The aim of this thesis is to develop the dimension theory of self-affine carpets in several directions. Self-affine carpets are an important class of planar self-affine sets which have received a great deal of attention in the literature on fractal geometry over the last 30 years. These constructions are important for several reasons. In particular, they provide a bridge between the relatively well-understood world of self-similar sets and the far from understood world of general self-affine sets. These carpets are designed in such a way as to facilitate the computation of their dimensions, and they display many interesting and surprising features which the simpler self-similar constructions do not have. For example, they can have distinct Hausdorff and packing dimensions and the Hausdorff and packing measures are typically infinite in the critical dimensions. Furthermore, they often provide exceptions to the seminal result of Falconer from 1988 which gives the `generic' dimensions of self-affine sets in a natural setting. The work in this thesis will be based on five research papers I wrote during my time as a PhD student. The first contribution of this thesis will be to introduce a new class of self-affine carpets, which we call box-like self-affine sets, and compute their box and packing dimensions via a modified singular value function. This not only generalises current results on self-affine carpets, but also helps to reconcile the `exceptional constructions' with Falconer's singular value function approach in the generic case. This will appear in Chapter 2 and is based on a paper which appeared in 'Nonlinearity' in 2012. In Chapter 3 we continue studying the dimension theory of self-affine sets by computing the Assouad and lower dimensions of certain classes. The Assouad and lower dimensions have not received much attention in the literature on fractals to date and their importance has been more related to quasi-conformal maps and embeddability problems. This appears to be changing, however, and so our results constitute a timely and important contribution to a growing body of literature on the subject. The material in this Chapter will be based on a paper which has been accepted for publication in 'Transactions of the American Mathematical Society'. In Chapters 4-6 we move away from the classical setting of iterated function systems to consider two more exotic constructions, namely, inhomogeneous attractors and random 1-variable attractors, with the aim of developing the dimension theory of self-affine carpets in these directions. In order to put our work into context, in Chapter 4 we consider inhomogeneous self-similar sets and significantly generalise the results on box dimensions obtained by Olsen and Snigireva, answering several questions posed in the literature in the process. We then move to the self-affine setting and, in Chapter 5, investigate the dimensions of inhomogeneous self-affine carpets and prove that new phenomena can occur in this setting which do not occur in the setting of self-similar sets. The material in Chapter 4 will be based on a paper which appeared in 'Studia Mathematica' in 2012, and the material in Chapter 5 is based on a paper, which is in preparation. Finally, in Chapter 6 we consider random self-affine sets. The traditional approach to random iterated function systems is probabilistic, but here we allow the randomness in the construction to be provided by the topological structure of the sample space, employing ideas from Baire category. We are able to obtain very general results in this setting, relaxing the conditions on the maps from `affine' to `bi-Lipschitz'. In order to get precise results on the Hausdorff and packing measures of typical attractors, we need to specialise to the setting of random self-similar sets and we show again that several interesting and new phenomena can occur when we relax to the setting of random self-affine carpets. The material in this Chapter will be based on a paper which has been accepted for publication by 'Ergodic Theory and Dynamical Systems'.

