Thesis (MScEng)--Stellenbosch University, 2003. / ENGLISH ABSTRACT: Data volumes produced by the next generation of earth observation sensors have increased greatly in recent years. Sensors are generating more data than can be easily stored onboard satellites and transmitted to the ground-stations. There are two strategies for solving this problem. The first is to process all images onboard the satellite, and only extract the useful or valuable information. The second is to use a compression algorithm to reduce the data volume. This thesis looks at both strategies and then focusses on an evaluation of the Embedded Zerotree Wavelet (EZW) algorithm, a wavelet-based lossy image compression algorithm, as a solution to reduce the data volumes. Possible hardware implementation strategies for this algorithm are also explored. Finally, a suggested implementation of the EZW algorithm is compared with the FlexWave-II system and with JPEG2000. / AFRIKAANSE OPSOMMING: Die data volumes wat deur die nuwe generasie van aardobservasiesensore geproduseer word, het dramaties vergroot in die laaste paar jaar. Daar word nou meer data geproduseer as wat aanboord van die satelliet gestoor kan word en meer as wat in die beperkte kommunikasietyd aan die grondstasie gestuur kan word. Daar is twee strategiee om hierdie probleem aan te spreek. Eerstens kan beelde aanboord die satelliet verwerk word om die belangrikste of waardevolste inligting uit te haal en die res van die data word dan geskrap. Die alternatief is om 'n beeldkompressie-algoritme te gebruik om die data te verminder. Hierdie tesis ondersoek hierdie strategieë en fokus dan op 'n evaluasie van die "Embedded Zerotree Wavelet" -algoritme. Die EZW-algoritme is 'n verlieserige, golfie-gebaseerde beeldkompressie-algoritme. Moontlike hardeware-implementeringsopsies word ondersoek en die resultate van een voorgestelde opsie word vergelyk met die FlexWave-II stelsel asook die nuwe JPEG2000-standaard.

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Biomedical images contain a great deal of information that is useful and a great deal that is not. Computational analysis and interpretation of biomedical images involves extraction of some or all of the useful information. The useless information can take the form of unwanted clutter or noise that can obscure the useful information or inhibit the interpretation. Various mathematical and computational processes may be applied to reduce the effects of noise and distracting content. The most successful approaches involve the use of mathematical or computational models that express the properties of the required information. Interpretation of images involves finding objects or structures in the image that match the properties of the model. This dissertation describes the development and application of different models required for the interpretation of a variety of different image types arising from clinical medicine or biomedical research. These include:* neural network models, * Point Distribution Models, and the associated Active Shape Models, which have become part of the research toolkit of many academic and commercial organisations, * models of the appearance of nerve fibres in noisy confocal microscope images,* models of pose changes in carpal bones during wrist motion, A number of different application problem are described, in which variants of these methods have been developed and used: * cytogenetics, * proteomics, * assessing bone quality, * segmentation of magnetic resonance images, * measuring nerve fibres * inferring 3D motion from 2D cinefluoroscopy sequences. The methods and applications represented here encompass the progression of biomedical image analysis from early developments, where computational power became adequate to the challenges posed by biomedical image data, to recent, highly computationally-intensive methods.

Image recovery and segmentation are always the fundamental tasks in image processing field, because of their so many contributions in practical applications. As in the past ten years, variational methods have achieved a great success on these two issues, in this thesis, we continue to work on proposing several new variational approaches for restoring and segmenting an image. This thesis contains two parts. The first part addresses recovering an image and the second part emphasizes on segmenting. Along with the wide utilization of magnetic resonance imaging (MRI) technique, we particularly deal with blurry images corrupted by Rician noise. In chapter 1, two new convex variational models for recovering an image corrupted by Rician noise with blur are presented. These two models are motivated by the non-convex maximum-a-posteriori (MAP) model proposed in the prior papers. In the first method, we use an approximation item to the zero order of the modified Bessel function in the MAP model and add an entropy-like item to obtain a convex model. Through studying on the statistical properties of Rician noise, we bring up a strictly convex model by adding an additional data-fidelity term in the MAP model in the second method. Primal-dual methods are applied to solve the models. The simulation outcomes show that our models outperform some existed effective models in both recovery image quality and computational time. Cone beam CT (CBCT) is routinely applied in image guided radiation therapy (IGRT) to help patient setup. Its imaging dose, however, is still a concern, limiting its wide applications. It has been an active research topic to develop novel technologies for radiation dose reduction. In chapter 2, we propose an improvement of practical CBCT dose control scheme - temporal non-local means (TNLM) scheme for IGRT. We denoise the scanned image with low dose by using the previous images as prior knowledge. We combine deformation image registration and TNLM. Different from the TNLM, in the new method, for each pixel, the search range is not fixed, but based on the motion vector between the prior image and the obtained image. By doing this, it is easy to find the similar pixels in the previous images, but also can reduce the computational time since it does not need large search windows. The phantom and patient studies illuminate that the new method outperforms the original one in both image quality and computational time. In the second part, we present a two-stage method for segmenting an image corrupted by blur and Rician noise. The method is motivated by the two-stage segmentation method developed by the authors in 2013 and restoration method for images with Rician noise. First, based on the statistical properties of Rician noise, we present a new convex variant of the modified Mumford-Shah model to get the smooth cartoon part {dollar}u{dollar} of the image. Then, we cluster the cartoon {dollar}u{dollar} into different parts to obtain the final contour of different phases of the image. Moreover, {dollar}u{dollar} from the first stage is unique because of the convexity of the new model, and it needs to be computed only once whenever the thresholds and the number of the phases {dollar}K{dollar} in the second stage change. We implement the simulation on the synthetic and real images to show that our model outperforms some existed segmentation models in both precision and computational time

