Multi-resolution analysis has been a very popular technique in the recent years. Wavelets have been used extensively to perform multi resolution image expansion and analysis. DCT, however, has been used to compress image but not for multi resolution image analysis. This thesis is an attempt to explore the possibilities of using DCT for multi-resolution image analysis. Naive implementation of block DCT for multi-resolution expansion has many difficulties that lead to signal distortion. One of the main causes of distortion is the blocking artifacts that appear when reconstructing images transformed by DCT. The new algorithm is based on line DCT which eliminates the need for block processing. The line DCT is one dimensional array based on cascading the image rows and columns in one transform operation. Several images have been used to test the algorithm at various resolution levels. The reconstruction mean square error rate is used as an indication to the success of the method. The proposed algorithm has also been tested against the traditional block DCT.

Distributed three-dimensional (3D) graphics applications exhibit both resemblance and uniqueness in comparison with conventional streaming media applications. The resemblance relates to the large data volume and the bandwidth-limited and error-prone transmission channel. The uniqueness is due to the polygon-based representation of 3D geometric meshes and their accompanying attributes such as textures. This specific data format introduces sophisticated rendering computation to display graphics models and therefore places an additional constraint on the streaming application. The objective of this research is to provide scalable, error-resilient, and time-efficient solutions for high-quality 3D graphics applications in distributed and resource-constrained environments. Resource constraints range from rate-limited and error-prone channels to insufficient data-reception, computing, and display capabilities of client devices. Optimal resource treatment with transmission and rendering scalability is important under such circumstances. The proposed research consists of three milestones. In the first milestone, we develop a joint mesh and texture optimization framework for scalable transmission and rendering of textured 3D models. Then, we address network behaviors and develop a hybrid retransmission and error protection mechanism for the on-demand delivery of 3D models. Next, we advance from individual 3D models to 3D scene databases, which contain numerous objects interacting in one geometric space, and study joint application and transport approaches. By properly addressing the properties of 3D scenes represented in multi-resolution hierarchies, we develop a joint source and channel coding method and a multi-streaming framework for streaming the content-rich 3D scene databases toward optimized transmission and rendering scalability under resource constraints.

Image descriptors play an important role in image representation and analysis. Multi-resolution image descriptors can effectively characterize complex images and extract their hidden information. Wavelets descriptors have been widely used in multi-resolution image analysis. However, making the wavelets transform shift and rotation invariant produces redundancy and requires complex matching processes. As to other multi-resolution descriptors, they usually depend on other theories or information, such as filtering function, prior-domain knowledge, etc.; that not only increases the computation complexity, but also generates errors. We propose a novel multi-resolution scheme that is capable of transforming any kind of image descriptor into its multi-resolution structure with high computation accuracy and efficiency. Our multi-resolution scheme is based on sub-sampling an image into an odd-even image tree. Through applying image descriptors to the odd-even image tree, we get the relative multi-resolution image descriptors. Multi-resolution analysis is based on downsampling expansion with maximum energy extraction followed by upsampling reconstruction. Since the maximum energy usually retained in the lowest frequency coefficients; we do maximum energy extraction through keeping the lowest coefficients from each resolution level. Our multi-resolution scheme can analyze images recursively and effectively without introducing artifacts or changes to the original images, produce multi-resolution representations, obtain higher resolution images only using information from lower resolutions, compress data, filter noise, extract effective image features and be implemented in parallel processing.

Image descriptors play an important role in image representation and analysis. Multi-resolution image descriptors can effectively characterize complex images and extract their hidden information. Wavelet descriptors have been widely used in multi-resolution image analysis. However, making the wavelet transform shift and rotation invariant produces redundancy and requires complex matching processes. As to other multi-resolution descriptors, they usually depend on other methods, such as filtering function, prior-domain knowledge, etc.; that not only increases the computation complexity, but also generates errors. We propose a novel multi-resolution scheme that is capable of transforming any kind of image descriptor into its multi-resolution structure with high computation accuracy and efficiency. Our multi-resolution scheme is based on sub-sampling each image into an odd-even image tree. Through applying image descriptors to the odd-even image tree, we get the relative multi-resolution image descriptors. Multi-resolution analysis is based on downsampling expansion with maximum energy extraction followed by upsampling reconstruction. Since the maximum energy usually retained in the lowest frequency coefficients; we do maximum energy extraction through keeping the lowest coefficients from each resolution level. Our multi-resolution scheme can analyze images recursively and effectively without introducing artifacts or changes to the original images, produce multi-resolution representations, obtain higher resolution images only using information from lower resolutions, compress data, filter noise, extract effective image features and be implemented in parallel processing.