La perception visuelle du mouvement est essentielle à l’exécution de déplacements sécuritaires ainsi qu’à l’interaction efficace avec notre environnement. C’est pourquoi il est nécessaire de comprendre la nature des mécanismes responsables de l’analyse de l’information sur le mouvement, ainsi que l’effet du vieillissement sur la réponse de ces mécanismes. Deux études seront présentées. La première avait pour but l’analyse des mécanismes responsables de la perception du mouvement de rotation fractale, nouveau stimulus introduit par Benton, O’Brien & Curran (2007). Ce type de stimulus a été créé afin d’isoler les mécanismes sensibles à la forme. Plusieurs auteurs ont suggéré que les mécanismes sensibles au mouvement de deuxième ordre utiliseraient les indices de position afin d’extraire l’information sur le mouvement (Seiffert & Cavanagh, 1998). Ainsi, la présente étude visait à déterminer si la rotation fractale est analysée par de tels mécanismes. Les résultats obtenus suggèrent que les mécanismes sensibles à la rotation fractale seraient basés sur l’orientation; tandis que ceux sensibles à la rotation de premier ordre, basés sur l’énergie. De plus, une certaine dissociation des mécanismes responsables du traitement de la rotation fractale et de premier ordre serait présente. La deuxième étude avait pour but, quant à elle, d’établir l’effet du vieillissement sur l’intégration du mouvement de premier et deuxième ordre. Les résultats indiquent que les mécanismes sensibles au mouvement de deuxième ordre seraient davantage affectés, comparativement à ceux de premier ordre. Ainsi, les fonctions visuelles requérant une intégration corticale de plus haut niveau seraient davantage affectées par l’effet du vieillissement. / Motion perception ensures the execution of safe navigation, as well as efficient interaction with the environment. As such, it is essential to understand the nature of mechanisms ensuring motion perception, as well as effects of aging on their response. Two studies will be presented. The first aimed at identifying the nature of mechanisms responsible for the perception of fractal rotation, a novel stimulus introduced by Benton et al. (2007). This stimulus has been created to isolate form sensitive mechanisms. Several authors have suggested that second-order motion sensitive mechanisms use position cues to extract motion (Seiffert & Cavanagh, 1998). Hence, the following study aimed at determining whether fractal rotation is analyzed by such mechanisms or not. Results suggest fractal rotation sensitive mechanisms use orientation changes, whereas first-order sensitive mechanisms use energy. Moreover, dissociation between first-order and fractal rotation mechanisms has been observed. The second study aimed at establishing the effect of aging on first- and second-order motion integration. Results indicate second-order sensitive mechanisms would be more affected by aging, than first-order mechanisms. Accordingly, visual functions requiring higher order cortical integration are more likely to be more affected by aging.

L'agglomération humide est une étape cruciale dans la technologie de mise en forme des poudres de par son fort impact sur la qualité finale des produits élaborés. Malgré son intérêt lors de l'élaboration de nombreux produits (aliment, pharmaceutique, génie civil,…), ainsi que les différents modes technologiques (malaxeurs horizontaux, verticaux, à faible ou fort de taux de cisaillement, lit fluidisé, …), elle reste insuffisamment maîtrisée de par la difficulté à proposer des diagrammes de fonctionnement opérationnels qui couplent les contributions croisées des procédés et des produits. Ce travail de thèse s'inscrit dans cette problématique et porte sur l'étude des mécanismes d'agglomération en lien avec les caractéristiques de la formulation et les paramètres opératoires. L'identification et la représentation du mode d'assemblage des particules au cours de l'opération de mouillage/malaxage est l'un des enjeux central de ce travail. A partir d'expériences menées avec deux types de poudres alimentaires (semoule de blé dur et poudre de lait), l'agglomération est induite soit par contacts humides en malaxeur à faible taux de cisaillement soit par des collisions entre les particules collantes en lit fluidisé. Les mécanismes d'agglomération humide de la semoule de blé dur développés dans un malaxeur à faible cisaillement sont décrits selon un processus de morphogénèse qui corrèle la taille des agglomérats à leur texture via une dimension fractale. L'influence des propriétés physicochimiques des liants liquides sur les mécanismes d'agglomération est étudiée au regard des paramètres du modèle fractal. L'étude fine des distributions des propriétés hydrotexturales et dimensionnelles des structures agglomérées a permis d'identifier leur « règle » d'agencement : association par même classe hydro-texturale et dimensionnelle. Les régimes d'agglomération en fonction du mode d'apport d'eau (débit faible, débit fort) sont étudiés en se basant sur la notion de flux d'atomisation adimensionné. En ce qui concerne l'agglomération de la poudre de lait en lit fluidisé, les mécanismes d'agglomération sont étudiés en suivant l'évolution des tailles et des teneurs en eau des échantillons prélevés durant l'opération de mouillage/séchage et par la suite l'étude de l'impact de certaines conditions opératoires et de formulation sur les propriétés des agglomérats finaux et les régimes d'agglomération. Un lien entre les procédés est discuté et ouvre sur une requalification des régimes d'écoulement granulaire ainsi que de la réactivité de surface des particules. / Wet agglomeration is a crucial step in the shaping technology of powders because of its strong impact on the final quality of the elaborated products. Despite its interest in the elaboration of many products (food, pharmaceutical, engineering,...) as well as different technological process (horizontal mixers, vertical, low or high shear rate, fluidized bed, ...), it remains insufficiently mastered due to the difficulty in establishing operating diagrams taking into account, in the same time, products and process contributions. This thesis focuses on the study of the agglomeration mechanisms related to the characteristics of the formulation and process parameters. The identification and representation of the way particles come together during the wetting / mixing operation is one of the central challenges of this work. From experiments with two different food powders (durum wheat semolina and milk powder), agglomeration is induced either by wet contacts in mixer at low shear rate or by collisions between sticky particles in a fluidized bed. Mechanisms of semolina wet agglomeration developed in a low shear mixer are described as a process of morphogenesis that correlates the agglomerates size to their texture via a fractal dimension. The influence of the liquid binder physicochemical properties on the agglomeration mechanisms is studied according to the values taken by the fractal parameters of the model. The detailed study of the distribution of size and textural properties of agglomerated structures make it possible to identify the rule that lead to their layout: the association is mainly possible between structures belonging to the same class concerning their hydro-textural and dimensional characteristics. Agglomeration regimes depending on the mode of water supply (low flow, high flow) are studied based on the notion of dimensionless spray flux. Concerning milk powder agglomeration in a fluidized bed, agglomeration mechanisms are studied by following the evolution of the size and water content of the samples taken during the operation of wetting / drying and thereafter studying the impact of some operational conditions and formulation on the properties of the final agglomerates and agglomeration regimes. A link between the processes (low shear mixer and fluidized bed) is discussed and opens onto a redefinition of granular flow regimes and the surface reactivity of particles.

