Function-valued Mappings and SSIM-based Optimization in Imaging

In a few words, this thesis is concerned with two alternative approaches to imag- ing, namely, Function-valued Mappings (FVMs) and Structural Similarity Index Measure (SSIM)-based Optimization. Briefly, a FVM is a mathematical object that assigns to each element in its domain a function that belongs to a given function space. The advantage of this representation is that the infinite dimensionality of the range of FVMs allows us to give a more accurate description of complex datasets such as hyperspectral images and diffusion magnetic resonance images, something that can not be done with the classical representation of such data sets as vector-valued functions. For instance, a hyperspectral image can be described as a FVM that assigns to each point in a spatial domain a spectral function that belongs to the function space L2(R); that is, the space of functions whose energy is finite. Moreoever, we present a Fourier transform and a new class of fractal transforms for FVMs to analyze and process hyperspectral images. Regarding SSIM-based optimization, we introduce a general framework for solving op- timization problems that involve the SSIM as a fidelity measure. This framework offers the option of carrying out SSIM-based imaging tasks which are usually addressed using the classical Euclidean-based methods. In the literature, SSIM-based approaches have been proposed to address the limitations of Euclidean-based metrics as measures of vi- sual quality. These methods show better performance when compared to their Euclidean counterparts since the SSIM is a better model of the human visual system; however, these approaches tend to be developed for particular applications. With the general framework that it is presented in this thesis, rather than focusing on particular imaging tasks, we introduce a set of novel algorithms capable of carrying out a wide range of SSIM-based imaging applications. Moreover, such a framework allows us to include the SSIM as a fidelity term in optimization problems in which it had not been included before

Gradient-based image and video quality assessment

У овој дисертацији разматране су објективне мере процене квалитета слике и видеа са потпуним и делимичним референцирањем на изворни сигнал. За потребе евалуације квалитета развијене су поуздане, рачунски ефикасне мере, засноване на очувању информација о градијенту. Мере су тестиране на великом броју тест слика и видео секвенци, различитих типова и степена деградације. Поред јавно доступних база слика и видео секвенци, за потребе истраживања формиране су и нове базе видео секвенци са преко 300 релевантних тест узорака. Поређењем доступних субјективних и објективних скорова квалитета показано је да је објективна евалуација квалитета веома сложен проблем, али га је могуће решити и доћи до високих перформанси коришћењем предложених мера процене квалитета слике и видеа.U ovoj disertaciji razmatrane su objektivne mere procene kvaliteta slike i videa sa potpunim i delimičnim referenciranjem na izvorni signal. Za potrebe evaluacije kvaliteta razvijene su pouzdane, računski efikasne mere, zasnovane na očuvanju informacija o gradijentu. Mere su testirane na velikom broju test slika i video sekvenci, različitih tipova i stepena degradacije. Pored javno dostupnih baza slika i video sekvenci, za potrebe istraživanja formirane su i nove baze video sekvenci sa preko 300 relevantnih test uzoraka. Poređenjem dostupnih subjektivnih i objektivnih skorova kvaliteta pokazano je da je objektivna evaluacija kvaliteta veoma složen problem, ali ga je moguće rešiti i doći do visokih performansi korišćenjem predloženih mera procene kvaliteta slike i videa.This thesis presents an investigation into objective image and video quality assessment with full and reduced reference on original (source) signal. For quality evaluation purposes, reliable, computational efficient, gradient-based measures are developed. Proposed measures are tested on different image and video datasets, with various types of distorsions and degradation levels. Along with publicly available image and video quality datasets, new video quality datasets are maded, with more than 300 relevant test samples. Through comparison between available subjective and objective quality scores it has been shown that objective quality evaluation is highly complex problem, but it is possible to resolve it and acchieve high performance using proposed quality measures