Dynamic signal control provides significant benefits in terms of travel time, travel time reliability, and other performance measures of transportation systems. The goal of this research is to develop and evaluate a methodology to support the planning for operations of dynamic signal control utilizing a multi-resolution analysis approach. The multi-resolution analysis modeling combines analysis, modeling, and simulation (AMS) tools to support the assessment of the impacts of dynamic traffic signal control. Dynamic signal control strategies are effective in relieving congestions during non-typical days, such as those with high demands, incidents with different attributes, and adverse weather conditions. This research recognizes the need to model the impacts of dynamic signal controls for different days representing, different demand and incident levels. Methods are identified to calibrate the utilized tools for the patterns during different days based on demands and incident conditions utilizing combinations of real-world data with different levels of details. A significant challenge addressed in this study is to ensure that the mesoscopic simulation-based dynamic traffic assignment (DTA) models produces turning movement volumes at signalized intersections with sufficient accuracy for the purpose of the analysis. Although, an important aspect when modeling incident responsive signal control is to determine the capacity impacts of incidents considering the interaction between the drop in capacity below demands at the midblock urban street segment location and the upstream and downstream signalized intersection operations. A new model is developed to estimate the drop in capacity at the incident location by considering the downstream signal control queue spillback effects. A second model is developed to estimate the reduction in the upstream intersection capacity due to the drop in capacity at the midblock incident location as estimated by the first model. These developed models are used as part of a mesoscopic simulation-based DTA modeling to set the capacity during incident conditions, when such modeling is used to estimate the diversion during incidents. To supplement the DTA-based analysis, regression models are developed to estimate the diversion rate due to urban street incidents based on real-world data. These regression models are combined with the DTA model to estimate the volume at the incident location and alternative routes. The volumes with different demands and incident levels, resulting from DTA modeling are imported to a microscopic simulation model for more detailed analysis of dynamic signal control. The microscopic model shows that the implementation of special signal plans during incidents and different demand levels can improve mobility measures.

La visualisation de données est un aspect important de la recherche scientifique dans de nombreux domaines.Elle permet d'aider à comprendre les phénomènes observés voire simulés et d'en extraire des informations à des fins notamment de validations expérimentales ou tout simplement pour de la revue de projet.Nous nous intéressons dans le cadre de cette étude doctorale à la visualisation de données volumiques en imagerie médicale et biomédicale, obtenues grâce à des appareils d'acquisition générant des champs scalaires ou vectoriels représentés sous forme de grilles régulières 3D.La taille croissante des données, due à la précision grandissante des appareils d'acquisition, impose d'adapter les algorithmes de visualisation afin de pouvoir gérer de telles volumétries.De plus, les GPUs utilisés en visualisation de données volumiques, se trouvant être particulièrement adaptés à ces problématiques, disposent d'une quantité de mémoire très limitée comparée aux données à visualiser.La question se pose alors de savoir comment dissocier les unités de calculs, permettant la visualisation, de celles de stockage.Les algorithmes se basant sur le principe dit "out-of-core" sont les solutions permettant de gérer de larges ensembles de données volumiques.Dans cette thèse, nous proposons un pipeline complet permettant de visualiser et de traiter, en temps réel sur GPU, des volumes de données dépassant très largement les capacités mémoires des CPU et GPU.L'intérêt de notre pipeline provient de son approche de gestion de données "out-of-core" permettant de virtualiser la mémoire qui se trouve être particulièrement adaptée aux données volumiques.De plus, cette approche repose sur une structure d'adressage virtuel entièrement gérée et maintenue sur GPU.Nous validons notre modèle grâce à plusieurs applications de visualisation et de traitement en temps réel.Tout d'abord, nous proposons un microscope virtuel interactif permettant la visualisation 3D auto-stéréoscopique de piles d'images haute résolution.Puis nous validons l'adaptabilité de notre structure à tous types de données grâce à un microscope virtuel multimodale.Enfin, nous démontrons les capacités multi-rôles de notre structure grâce à une application de visualisation et de traitement concourant en temps réel. / Data visualisation is an essential aspect of scientific research in many fields.It helps to understand observed or even simulated phenomena and to extract information from them for purposes such as experimental validations or solely for project review.The focus given in this thesis is on the visualisation of volume data in medical and biomedical imaging.The acquisition devices used to acquire the data generate scalar or vector fields represented in the form of regular 3D grids.The increasing accuracy of the acquisition devices implies an increasing size of the volume data.Therefore, it requires to adapt the visualisation algorithms in order to be able to manage such volumes.Moreover, visualisation mostly relies on the use of GPUs because they suit well to such problematics.However, they possess a very limited amount of memory compared to the generated volume data.The question then arises as to how to dissociate the calculation units, allowing visualisation, from those of storage.Algorithms based on the so-called "out-of-core" principle are the solutions for managing large volume data sets.In this thesis, we propose a complete GPU-based pipeline allowing real-time visualisation and processing of volume data that are significantly larger than the CPU and GPU memory capacities.The pipeline interest comes from its GPU-based approach of an out-of-core addressing structure, allowing the data virtualisation, which is adequate for volume data management.We validate our approach using different real-time applications of visualisation and processing.First, we propose an interactive virtual microscope allowing 3D auto-stereoscopic visualisation of stacks of high-resolution images.Then, we verify the adaptability of our structure to all data types with a multimodal virtual microscope.Finally, we demonstrate the multi-role capabilities of our structure through a concurrent real-time visualisation and processing application.