Cette thèse propose d’étudier l’évolution des hiérarchies des villes et de la croissance urbaine en s’appuyant sur le cas du Maroc. Le Maroc a connu ces dernières décennies un processus d’urbanisation soutenu, tant dans les grandes villes que dans les petites et moyennes villes. D’où la nécessité de procéder à une structuration démographique urbaine primatiale qui exige une coordination entre certaines politiques économiques nationales et les politiques d’aménagement menées par les grandes métropoles afin de faire preuve d’une réelle efficacité. Une politique d’aménagement résolument tournée jusqu’ici vers la gestion de la pression urbaine dans les grandes métropoles. Ce qui a conduit par conséquent à une polarisation des activités dans quelques régions du territoire. Ainsi, cette thèse se structure autour de trois chapitres. Le premier chapitre examine la loi rang-taille et l’apport des économistes et des géographes dans ce processus. Le second chapitre analyse les trois approches théoriques qui traitent la question de la croissance urbaine notamment les théories de la croissance aléatoire, de la croissance déterministe et l’intersection de ces deux approches dites d’hybrides. Enfin, le dernier chapitre est basé sur une étude empirique à l’échelle régionale afin de recenser les déterminants de la croissance urbaine des régions marocaine. Le travail engagé dans cette thèse s’appuie sur des bases de données originales fournies par le Haut-Commissariat au Plan permettant de recenser la taille des agglomérations marocaines et utilise un ensemble d’instruments statistiques et économétriques. Les différents résultats obtenus s’inscrivent dans le prolongement de différentes études effectuées en sciences régionales. Ces résultats indiquent que les hiérarchies urbaines marocaines sont appelées à changer dans les décennies à venir, mais également que la croissance économique des régions du Maroc n’affecte pas immédiatement la croissance de la population urbaine. / This thesis proposes to study the evolution of city hierarchies and urban growth based on the case of Morocco. This country has experienced in recent decades a sustained urbanization process, both in large cities and small and medium-sized cities. Hence the need to proceed to a primatial urban demographic structure that requires coordination between certain national economic policies and planning policies carried out by major cities to be truly effective. A development policy resolutely turned so far towards the management of urban pressure in major cities. This led to a polarization of activities in some regions of the territory. Thus, this thesis is divided into three chapters. The first chapter examines the rank-size law and the contribution of economists and geographers in this process. The second chapter analyzes the three theoretical approaches that deal with the issue of urban growth, in particular theories of random growth, deterministic growth and the intersection of these two approaches, called hybrid. Finally, the last chapter is based on an empirical study at the regional level to identify the determinants of urban growth in Moroccan regions. The work undertaken in this thesis is based on original databases provided by the Office of the “Haut-Commissariat au Plan” to identify the size of Moroccan agglomerations and uses a set of statistical and econometric instruments. The various results obtained are a continuation of various studies carried out in regional sciences. These results indicate that Moroccan urban hierarchies are destined to change in the decades to come, but also that the economic growth of the regions of Morocco does not immediately affect the growth of the urban population.

