New adaptive vector filter using fuzzy metrics

Morillas, Samuel; Gregori, Valentı́n; Perís-Fajarnés, Guillermo; Sapena, Almanzor

doi:10.1117/1.2767335

Cited by 54 publications

(37 citation statements)

References 42 publications

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“…For instance, the concepts of principal and strong fuzzy metric were motivated by the study of the p-convergence, [31], and the generalization of non-Archimedean fuzzy metrics, [44], respectively. Moreover, recently, fuzzy metrics have been applied to colour image filtering by replacing classical metrics and some improvements have been achieved [2,3,[34][35][36][37][38][39]. In this context, the presence of the t parameter is indeed a key issue because it allows the fuzzy metric to perform adaptively which is beneficial to improve performance.…”

Section: Introductionmentioning

confidence: 99%

Some questions in fuzzy metric spaces

Gregori

MiòAna

Morillas

2012

Fuzzy Sets and Systems

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ElsevierGregori Gregori, V.; Morillas Gómez, S.; Miñana Prats, JJ. (2012) AbstractThe George and Veeramani's fuzzy metric defined by M * (x, y, t) = min{x,y}+t max{x,y}+t on [0, ∞[ (the set of non-negative real numbers) has shown some advantages in front of classical metrics in the process of filtering images. In this paper we study from the mathematical point of view this fuzzy metric and other fuzzy metrics related to it. As a consequence of this study we introduce, throughout the paper, some questions relative to fuzzy metrics. Also, as another practical application, we show that this fuzzy metric is useful for measuring perceptual colour differences between colour samples.

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Section: Introductionmentioning

confidence: 99%

Some questions in fuzzy metric spaces

Gregori

MiòAna

Morillas

2012

Fuzzy Sets and Systems

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“…To do so, we used the fuzzy metric in Eq. (11) [32], because it was successfully employed in previous works [33,34] and was able to compare those values, taking into account the weighted average and standard deviation of the D j values [Eqs. (12) and (13), respectively]:…”

Section: Step 2: Consistency Of Each Color Pairmentioning

confidence: 99%

Method to determine the degrees of consistency in experimental datasets of perceptual color differences

Morillas¹,

Gómez‐Robledo²,

Huertas³

et al. 2016

J. Opt. Soc. Am. A

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We propose a fuzzy method to analyze datasets of perceptual color differences with two main objectives: to detect inconsistencies between couples of color pairs and to assign a degree of consistency to each color pair in a dataset. This method can be thought as the outcome of a previous one developed for a similar purpose [J. Mod. Opt. 56, 1447], whose performance is compared with the proposed one. In this work, we present the results achieved using the dataset employed to develop the current CIE/ISO color-difference formula, CIEDE2000, but the method could be applied to any dataset. Specifically, in the mentioned dataset, we find that some couples of color pairs have contradictory information, which can interfere in the successful development of future colordifference formulas as well as in checking the performance of current ones.

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“…An interesting aspect in this type of fuzzy metric is that it includes in its definition a parameter t. This feature has been successfully used in engineering applications such color image filtering [7,14,15] and perceptual color differences [5,13]. From the mathematical point of view it allows to introduce novel (fuzzy metric) concepts that only have natural sense in the fuzzy metric setting.…”

Section: Introductionmentioning

confidence: 99%