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In recent years harmonic analysis on combinatorial graphs has attracted considerable attention. The interest is stimulated in part by multiple existing and potential applications of analysis on graphs to information theory, signal analysis, image processing, computer sciences, learning theory, and astronomy. My thesis is devoted to sampling, interpolation, approximation, and multi-resolution on graphs. The results in the existing literature concern mainly with these theories on unweighted graphs. My main objective is to extend existing theories and obtain new results about sampling, interpolation, approximation, and multi-resolution on general combinatorial graphs such as directed, undirected and weighted. / Mathematics

Road extraction from satellite or aerial imagery is a popular topic in remote sensing, and there are many road extraction algorithms suggested by various researches. However, the need of reliable remotely sensed road information still persists as there is no sufficiently robust road extraction algorithm yet. In this study, we explore the road extraction problem taking advantage of the multi-resolution analysis and adaptive boosting based classifiers. That is, we propose a new road extraction algorithm exploiting both spectral and structural features of the high resolution multi-spectral satellite images. The proposed model is composed of three major components / feature extraction, classification and road detection. Well-known spectral band ratios are utilized to represent reflectance properties of the data whereas a segmentation operation followed by an elongatedness scoring technique renders structural evaluation of the road parts within the multi-resolution analysis framework. The extracted features are fed into Adaptive Boosting (Adaboost) learning procedure, and the learning method iteratively combines decision trees to acquire a classifier with a high accuracy. The road network is identified from the probability map constructed by the classifier suggested by Adaboost. The algorithm is designed to be modular in the sense of its extensibility, that is / new road descriptor features can be easily integrated into the existing model. The empirical evaluation of the proposed algorithm suggests that the algorithm is capable of extracting majority of the road network, and it poses promising performance results.

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Recent advances in telecommunications, collaborated with the development of image and video processing and acquisition devices has lead to a spectacular growth of the amount of the visual content data stored, transmitted and exchanged over Internet. Within this context, elaborating efficient tools to access, browse and retrieve video content has become a crucial challenge. In Chapter 2 we introduce and validate a novel shot boundary detection algorithm able to identify abrupt and gradual transitions. The technique is based on an enhanced graph partition model, combined with a multi-resolution analysis and a non-linear filtering operation. The global computational complexity is reduced by implementing a two-pass approach strategy. In Chapter 3 the video abstraction problem is considered. In our case, we have developed a keyframe representation system that extracts a variable number of images from each detected shot, depending on the visual content variation. The Chapter 4 deals with the issue of high level semantic segmentation into scenes. Here, a novel scene/DVD chapter detection method is introduced and validated. Spatio-temporal coherent shots are clustered into the same scene based on a set of temporal constraints, adaptive thresholds and neutralized shots. Chapter 5 considers the issue of object detection and segmentation. Here we introduce a novel spatio-temporal visual saliency system based on: region contrast, interest points correspondence, geometric transforms, motion classes' estimation and regions temporal consistency. The proposed technique is extended on 3D videos by representing the stereoscopic perception as a 2D video and its associated depth

Abstract Cognitive Radio (CR) improves the efficiency of spectrum utilization by allowing non- licensed users to utilize bands when not occupied by licensed users. In this thesis, we address several challenges currently limiting the wide use of cognitive radios. These challenges include identification of unoccupied bands, energy consumption and other technical challenges. Improved accuracy edge detection techniques are developed for CR to mitigate both noise and estimation error variance effects. Next, a reduced complexity Simplified DFT (SDFT) is proposed for use in CR. Then, a sub-Nyquist rate A to D converter is introduced to reduce energy consumption. Finally, a novel multi-resolution PSD estimation based on expectation-maximization algorithm is introduced that can obtain a more accurate PSD within a specified sensing time.

