<p>Problemi klasifikacije i segmentacije digitalnih slika su veoma<br />aktuelni i zastupljeni u praksi. Potreba za modelima koji razmatraju<br />ovu problematiku u poslednjih nekoliko decenija ubrzanim tempom<br />poprima sve veći značaj i obim u svakodnevnom životu. Koriste se u<br />računarskoj grafici, prepoznavanju oblika, medicinskoj analizi slika,<br />saobraćaju, analizi dokumenata, pokreta i izraza lica i sl.<br />U okviru ove disertacije, predstavljeno istraživanje motivisano je<br />primenama razvijenih modela u klasifikaciji i segmentaciji<br />digitalnih slika. Istraživanje obuhvata dva segmenta. Ovi segmenti<br />povezani su terminom neodređenosti, koji je uz upotrebu adekvatnog<br />matematičkog aparata (teorije fazi skupova), ugrađen u modele razvije<br />za primenu u obradi slike.<br />Jedan pravac istraživanja baziran je na teoriji fazi skupova, t-<br />normama, t-konormama, operatorima agregacije i agregiranim<br />funkcijama rastojanja. U okviru toga, istraživanje je sprovedeno sa<br />struktuiranom matematičkom podlogom, izložene su osnovne<br />definicije, teoreme, kao i osobine korištenih operatora, prošireni<br />su teorijski koncepti t-normi i t-konormi. Definisani su novi tipovi<br />operatora agregacije i njihovom primenom konstruisane su nove<br />funkcije rastojanja, čija je upotreba diskutovana kroz uspešnost u<br />procesu segmentacije digitalnih slika.<br />Drugi pravac istraživanja, izložen u ovoj disertaciji, obuhvata više<br />inženjerski pristup rešavanju problema klasifikacije tekstura<br />digitalnih slika. U skladu sa tim, detaljno je analizirana i<br />diskutovana klasa lokalnih binarnih deskriptora teksture.<br />Inspirisana uspešnošću pomenute LBP klase deskriptora, uvedena je<br />jedna nova podfamilija &alpha;-deskriptora teksture. Uvedeni model<br />deskriptora formiran je na temeljima idejnih principa lokalnih<br />binarnih kodova i bazičnih pojmova iz teorije fazi skupova. Praktična<br />upotreba i značaj predstavljenog modela demonstrirani su kroz veoma<br />uspešne procese klasifikacije na nekoliko javno dostupnih baza slika.</p> / <p>Classification and segmentation problems of digital images is a very attractive<br />topic and has been making impact in many different applied disciplines. In the<br />past few decades, the demand for models that address these issues has been<br />gaining momentum and applications in everyday life. These models are used in<br />computer graphics, shape recognition, medical image analysis, traffic, document<br />analysis, facial movements and expressions, etc.<br />The research within this doctoral dissertation was motivated by the application of<br />developed methods in classification and segmentation tasks. The conducted<br />research covered two segments, which were linked by the term of indeterminacy,<br />with the usage of the theory of fuzzy sets, which is incorporated into methods<br />developed for application in image processing.<br />One direction of the research was founded on the theory of fuzzy sets, t-norms,<br />t-conorms, aggregation operators, and aggregated distance functions. Within this<br />framework, the research was conducted with a structured mathematical<br />background. Firstly, basic definitions, theorems and characteristics of the used<br />operators were presented, followed by the theoretical concepts of t-norms and tconorms<br />that were extended. New types of aggregation operators and distance<br />functions were defined, and finally, their contribution in the digital image<br />segmentation process was explored and discussed.<br />The second direction of the research presented in this dissertation involved more<br />of an engineering-type of approach to solving the problem of the classification of<br />digital image textures. To that end, a class of local binary texture descriptors<br />(LBPs) was analyzed and discussed in detail. Inspired by the results of the<br />above-mentioned LBP descriptors, one new sub-family of the $\alpha$-<br />descriptors was introduced by the author. The introduced descriptor model was<br />based on the conceptual principles of LBPs and basic definitions from the fuzzy<br />set theory. Its practical usage and importance were established and reflected in<br />very successful classification results, achieved in the application on several<br />publicly available image datasets.</p>