Optimization methods have been widely utilized in the field of imaging science, such as image denoising, image segmentation, image contrast adjustment, high dynamic rang imaging, etc. In recent decades, it is becoming more and more popular to re- formulate an image processing problem into an energy minimization problem, then solve for the minimizer by some optimization based methods. In this thesis, we concern solving three popular issues in image processing and computational photography by optimization based methods, which are image segmentation, bit-depth expansion, and high dynamic range image tone mapping problems. The contribution of this thesis can be illustrated in three parts separately according to different topics. For the image segmentation problem, we present a multi-phase image segmentation model based on the histogram of the Gabor feature space, which consists of responses from a set of Gabor filters with various orientations, scales and frequencies. Our model replaces the error function term in the original fuzzy region competition model with squared 2-Wasserstein distance function, which is a metric to measure the distance of two histogram. The energy functional is minimized by alternating direction method of multiplier, and the existence of the closed-form solutions is guaranteed when the exponent of the fuzzy membership term being 1 or 2. The experimental results show the advantage of our proposed method compared to other recent methods. As for the bit-depth expansion problem, we develop a variational approach containing an energy functional to determine a local mapping function for bit-depth expansion via a smoothing technique, such that each pixel can be adjusted locally to a high bit-depth value. In order to enhance the contrast of the low bit-depth images, we make use of the histogram equalization technique for such local mapping function. Both bit-depth expansion and histogram equalization terms can be combined together into the resulting objective function. In order to minimize the differences among the local mapping functions at the nearby pixel locations, the spatial regularization of the mapping is incorporated in the objective function. Regarding the tone mapping problem for high dynamic range images, we pro- pose a computational tone mapping operator which makes use of a localized gamma correction. Our tone mapping operator combines the two subproblems in the tone mapping problem, i.e. luminance compression and color rendering, into one general framework. The bright regions and dark regions can be distinguished and treated differently. In our method, we propose two adjustment rules according to the perceptual preference of human visual system towards contrast and colors respectively. The resulting tone mapped images have a natural looking and the highest score in our observer subjective test. Based on the motivation of our computational tone mapping operator, we propose a variational method for image tone mapping problem. The core idea is to minimize the difference of the local contrast between the tone mapped image and the high dynamic range image under some constraints. The energy functional contains a local contrast fidelity term and a L-2 total variation regularization term. Local gamma correction is also applied as our previous computational model and the unknown variables are the non-uniform gamma values. The non-uniform gamma values for each pixel can be obtained by minimizing the fidelity term, while the smoothing term ensures the gamma values for nearby pixels not varying too much from each other. The results by both our computational and variational tone mapping operators show advantage in preserving the detailed image contents in the bright and dark regions. Keywords: optimization, alternating direction method of multipliers, variational model, image segmentation, Mumford-Shah model, Gabor filter, contrast adjustment, histogram equalization, bit-depth expansion, dynamic range, HDR imaging, tone mapping operators, gamma correction, color rendering.

Mankind’s scientific, technological, artistic, and intellectual capacities are complemented by an impressive list of physical achievements; nevertheless, it is the remarkable inner abilities that testify to the human being as God’s crowning creation. The single most distinctive aspect of Adam’s creation is that he was created in the image of God and his nature bears that image. But what exactly is the image of God in man? The image of God consists of the spiritual part of a human that reflects the character of God and is the only firm basis for advocating human dignity and the gracious redemption of sinners. Although modern scholarship, particularly Old Testament scholarship, have argued for man’s function through his physical body as the meaning of or forming an integral part of the image of God, the view that God’s image is found in the spiritual aspect of the human being is more faithful to the biblical text. This dissertation argues for the spiritual interpretation of God’s image by providing a historical-grammatical reading of the relevant texts and a proper theological understanding of the image and likeness of God. The first chapter provides the history of interpretation by describing the important personalities and their methods, and explaining the evolution of the topic that has lead to the modern departures from the traditional view. The second chapter discusses the data that supports the thesis by analyzing selected issues in current scholarship that leads to a physical and functional view of the image of God and why I disagree with their conclusions. The third chapter provides a historical-grammatical reading of selected texts that demonstrate the reasonableness of a spiritual interpretation of the image of God, and why it should be defended. The fourth chapter examines the counter claims to the thesis and presents a defense to the findings of this study. The fifth chapter briefly summarizes the most important findings and provides a conclusion.

