which are localized both in location and in scale. Up to now, the finite difference method is the primary numerical algorithm for Perona-Malik model, which can bring artifact into the images due to the nonsmoothness of the basis function of the finite difference method [ 15 , 16 ] as has been said before. The multilevel wavelet numerical method for the nonlinear PDEs has been proposed over ten years, which can take full advantage of the adaptability of the wavelet analysis [ 17 ].…”

Section: Introductionmentioning

confidence: 99%

HPM-Based Dynamic Sparse Grid Approach for Perona-Malik Equation

Mei

Zhu

2014

The Scientific World Journal

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The Perona-Malik equation is a famous image edge-preserved denoising model, which is represented as a nonlinear 2-dimension partial differential equation. Based on the homotopy perturbation method (HPM) and the multiscale interpolation theory, a dynamic sparse grid method for Perona-Malik was constructed in this paper. Compared with the traditional multiscale numerical techniques, the proposed method is independent of the basis function. In this method, a dynamic choice scheme of external grid points is proposed to eliminate the artifacts introduced by the partitioning technique. In order to decrease the calculation amount introduced by the change of the external grid points, the Newton interpolation technique is employed instead of the traditional Lagrange interpolation operator, and the condition number of the discretized matrix different equations is taken into account of the choice of the external grid points. Using the new numerical scheme, the time complexity of the sparse grid method for the image denoising is decreased to O(4J+2j) from O(43J), (j ≪ J). The experiment results show that the dynamic choice scheme of the external gird points can eliminate the boundary effect effectively and the efficiency can also be improved greatly comparing with the classical interval wavelets numerical methods.

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A generalization of the Perona-Malik anisotropic diffusion method using restricted dissimilarity functions

Cited by 6 publications

References 28 publications

Diffusion‐steered super‐resolution method based on the Papoulis–Gerchberg algorithm

Diffusion‐steered super‐resolution method based on the Papoulis–Gerchberg algorithm

From Restricted Equivalence Functions on $L^{n}$ to Similarity Measures Between Fuzzy Multisets

HPM-Based Dynamic Sparse Grid Approach for Perona-Malik Equation

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