Texture is one of the primary visual attributes used to describe patterns found in nature. Several texture analysis methods have been used as powerful tools for real applications involving analysis and computer vision. However, existing methods do not successfully discriminate the complexity of texture patterns. Such methods disregard the possibility of describing image structures by means of measures such as the fractal dimension. Fractality-based measures allow a non-integer geometric interpretation with applications in areas such as mathematics, physics, and biology. With this gap in mind, the central hypothesis of this thesis is that textures can be described as irregular fractal surfaces due to their complex geometry; such geometry can be exploited for image analysis and computer vision. By exploring such possibilities, pushing the limits of the state-of-the-art, this thesis starts with an analysis of texture features achieved by means of agents on image surfaces. To do so, we used the Bouligand-Minkowski fractal dimension, swarm-system Artificial Crawlers, and non-linear diffusion of Perona-Malik, techniques that led to methodologies with efficacy and efficiency comparable to the state-of-the-art. Our first method combines fractal dimension with random walks on the surface of images. In a second approach, non-linear diffusion is used to represent texture images at different scales, which are described via their fractal dimension for image classification purposes. In a third proposal, we employ fractal dimension concepts over multiple scales derived from the same image for a richer texture description. One of the purposes is the automatic detection of diseases in soybean leaves. Finally, texture characteristics were exploited in a method based on complex networks used to analyze the agglomeration of particles in nanotechnology images. The results achieved in the four methodologies described in this thesis demonstrated the potential of using texture features in tasks of classification and pattern recognition. The contributions of this work shall support significant advances in materials engineering, computer vision, and agriculture. / A textura é um dos principais atributos visuais para a descrição de padrões encontrados na natureza. Diversos métodos de análise de textura têm sido usados como uma poderosa ferramenta para aplicações reais que envolvem análise de imagens e visão computacional. Entretanto, os métodos existentes não conseguem discriminar com sucesso a complexidade dos padrões de textura. Tais métodos desconsideram a possibilidade de se descrever estruturas de imagens por meio de medidas como a dimensão fractal. Medidas baseadas em fractalidade permitem uma interpretação geométrica não-inteira que possui aplicações encontradas em áreas como matemática, física, e biologia. Sobre esta lacuna metodológica, a hipótese central desta tese é que texturas presentes na natureza podem ser medidas como superfícies fractais irregulares devido à sua geometria complexa, o que pode ser explorado para fins de análise de imagens e visão computacional. Para superar tais limitações, avançando o estado da arte, esta tese se inicia com uma análise das características de texturas baseada em caminhadas aleatórias de agentes sobre superfícies de imagens. Esta primeira análise leva a um método que combina dimensão fractal com caminhadas de agentes sobre a superfície de imagens. Em uma segunda abordagem, usa-se a difusão não-linear para representar imagens de texturas em diferentes escalas, as quais são descritas via dimensão fractal para fins de classificação de imagens. Em uma terceira proposta, emprega-se a dimensão fractal sobre múltiplas escalas derivadas de uma mesma imagem com o propósito de se realizar a descrição multi-escala de texturas. Um dos propósitos específicos foi a detecção automática de doenças em folhas de soja. Por último, as características de textura foram exploradas segundo uma metodologia baseada em redes complexas para análise de aglomeração de partículas em imagens de nanotecnologia. Os resultados alcançados nesta tese demonstraram o potencial do uso de características de textura. Para tanto foram usadas técnicas de dimensão fractal de Bouligand-Minkowski, multiagentes Artificial Crawlerse difusão não-linear de Perona-Malik, os quais alcançaram eficácia e eficiência comparáveis ao do estado da arte. As contribuições obtidas devem suportar avanços significativos nas áreas de engenharia de materiais, visão computacional, e agricultura.

