Perceptual similarity between color images using fuzzy metrics

“NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Visual Communication and Image Representation. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Visual Communication and Image Representation, [Volume 34, January 2016, Pages 230–235] https://doi.org/10.1016/j.jvcir.2015.04.003In many applications of the computer vision field measuring the similarity between (color) images is of paramount importance. However, the commonly used pixelwise similarity measures such as Mean Absolute Error, Peak Signal to Noise Ratio, Mean Squared Error or Normalized Color Difference do not match well with perceptual similarity. Recently, it has been proposed a method for gray-scale image similarity that correlates quite well with the perceptual similarity and it has been extended to color images. In this paper we use the basic ideas in this recent work to propose an alternative method based on fuzzy metrics for perceptual color image similarity. Experimental results employing a survey of observations show that the global performance of our proposal is competitive with best state of the art methods and that it shows some advantages in performance for images with low correlation among some image channels. (C) 2015 Elsevier Inc. All rights reserved.Grecova, S.; Morillas Gómez, S. (2016). Perceptual similarity between color images using fuzzy metrics. Journal of Visual Communication and Image Representation. 34:230-235. doi:10.1016/j.jvcir.2015.04.003S2302353

Fuzzy metrics: research in axiomatics and applications in color image processing problems

Maģistra darbs sastāv no divām savā starpā saistītām, bet zināmā mērā ļoti atšķirīgām daļām. Pirmajā daļā, kurai pamatos ir teorētisks raksturs, apskatīti klasisku un nestriktu metrisku telpu teoriju jautājumi, kā arī izstrādāta jauna alternatīva nestriktas metrikas definīcija. Otrajai daļai ir vairāk praktisks raksturs un tā ir lielā mērā informātikas jomā. Tajā ir piedāvāts krāsainu attēlu līdzības mērs, kas izstrādāts ņemot vērā cilvēka vizuālo uztveri. Šis mērs ir konstruēts uz nestriktu metriku pamata. Atslēgas vārdi: metriska telpa, nestrikta metriska telpa, attēlu apstrāde, uztveres krāsainu attēlu līdzībaThe master thesis consists of two interrelated, but in a certain sense essentially different parts. In the first, mainly theoretical, part some problems of classical and fuzzy metric space theories are discussed, as well as a new alternative definition of a fuzzy metric is introduced. The second part is more practical and to a large extend lies in the informatics field. A new color image similarity measure is proposed which is developed taking into account human visual perception. This measure is based on fuzzy metrics. Keywords: metric space, fuzzy metric space, image processing, perceptual color image similarit

Arithmetics of type 2 fuzzy numbers

Šajā darbā tiek apskatīti nestriktu kopu teorijas pamati un daži ar to saistītie speciālie jautājumi. Uzsvērts nestriktu kopu teorijas nozīmīgums, parādot, cik plaši tā tiek pielietota dažādās zinātnes nozarēs. Aprakstīti nestriktu kopu teorijas galvenie attīstības posmi. Dota pirmā un otrā tipa nestriktas kopas definīcija, ilustrēta nestriktu kopu struktūra, definētas operācijas ar nestriktām kopām, kā arī pievienoti nestriktu kopu piemēri. Apskatīti speciāla veida pirmā tipa nestriktas kopas - pirmā tipa nestriktie skaitļi -, un ieviests otrā tipa nestrikta skaitļa jēdziens. Apskatītas aritmētiskās operācijas ar pirmā tipa nestriktiem skaitļiem. Izmantojot Zadē turpinājuma principu, likti pamati otrā tipa nestrikto skaitļu aritmētikai.Atslēgas vārdi: nestrikta kopa, pirmā un otrā tipa nestrikts skaitlis, turpinājuma princips, nestrikta aritmētikaIn the present work the foundations of fuzzy set theory and some related special questions are discussed. The significance of fuzzy set theory is emphasized by its application in various scientific fields. The stages of fuzzy set theory development are also described in this work. The definitions of type-1 and type-2 fuzzy sets are given with the subsequent study of their structure and corresponding operations. The properties of fuzzy sets are also illustrated by several examples. Particular sort of type-1 fuzzy sets, called type-1 fuzzy numbers, are discussed, and the concept of type-2 fuzzy number is introduced. Arithmetic operations of type-1 fuzzy numbers are depicted, and the basics of type-2 fuzzy arithmetic are established by using Zadeh's extension principle.Keywords: fuzzy set, type-1 and type-2 fuzzy number, extension principle, fuzzy arithmeti