Subsurface processes are usually characterized by rare field experiments, sparse measurements,multi-resolution interpretations, stochastic description, related uncertainties and computational complexity. Over the last few decades, different computational techniques and strategies have become indispensable tools for flow and solute transport prediction in heterogeneous porousmedia. This thesis develops a multi-resolution approach based on Fup basis functions with compactsupport, enabling the use of an efficient and adaptive procedure, closely related to currentunderstood physical interpretation. All flow and transport variables, as well as intrinsic heterogeneity,are described in a multi-resolution representation, in the form of a linear combination ofFup basis functions. Each variable is represented on a particular adaptive grid with a prescribedaccuracy. The methodology is applied to solving problems with sharp fronts, and to solving flowand advective transport in highly heterogeneous porous media, under mean uniform flow conditions.The adaptive Fup collocation method, through the well known method of lines, efficientlytracks solutions with sharp fronts, resolving locations and frequencies at all spatial and/or temporalscales. The methodology yields continuous velocity fields and fluxes, enabling accurate andreliable transport analysis. Analysis of the advective transport proves the robustness of the firstordertheory for low and mild heterogeneity. Moreover, due to the accuracy of the improved Monte-Carlo methodology, this thesis presents the effects of high heterogeneity on ensembleflow and travel time statistics. The difference between Eulerian and Lagrangian velocity statisticsand the importance of higher travel time moments are indicative of high heterogeneity. The thirdtravel time moment mostly describes a peak and late arrivals, while higher moments are requiredfor early arrivals which are linked with the largest uncertainty. A particular finding is the linearityof all travel time moments, which implies that in the limit an advective transport in multi-Gaussian field becomes Fickian. By comparison, the transverse displacement pdf converges to aGaussian distribution around 20 integral scales after injection, even for high heterogeneity. Thecapabilities of the presented multi-resolution approach, and the quality of the obtained results,open new areas for further research. / Markprocesser karakteriseras ofta av fåtaliga fältexperiment, glesa mätningar, heterogenitet påolika skalor, slumpmässighet och relaterade osäkerheter, samt beräkningsmässiga svårigheter.Under de senaste årtiondena har olika beräkningstekniker och strategier blivit ovärderliga verktygför att förutspå vattenflöde och ämnestransport i heterogena porösa medier. Denna doktorsavhandling utvecklar ett angreppssätt med flerskaliga upplösningar baserat på Fup basis funktionermed kompakt stöd, som möjliggör en effektiv och anpassningsbar procedur, nära relaterad tillrådande fysiska tolkningar. Alla flödes- och transportvariabler, så väl som heterogeniteten, beskrivsav en flerskaligt upplöst representation, i form av linjära kombinationer av Fup basis funktioner.Varje variabel representeras på ett speciellt anpassningsbar gridnät med given noggrannhet.Metoden appliceras för att lösa problem med skarpa fronter, samt vattenflöde och advektivämnestransport i starkt heterogena porösa medier. Adaptive Fup collocation metoden tillsammansmed den välkända Method of lines, spårar effektivt lösningar med skarpa fronter och löserupp positioner och frekvenser på alla rums- och/eller tidsskalor. Metoden ger kontinuerliga hastighetsfältoch flöden, och möjliggör noggrann och tillförlitlig transportanalys. Analys av advektivtransport understöder stabiliteten i första-ordningens transport teori för låg och mild heterogenitet.Utöver detta, som resultat av noggrannheten i den förbättrade Monte-Carlo metodiken, visardenna avhandling effekten av hög heterogenitet på ensemble statistiken för flöden och transporttider.Skillnaden mellan Eulerisk och Lagrangian hastighetsstatistik och betydelsen av högrestatistiska moment för transporttider, indikerar hög heterogenitet. Det tredje transporttidsmomentetbeskriver huvudsakligen sannolikhetspiken och de långa transporttiderna, medan högremoment behövs för de korta transporttiderna, som har den största osäkerheten. En speciell upptäcktär linjäariteten i transporttidsmoment, som indikerar att advektiv transport i multi-Gaussiska fält blir Gaussisk i gränsen. Som jämförelse konvergerar sannolikhetsfunktioner förden transversella transportförflyttningen mot en Gaussisk fördelning vid runt 20 korrelationslängder efter injektion, även för hög heterogenitet. Förmågan i det presenterade angreppssättet med flerskalig upplösning, och resultatens noggrannhet, öppnar nya områden för fortsatt forskning. / QC 20100714