No description available.

The goal in this thesis is to develop a novel statistical approach to identity functional interactions between regions in a brain network. Wavelets are effective for capturing time varying properties of non-stationary signals because they have compact support that can be compressed or stretched according to the dynamic properties of the signal. Wavelets provide a multi-scale decomposition of signals and thus can be few for exploring potential cross-scale interactions between signals. To achieve this, we propose the scale-specific sub-processes of a multivariate locally stationary wavelet stochastic process. Under this proposed framework, a novel cross-scale dependence measurement is developed, which provides a measure for dependence structure of components at different scales of multivariate time series. Extensive simulation experiments are conducted to demonstrate that the theoretical properties hold in practice. The developed cross-scale analysis is performed on the electroencephalogram (EEG) data to study alterations in the functional connectivity structure in children diagnosed with attention deficit hyperactivity disorder (ADHD). Our approach identified novel interesting cross-scale interactions between channels in the brain network. The proposed framework can be extended to other signals, which can also capture the statistical association between the stocks at different time scales.

No description available.

Thesis (PhD)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: Multi-resolution analysis (MRA) has become a very popular eld of mathematical study in the past two decades, being not only an area rich in applications but one that remains lled with open problems. Building on the foundation of re nability of functions, MRA seeks to lter through levels of ever-increasing detail components in data sets { a concept enticing to an age where development of digital equipment (to name but one example) needs to capture more and more information and then store this information in di erent levels of detail. Except for designing digital objects such as animation movies, one of the most recent popular research areas in which MRA is applied, is inpainting, where \lost" data (in example, a photograph) is repaired by using boundary values of the data set and \smudging" these values into the empty entries. Two main branches of application in MRA are subdivision and wavelet analysis. The former uses re nable functions to develop algorithms with which digital curves are created from a nite set of initial points as input, the resulting curves (or drawings) of which possess certain levels of smoothness (or, mathematically speaking, continuous derivatives). Wavelets on the other hand, yield lters with which certain levels of detail components (or noise) can be edited out of a data set. One of the greatest advantages when using wavelets, is that the detail data is never lost, and the user can re-insert it to the original data set by merely applying the wavelet algorithm in reverse. This opens up a wonderful application for wavelets, namely that an existent data set can be edited by inserting detail components into it that were never there, by also using such a wavelet algorithm. In the recent book by Chui and De Villiers (see [2]), algorithms for both subdivision and wavelet applications were developed without using Fourier analysis as foundation, as have been done by researchers in earlier years and which have left such algorithms unaccessible to end users such as computer programmers. The fundamental result of Chapter 9 on wavelets of [2] was that feasibility of wavelet decomposition is equivalent to the solvability of a certain set of identities consisting of Laurent polynomials, referred to as Bezout identities, and it was shown how such a system of identities can be solved in a systematic way. The work in [2] was done in the univariate case only, and it will be the purpose of this thesis to develop similar results in the bivariate case, where such a generalization is entirely non-trivial. After introducing MRA in Chapter 1, as well as discussing the re nability of functions and introducing box splines as prototype examples of functions that are re nable in the bivariate setting, our fundamental result will also be that wavelet decomposition is equivalent to solving a set of Bezout identities; this will be shown rigorously in Chapter 2. In Chapter 3, we give a set of Laurent polynomials of shortest possible length satisfying the system of Bezout identities in Chapter 2, for the particular