La mise en correspondance stéréoscopique consiste à retrouver dans les images couleur gauche et droite les primitives homologues. Dans ce but, des mesures de similarité entre les pixels dans une paire d’images sont calculées. Un coût de correspondance est généralement calculé à chaque pixel de l’image gauche pour tous les décalages dans un champ prédéfini, c'est à dire pour un ensemble limité de pixels candidats dans l’image droite. Ensuite, le pixel candidat qui minimise le coût est retenu et sa position donne la disparité. Les coûts de mise en correspondance supposent que les pixels homologues ont presque les mêmes composantes couleur. Les composantes couleur sont dégradées par le dématriçage quand les images couleur ont été acquises par un caméra équipée d'un seul capteur. L'idée est de tenter une mise en correspondance directement à partir des images CFA. De cette façon, il serait possible de travailler sur des intensités de couleurs dont on est sûr. Le fait de travailler sur les images CFA soulève différents problèmes. Tout d'abord, le nombre d'informations est considérablement réduit par rapport à une image couleur idéale: nous en avons trois fois moins. Il faut donc que nous travaillions avec des outils capables de pallier cette carence. Ensuite, rien ne nous permet d'affirmer que des pixels homologues vont être codés dans des couleurs similaires dans les deux images stéréoscopiques CFA. Nous suggérons d'estimer partiellement les éléments manquants et ensuite de mettre en correspondance les pixels. Nous avons prouvé que ce dématriçage partiel donne de meilleurs résultats que le dématriçage total. / Most color stereovision setups include single-sensor cameras which provide Color Filter Array (CFA) images. In those images, a single color component is sampled at each pixel rather than the three required ones (R,G,B). We show that standard demosaicing techniques, used to determine the two missing color components, are not well adapted when the resulting color pixels are compared for estimating the disparity map. In order to avoid this problem while exploiting color information, we propose a partial demosaicing designed for dense stereovision based on pairs of Bayer CFA images. Finally, experimental results obtained with benchmark stereo image pairs show that stereo matching applied to partially demosaiced images outperforms stereo matching applied to standard demosaiced images.

The problem of restoring an image distorted by a system consisting of a stochastic impulse response in conjuction with additive noise is investigated. The method of constrained least squares is extended to this problem, and leads to the development of a new technique based on the minimization of a weighted error function. Results obtained using the new method are compared with those obtained by constrained least squares, and by the Wiener filter and approximations thereof. It is found that the new technique, "Weighted Least Squares", gives superior results if the noise in the impulse response is comparable to or greater than the additive noise. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

Au cours des XIXe et XXe siècles, l’Iran, pays mal connu mais distingué par son histoire, attire l’attention de plusieurs intellectuels occidentaux. Ainsi certains d’entre eux prennent la route et vont à la rencontre de ce pays et ses habitants. Notre étude concerne les récits de voyage de dix écrivains-voyageurs français, suisses et anglais qui ont sillonné les routes de l’Iran entre 1854 (Gobineau) et 1954 (Bouvier) ; parmi eux, la moitié sont des femmes. À travers leurs témoignages écrits et picturaux, chacun de ces écrivains-voyageurs a livré une image de la Perse différente des autres. Mais pourquoi cette divergence d’images ? En effet, sans négliger les spécifiés régionales et culturelles, il est manifeste que la vision du monde de chacun contribue à la naissance de cette image. De plus, en l’espace d’un siècle, secoué d’événements politiques, économiques et sociaux comme les deux Guerres mondiales, l’Europe voit ses rapports modifiés envers ses Autres. Ainsi l’Iran devient tour à tour une terre d’étude, terre d’aventure et terre idéale et spirituelle pour ceux qui ne peuvent plus rester en Europe. En outre, au long de cette période, le genre de la littérature de voyage a notablement évolué. Tous ces facteurs se croisent pour donner de la Perse une image multiple. / During the nineteenth and twentieth centuries, Iran, a country not well known but distinguished by its history, attracted the attention of several Western intellectuals. Thus some of them take the road and go to visit this country and its population. Our study is about the travel stories of ten travel writers from France, Switzerland and Britannia who traveled to Iran between 1854 (Gobineau) and 1954 (Bouvier); Among them, half are women. Through their written and pictorial testimonies, each of these travel writers have delivered an image of Persia different from the others. But why this divergence of images? Indeed, without neglecting the regional and cultural specify, it is clear that the world vision of every one contributed to the appearance of this image. Furthermore, during a century, shaken by political, economical and social events like the two World Wars, Europe sees its relations modified with its “Others”. Thus Iran becomes in turn a land of study, a land of adventure and an ideal and spiritual land for those who can no longer remain in Europe. In addition, during this period, the genre of travel writing has evolved significantly. All these factors intersect to give a multiple images of Persia.

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