Made available in DSpace on 2014-12-17T14:55:16Z (GMT). No. of bitstreams: 1 RafaelBG_TESE.pdf: 2529249 bytes, checksum: b16afb21de612f10dcfa5acb69028967 (MD5) Previous issue date: 2013-08-02 / Conselho Nacional de Desenvolvimento Cient?fico e Tecnol?gico / Visual attention is a very important task in autonomous robotics, but, because of its complexity, the processing time required is significant. We propose an architecture for feature selection using foveated images that is guided by visual attention tasks and that reduces the processing time required to perform these tasks. Our system can be applied in bottom-up or top-down visual attention. The foveated model determines which scales are to be used on the feature extraction algorithm. The system is able to discard features that are not extremely necessary for the tasks, thus, reducing the processing time. If the fovea is correctly placed, then it is possible to reduce the processing time without compromising the quality of the tasks outputs. The distance of the fovea from the object is also analyzed. If the visual system loses the tracking in top-down attention, basic strategies of fovea placement can be applied. Experiments have shown that it is possible to reduce up to 60% the processing time with this approach. To validate the method, we tested it with the feature algorithm known as Speeded Up Robust Features (SURF), one of the most efficient approaches for feature extraction. With the proposed architecture, we can accomplish real time requirements of robotics vision, mainly to be applied in autonomous robotics / A aten??o visual ? uma importante tarefa em rob?tica aut?noma, mas devido ? sua complexidade, o tempo de processamento necess?rio ? significativo. Prop?e-se uma arquitetura para sele??o de features usando imagens foveadas que ? guiada por tarefas envolvendo aten??o visual e que reduz o tempo de processamento para realizar tais tarefas. O sistema proposto pode ser aplicado para aten??o bottom-up ou top-down. O modelo de foveamento determina quais escalas devem ser utilizadas no algoritmo de extra??o de features. O sistema ? capaz de descartar features que n?o s?o essenciais para a realiza??o da tarefa e, dessa forma, reduz o tempo de processamento. Se a f?vea ? corretamente posicionada, ent?o ? poss?vel reduzir o tempo de processamento sem comprometer o desempenho da tarefa. A dist?ncia da f?vea para o objeto tamb?m ? analisada. Caso o sistema visual perca o tracking na aten??o top-down, estrat?gias b?sicas de reposicionamento da f?vea podem ser aplicadas. Experimentos demonstram que ? poss?vel reduzir em at? 60% o tempo de processamento com essa abordagem. Para validar o m?todo proposto, s?o realizados testes com o algoritmo de extra??o de features SURF, um dos mais eficientes existentes. Com a arquitetura proposta para sele??o de features, ? poss?vel cumprir requisitos de um sistema de vis?o em tempo-real com poss?veis aplica??es na ?rea de rob?tica

Made available in DSpace on 2014-12-17T14:55:40Z (GMT). No. of bitstreams: 1 RafaelBG.pdf: 2393943 bytes, checksum: 45924e13c3c73c1eaaf09dcc478bd70e (MD5) Previous issue date: 2009-08-07 / Conselho Nacional de Desenvolvimento Cient?fico e Tecnol?gico / We propose a new approach to reduction and abstraction of visual information for robotics vision applications. Basically, we propose to use a multi-resolution representation in combination with a moving fovea for reducing the amount of information from an image. We introduce the mathematical formalization of the moving fovea approach and mapping functions that help to use this model. Two indexes (resolution and cost) are proposed that can be useful to choose the proposed model variables. With this new theoretical approach, it is possible to apply several filters, to calculate disparity and to obtain motion analysis in real time (less than 33ms to process an image pair at a notebook AMD Turion Dual Core 2GHz). As the main result, most of time, the moving fovea allows the robot not to perform physical motion of its robotics devices to keep a possible region of interest visible in both images. We validate the proposed model with experimental results / N?s propomos uma nova abordagem para reduzir e abstrair informa??es visuais para aplica??es de vis?o rob?tica. Basicamente, usamos uma representa??o emmulti-resolu??o em combina??o com uma f?vea m?vel para reduzir a quantidade de informa??es de uma imagem. Apresentamos a formaliza??o matem?tica do modelo em conjunto com fun??es de mapeamento que auxiliam na utiliza??o do modelo. Propomos dois ?ndices (resolu??o e custo) que visam auxiliar na escolha das vari?veis do modelo proposto. Com essa nova abordagem te?rica, ? poss?vel aplicar diversos filtros, calcular disparidade est?reo e obter an?lise de movimento em tempo real (menos de 33ms para processar um par de imagens em um notebook AMD Turion Dual Core 2GHz). Como principal resultado, na maior parte do tempo, a f?vea m?vel permite ao rob? n?o realizar movimenta??o f?sica de seus dispositivos rob?ticos para manter uma poss?vel regi?o de interesse vis?vel nas duas imagens. Validamos o modelo proposto com resultados experimentais

Abstract Cognitive Radio (CR) improves the efficiency of spectrum utilization by allowing non- licensed users to utilize bands when not occupied by licensed users. In this thesis, we address several challenges currently limiting the wide use of cognitive radios. These challenges include identification of unoccupied bands, energy consumption and other technical challenges. Improved accuracy edge detection techniques are developed for CR to mitigate both noise and estimation error variance effects. Next, a reduced complexity Simplified DFT (SDFT) is proposed for use in CR. Then, a sub-Nyquist rate A to D converter is introduced to reduce energy consumption. Finally, a novel multi-resolution PSD estimation based on expectation-maximization algorithm is introduced that can obtain a more accurate PSD within a specified sensing time.