case of the Courant hat function, which will have been introduced as a linear box spline in Chapter 1. In Chapter 4, we investigate an application of our result in Chapter 3 to bivariate interpolatory subdivision. With the view to establish a general class of wavelets corresponding to the Courant hat function, we proceed in the subsequent Chapters 5 { 8 to develop a general theory for solving the Bezout identities of Chapter 2 separately, before suggesting strategies for reconciling these solution classes in order to be a simultaneous solution of the system. / AFRIKAAANSE OPSOMMING: Multi-resolusie analise (MRA) het in die afgelope twee dekades toenemende gewildheid geniet as 'n veld in wiskundige wetenskappe. Nie net is dit 'n area wat ryklik toepaslik is nie, maar dit bevat ook steeds vele oop vraagstukke. MRA bou op die grondleggings van verfynbare funksies en poog om deur vlakke van data-komponente te sorteer, of te lter, 'n konsep wat aanloklik is in 'n era waar die ontwikkeling van digitale toestelle (om maar 'n enkele voorbeeld te noem) sodanig moet wees dat meer en meer inligting vasgel^e en gestoor moet word. Behalwe vir die ontwerp van digitale voorwerpe, soos animasie- lms, word MRA ook toegepas in 'n mees vername navorsingsgebied genaamd inverwing, waar \verlore" data (soos byvoorbeeld in 'n foto) herwin word deur data te neem uit aangrensende gebiede en dit dan oor die le e data-dele te \smeer." Twee hooftakke in toepassing van MRA is subdivisie en gol e-analise. Die eerste gebruik verfynbare funksies om algoritmes te ontwikkel waarmee digitale krommes ontwerp kan word vanuit 'n eindige aantal aanvanklike gegewe punte. Die verkrygde krommes (of sketse) kan voldoen aan verlangde vlakke van gladheid (of verlangde grade van kontinue afgeleides, wiskundig gesproke). Gol es word op hul beurt gebruik om lters te bou waarmee gewensde dataof geraas-komponente verwyder kan word uit datastelle. Een van die grootste voordeel van die gebruik van gol es bo ander soortgelyke instrumente om data lters mee te bou, is dat die geraas-komponente wat uitgetrek word nooit verlore gaan nie, sodat die proses omkeerbaar is deurdat die gebruiker die sodanige geraas-komponente in die groter datastel kan terugbou deur die gol e-algoritme in trurat toe te pas. Hierdie eienskap van gol fies open 'n wonderlike toepassingsmoontlikheid daarvoor, naamlik dat 'n bestaande datastel verander kan word deur data-komponente daartoe te voeg wat nooit daarin was nie, deur so 'n gol e-algoritme te gebruik. In die onlangse boek deur Chui and De Villiers (sien [2]) is algoritmes ontwikkel vir die toepassing van subdivisie sowel as gol es, sonder om staat te maak op die grondlegging van Fourier-analise, soos wat die gebruik was in vroe ere navorsing en waardeur algoritmes wat ontwikkel is minder e ektief was vir eindgebruikers. Die fundamentele resultaat oor gol es in Hoofstuk 9 in [2], verduidelik hoe suksesvolle gol e-ontbinding ekwivalent is aan die oplosbaarheid van 'n sekere versameling van identiteite bestaande uit Laurent-polinome, bekend as Bezout-identiteite, en dit is bewys hoedat sodanige stelsels van identiteite opgelos kan word in 'n sistematiese proses. Die werk in [2] is gedoen in die eenveranderlike geval, en dit is die doelwit van hierdie tesis om soortgelyke resultate te ontwikkel in die tweeveranderlike geval, waar sodanige veralgemening absoluut nie-triviaal is. Nadat 'n inleiding tot MRA in Hoofstuk 1 aangebied word, terwyl die verfynbaarheid van funksies, met boks-latfunksies as prototipes van verfynbare funksies in die tweeveranderlike geval, bespreek word, word ons fundamentele resultaat gegee en bewys in Hoofstuk 2, naamlik dat gol e-ontbinding in die tweeveranderlike geval ook ekwivalent is aan die oplos van 'n sekere stelsel van Bezout-identiteite. In Hoofstuk 3 word 'n versameling van Laurent-polinome van korste moontlike lengte gegee as illustrasie van 'n oplossing van 'n sodanige stelsel van Bezout-identiteite in Hoofstuk 2, vir die besondere geval van die Courant hoedfunksie, wat in Hoofstuk 1 gede nieer word. In Hoofstuk 4 ondersoek ons 'n toepassing van die resultaat in Hoofstuk 3 tot tweeveranderlike interpolerende subdivisie. Met die oog op die ontwikkeling van 'n algemene klas van gol es verwant aan die Courant hoedfunksie, brei ons vervolglik in Hoofstukke 5 { 8 'n algemene teorie uit om die oplossing van die stelsel van Bezout-identiteite te ondersoek, elke identiteit apart, waarna ons moontlike strategie e voorstel vir die versoening van hierdie klasse van gelyktydige oplossings van die Bezout stelsel.