O sucesso das cirurgias de implantes depende de diversos fatores como a saúde sistêmica dos pacientes, qualidade e quantidades ósseas disponíveis e, o tipo de macro e microarquitetura dos implantes osseointegráveis. Este estudo propõe avaliar o tecido ósseo em radiografias panorâmicas antes e após cirurgias de implantes correlacionando com análises das Dimensões Fractais (DF), Intensidade de pixel (IP), Índice mentual (IM) e análises de estabilidade primária de implantes (AFR e TI). Foram analisadas 138 regiões de interesse de 50 pacientes, homens e mulheres com idade entre 22 e 77 anos cujas imagens pertencem ao banco de dados do curso de pós-graduação em Implantodontia da Universidade de Santos (Unimes). Foram obtidos dados cirúrgicos do ato da instalação dos implantes, análises de Frequência de Ressonância (AFR) e Torque de Inserção dos implantes (TI) e, com os dados quantitativos obtidos das radiografias panorâmicas antes e após a instalação dos implantes, DF, IP e IM foram realizados testes estatísticos de Correlação de Spearmam, Teste Kruskal Wallis e Wilcoxon para amostras relacionadas com auxílio do software IBM SPSS Advanced Statistics ® (IBM, USA) com nível de significância de 95% (p<0,05). Os resultados obtidos para as Correlações significantes foram entre a Idade e DF (r=-.647) e TI e DF (r=0.434). O teste de Wilcoxon identificou diferença significante (p>0,05) para as amostras relacionadas IP antes e IP depois (p=0,020 e 0,000) entre os grupos 1 e 2. Foram analisadas as possíveis diferenças entre as variáveis independentes para os grupos 1 e 2 em relação a Idade, com diferenças entre IP (p=0,046), TI (p=0,044), AFR_MD (p=0,040) e AFR_VL (p=0,010), em relação ao gênero encontrados diferenças entre as variáveis DF (p=0,039), IP_antes (p=0,001) e IP_depois (p=0,033). O estudo concluiu que a IP pode detectar alterações de mineralização óssea antes e após a instalação de implantes; DF é correlacionada com TI para pacientes jovens (até 45 anos) e, a análise da Idade e Gênero devem ser considerados na avaliação de exames por imagem para planejamento com implantes. / The success of dental implants depends on several factors as patient´s systemic health, bone quality and quantity, geometry of dental implants and their microarquitecture relationship to the alveolar bone. The aim of this study is to assess changes of alveolar bone of panoramic radiographs correlating with Fractal Dimension (FD), Pixel Intensity (PI), Mentual Index (MI) and Implant Stability Quocient (ISQ) measured with Insertion Torque (IT) and Resonance Frequency (RF). 138 regions of interest (ROI) of 50 participants (22 to 77 years old) have been analyzed, all data belonged to the Implantology graduate course of the Universidade de Santos (Unimes). Retrospective surgical data from dental implant surgeries were obtained (RF and IT) and statistically tested with ROI values achieved from DF, PI and MI of panoramic radiographs taken before and after all dental implants placement. Spearman correlation, Kruskal Wallis and Wilcoxon tests were done with the IBM SPSS Advanced Statistics ® software (IBM, USA), level of significance of 95% (p<0,05). Significant correlation was obtained between Age and DF (r=-.647) and TI and DF (r=0.434). Wilcoxon test identified significant difference (p>0,05) for related samples PI before and PI after implant (p=0,020 e 0,000) between groups 1 and 2. Possible differences were analyzed among the independent variables for groups 1 and 2 related to Age, the results showed differences between PI (p=0,046), IT (p=0,044), RF_MD (p=0,040) e RF_VL (p=0,010), between Gender the results showed differences between the variables FD (p=0,039), PI_before (p=0,001) e PI_after (p=0,033). The study concluded that PI can detect bone mineralization changes before and after dental implant placement. FD correlates with the variable IT for younger participants (22 to 45 years old). Age and Gender should be considered regarding imaging exams tests (FD and PI) for dental implant planning.

