Modeli neodređenosti u obradi digitalnih slika

Abstract

Problemi klasifikacije i segmentacije digitalnih slika su veoma aktuelni i zastupljeni u praksi. Potreba za modelima koji razmatraju ovu problematiku u poslednjih nekoliko decenija ubrzanim tempom poprima sve veći značaj i obim u svakodnevnom životu. Koriste se u računarskoj grafici, prepoznavanju oblika, medicinskoj analizi slika, saobraćaju, analizi dokumenata, pokreta i izraza lica i sl. U okviru ove disertacije, predstavljeno istraživanje motivisano je primenama razvijenih modela u klasifikaciji i segmentaciji digitalnih slika. Istraživanje obuhvata dva segmenta. Ovi segmenti povezani su terminom neodređenosti, koji je uz upotrebu adekvatnog matematičkog aparata (teorije fazi skupova), ugrađen u modele razvije za primenu u obradi slike. Jedan pravac istraživanja baziran je na teoriji fazi skupova, t- normama, t-konormama, operatorima agregacije i agregiranim funkcijama rastojanja. U okviru toga, istraživanje je sprovedeno sa struktuiranom matematičkom podlogom, izložene su osnovne definicije, teoreme, kao i osobine korištenih operatora, prošireni su teorijski koncepti t-normi i t-konormi. Definisani su novi tipovi operatora agregacije i njihovom primenom konstruisane su nove funkcije rastojanja, čija je upotreba diskutovana kroz uspešnost u procesu segmentacije digitalnih slika. Drugi pravac istraživanja, izložen u ovoj disertaciji, obuhvata više inženjerski pristup rešavanju problema klasifikacije tekstura digitalnih slika. U skladu sa tim, detaljno je analizirana i diskutovana klasa lokalnih binarnih deskriptora teksture. Inspirisana uspešnošću pomenute LBP klase deskriptora, uvedena je jedna nova podfamilija α-deskriptora teksture. Uvedeni model deskriptora formiran je na temeljima idejnih principa lokalnih binarnih kodova i bazičnih pojmova iz teorije fazi skupova. Praktična upotreba i značaj predstavljenog modela demonstrirani su kroz veoma uspešne procese klasifikacije na nekoliko javno dostupnih baza slika.

Classification and segmentation problems of digital images is a very attractive topic and has been making impact in many different applied disciplines. In the past few decades, the demand for models that address these issues has been gaining momentum and applications in everyday life. These models are used in computer graphics, shape recognition, medical image analysis, traffic, document analysis, facial movements and expressions, etc. The research within this doctoral dissertation was motivated by the application of developed methods in classification and segmentation tasks. The conducted research covered two segments, which were linked by the term of indeterminacy, with the usage of the theory of fuzzy sets, which is incorporated into methods developed for application in image processing. One direction of the research was founded on the theory of fuzzy sets, t-norms, t-conorms, aggregation operators, and aggregated distance functions. Within this framework, the research was conducted with a structured mathematical background. Firstly, basic definitions, theorems and characteristics of the used operators were presented, followed by the theoretical concepts of t-norms and tconorms that were extended. New types of aggregation operators and distance functions were defined, and finally, their contribution in the digital image segmentation process was explored and discussed. The second direction of the research presented in this dissertation involved more of an engineering-type of approach to solving the problem of the classification of digital image textures. To that end, a class of local binary texture descriptors (LBPs) was analyzed and discussed in detail. Inspired by the results of the above-mentioned LBP descriptors, one new sub-family of the $\alpha$- descriptors was introduced by the author. The introduced descriptor model was based on the conceptual principles of LBPs and basic definitions from the fuzzy set theory. Its practical usage and importance were established and reflected in very successful classification results, achieved in the application on several publicly available image datasets.