A avaliação do estado nutricional das plantas de milho usualmente é feita através de análises químicas ou pela diagnose visual das folhas da planta, esta última, sujeita a erros de interpretação já que a ausência de algum nutriente na planta gera um padrão de mudança específico na superfície da folha que depende do nível de ausência do nutriente. As dificuldades que apresentam neste processo e sua importância na agricultura, criam a necessidade de pesquisar sistemas automáticos para a avaliação do estado nutricional de plantas. Desta forma, este mestrado teve como objetivo principal o desenvolvimento de um sistema de visão artificial para verificar a possibilidade de identificação de níveis dos macronutrientes Cálcio, Enxofre, Magnésio, Nitrogênio e Potássio em plantas de milho através da análise da superfície das folhas usando métodos de visão computacional. Este projeto realiza uma revisão bibliográfica do estado da arte dos métodos de extração de características de cor, textura em escala de cinza e textura colorida utilizadas em processamento de imagens. A alta similaridade entre os sintomas produzidos pelas deficiências e a pouca similaridade entre amostras de uma mesma deficiência motivou o desenvolvimento de novos métodos de extração de características que pudessem fornecer dados necessários para uma correta separação entre as classes. Os resultados obtidos demonstraram que o sistema desenvolvido possibilita a predição de deficiências nutricionais em estágios iniciais do crescimento da planta usando unicamente a textura da superfície da folha como fonte de informação / The evaluation of the nutritional status of corn plants is usually done through chemical analysis or by visual diagnosis of the plant leaves. Visual diagnosis is subject to misinterpretation as the lack of some nutrient in the plant generates a specific pattern of change in the leaf surface that depends on the degree on which the nutrient is absent on the plant. The difficulties present in this process and its importance in agriculture creates the necessity to search automated systems for the assessment of nutritional status of plants. Thus, this dissertation had as main objective the development of an artificial vision system to verify the possibility of identifying levels of macronutrients calcium, sulfur, magnesium, potassium and nitrogen in corn plants by analyzing the surface of the leaves using computer vision methods. This project performs a review of the literature of the state of the art methods for feature extraction of color, grayscale and colored texture used in image processing. The high similarity between the symptoms caused by deficiencies and low similarity between samples of the same deficiency motivated the development of new methods for extracting features that could provide the data needed for a correct separation between classes. The results showed that the system enables the prediction of nutritional deficiencies in an initial stage of plant growth using only texture of the leaf surface as a source of information

Podemos dizer que as Catedrais Góticas, verdadeiras bíblias de pedra, são signos medievais que podem ser lidos já como o resultado da intercomunicação entre matemática-ciência-arte, uma vez que tais edificações surgiram de projeções arquitetônicas, da utilização de uma dada geometria assim como da execução de determinados conjuntos escultóricos. Podemos ainda ressaltar que essa intercomunicação se intensifica durante todo o Renascimento, exemplo máximo da união entre esses três campos do conhecimento. No Renascimento, a geometria dominante e a Euclidiana; os artistas enfrentavam as questões espaciais a partir de um ponto de vista fixo. A historia se transforma quando alguns matemáticos por volta de 1800 começam a pensar na possibilidade de outra geometria que não a de Euclides. Surge, então, um tipo de geometria que ficaria conhecida como geometria não-Euclidiana, uma geometria para ser utilizada em espaços curvos. As implicações dessa nova Geometria foram tão abrangentes que influiu na elaboração da Teoria da Relatividade, de Einstein. Um novo tipo de intercomunicação entre matemática-ciência-arte, que ajudou a resolver questões ligadas a quadrimensionalidade. Enfim, trata-se de uma intercomunicação que influenciou na produção de artistas como Picasso, Duchamp e Dali. / We can say that the Gothic Cathedral, veritable Bibles of stone, are medieval sign that can be read as a result of the intercommunication among mathematicsscience- art, since that one buildings appear from an architectonic projection, from the utilization of a given geometry just as from the execution of a group of sculpture. We can salient that this intercommunication intensifies during Renaissance, example maximum of the union among those three fields of knowledge. Into the Renaissance, the geometry dominant is the Euclidean, the artists faced the special questions from one fixed viewpoint. The story becomes different when some mathematicians around 1800 begin thinking on the possibility of another geometry that doesn\'t that of Euclids. Appears, then, a kind of geometry that would be known as non-Euclidean Geometry: a geometry to be used in curved space. The implications of that new Geometry was so in-depth that influenced the elaboration of Einsteins Relativity Theory. Therefore a new kind of intercommunication among mathematics-science-art, which it helped to resolve questions linked together to the fourth dimension. An intercommunication that influenced the production of artists like Picasso, Duchamp and Dali.

O objetivo do presente trabalho foi propor métodos de processamento de sinais e reconhecimento de padrões dos sinais de respostas de sensores de gás, utilizando técnicas e modelos da geometria fractal. Foram analisados e estudados os sinais de resposta de dois tipos de sensores. O primeiro sensor foi um dispositivo de óxido de estanho, cujo princípio de funcionamento baseia-se na mudança da resistividade do filme. Este forneceu sinais de respostas com características ruidosas como resposta à interação com as moléculas de gás. O segundo sensor foi um dispositivo Metal-Óxido-Semicondutor (MOS) com princípio de funcionamento baseado na geração de foto corrente, fornecendo respostas imagens bidimensionais. Para as análises dos sinais ruidosos do sensor de óxido de estanho, foi proposto um método de processamento baseado no modelo do movimento Browniano fracionário. Com este método foi possível a discriminação de gases combustíveis com uma taxa de acerto igual a 100%. Para as análises das respostas do tipo imagem do sensor MOS, foram propostos dois diferentes métodos. O primeiro foi embasado no princípio de compressão fractal de imagens e o segundo método proposto, foi baseado na análise e determinação da dimensão fractal multiescala. Ambos os métodos propostos mostram-se eficazes para a determinação da assinatura, como o reconhecimento, de todos os gases que foram utilizados nos experimentos. Os resultados obtidos no presente trabalho abrem novas fronteiras e perspectivas nos paradigmas de processamento de sinais e reconhecimento de padrões, quando utilizada a teoria da geometria fractal. / The aim of the present work was to propose methods for signal possessing and pattern, recognition from the signals response of gas sensors using models and techniques from the fractal geometry. The data studied and analyzed were obtained from two kinds of sensors. The first sensor was the tin oxide device, which detection principle is based on the resistivity changes of the tin oxide film and it provides noisy signals as response to the gas interaction. The second sensor was a metal-oxide-semiconductor (MOS) device, which has as the working principle the photocurrent generation. This sensor provides two-dimensional images signals. A method using a fractional Brownian motion was proposed to analyze the noise signal from the tin oxide device. The fuel gases discrimination employing this model was 100% successful. Two different methods were proposed to analyze the signal response from the MOS device. The first method was based on the fractal image compression technique and the second one was based on the analysis and determination of the multiscale fractal dimension. Both proposed methods have shown to be efficient tools for signature determination as the pattern recognition of all gases that were used in the experiment. The results obtained in the present work open new frontiers and perspectives inside the paradigms of the signal processing and pattern recognition by using the fractal theory.

Este trabalho apresenta um estudo sobre a morfologia de filmes finos de polianilina, fabricados por diferentes processos e depositados sobre diferentes substratos pela técnica de microscopia de força atômica (AFM). Os processos usados para a fabricação dos filmes foram o de espalhamento fluido, o de centrifugação, o de auto montagem e o eletroquímico. Os substratos usados foram: vidro, ouro/cromo/vidro, quartzo, ITO, silício e mica. Além da análise visual da qualidade dos filmes, ou seja, do grau de recobrimento do substrato e da uniformidade dos filmes, foram feitas análises de parâmetros quantitativos através de medidas de rugosidade. Usando modelos de crescimento como o de deposição balística e de análise de rugosidade, como o da densidade do espectro de potência, (transformada de Fourier da rugosidade da imagem em função da freqüência espectral) em superfícies auto-afins, foram obtidos parâmetros como: expoente de rugosidade, comprimento característico de correlação e dimensão fractal. Apesar dos filmes de polianilina serem sistemas extremamente complexos, - compostos de macromoléculas formando uma estrutura semicristalina - os parâmetros obtidos por esses modelos, que foram elaborados para sistemas bem mais simples, deram resultados muito bons e auto-coerentes. Como conclusão, mostramos que a conjuminação da técnica de microscopia de força atômica com esses modelos compõem um método poderoso para o estudo de filmes finos orgânicos. / This work presents a detailed study about the characteristic of thin films of polyaniline, fabricated by different methods and deposited over different substrates using Atomic Force Microscopy technique (AFM). The processes used for film depositions were casting, spin-coating, self-assembly, and the electrochemistry methods. The substrata used were: glass plates, gold/chromium/glass, quartz, ITO, silicon, and mica. Besides the visual analysis, that observes the film uniformity and verifies the coating degree of the substratum, the application of some mathematical models was employed to obtain quantitative parameters about the roughness of the film surfaces. From the ballistic deposition model, developed to explain growing processes, and the power spectrum density that takes the Fourier transform of the roughness in function of the spectral frequency, both developed for self-affine surfaces, it was obtained parameters as: the roughness exponent, the correlation characteristic length, and the fractal dimension. Despite the highly complex structure of the polyaniline - composed by macromolecules forming a semicrystalline structure- the obtained parameters by such models developed for very simple systems, provided reasonable and self-coherent results. As a final result of this work we showed that the synergy between the AFM technique and the above mentioned models compose a powerful method for the study of thin organic films.