La gravité d’Horava brise la symétrie de Lorentz avec l’introduction d’une foliation intrinsèque de l’espace-temps, définie par un champ scalaire, le khronon. Cette foliation privilégiée rend les solutions de trous noirs plus compliquées que celles de la relativité générale, due à l’apparition de nouveaux horizons: un horizon de matière pour les champs de matière; l’horizon de spin-0 pour les excitations scalaires du khronon, l’horizon de spin-2 pour les ondes gravitationnelles; finalement un horizon universel pour des modes instantanés apparaissant dans l’ultraviolet. On étudie des trous noirs en mouvement lent par rapport au référentiel privilégié. Ces solutions sont cruciales pour déterminer les susceptibilités des trous noirs et prédire leur émission d’ondes gravitationnelles, en particulier l’émission dipolaire des binaires de trous noirs. On trouve que pour des valeurs arbitraires des constantes de couplage, les trous noirs en mouvement lent souffrent de singularités de courbure à l’horizon universel. Des singularités à l’horizon de spin-0 sont aussi présentes mais peuvent être absorbées si l’on sacrifie les solutions plates à l’infini. Cependant, on a trouvé un sous-ensemble de l’espace de paramètres, de dimension un, où les trous noirs en mouvement lent sont partout réguliers et coincident avec ceux de la relativité générale. En particulier, ils n’émettent pas de radiation dipolaire. Remarquablement, ce sous-ensemble est favorisé par les contraintes récentes de l’événement GW170817 ainsi que les tests dans le système solaire. / Horava gravity breaks Lorentz symmetry by introducing a preferred spacetime foliation, which is defined by a timelike dynamical scalar field, the khronon. The presence of this preferred foliation makes black hole solutions more complicated than in General Relativity, with the appearance of multiple distinct event horizons: a matter horizon for matter fields; a spin-0 horizon for the scalar excitations of the khronon; a spin-2 horizon for tensorial gravitational waves; and even a universal horizon for instantaneously propagating modes appearing in the ultraviolet. We study how black hole solutions in Horava gravity change when the black hole is allowed to move with low velocity relative to the preferred foliation. These slowly moving solutions are a crucial ingredient to compute black hole sensitivities and predict gravitational wave emission (and particularly dipolar radiation) from the inspiral of binary black hole systems. We find that for generic values of the theory's three dimensionless coupling constants, slowly moving black holes present curvature singularities at the universal horizon. Singularities at the spin-0 horizon also arise unless one waives the requirement of asymptotic flatness at spatial infinity. Nevertheless, we find that in a one-dimensional subset of the parameter space of the theory's coupling constants, slowly moving black holes are regular everywhere, even though they coincide with the general relativistic ones (thus implying in particular the absence of dipolar gravitational radiation). Remarkably, this subset of the parameter space essentially coincides with the one selected by the recent constraints from GW170817 and by solar system tests.

Cette thèse porte sur la géométrie du champ libre Gaussien. Le champ libre Gaussien est un objet central en théorie quantique des champs et représente entre autre les fluctuations naturelles d'un potentiel électrique ou d’un modèle de dimères. La thèse commence dans le discret avec la démonstration d'un principe de Donsker en dimension plus grande que 1. Ce résultat est établi grâce à une nouvelle façon de représenter le champ libre en exprimant son gradient comme la partie gradient d'un champ de bruits blancs. Ensuite, les processus d'exploration du champ libre - ou ensembles locaux - introduits par Schramm-Sheffield sont étudiés en détail. Ces ensembles locaux généralisent de façon naturelle le concept de temps d'arrêt. On formalise cette théorie d'une nouvelle manière en procédant par analogie au cas 1D. Pour mieux comprendre le comportement du champs libre près des points d'intersection des ensembles locaux, un étude fine des oscillations du champ libre 2D près du bord s'avère utile. Enfin, la partie principale de cette thèse étudie des processus d'explorations particuliers – les processus SLE qui sont couplés naturellement avec le champ libre. On peut donner par exemple un sens aux lignes de niveau en utilisant le processus SLE_4 (Schramm-Sheffield). Nous avons utilisé ce couplage pour mieux comprendre la relation dite de KPZ qui intervient dans la théorie de la gravité quantique de Liouville. A l ‘aide de résultats fins sur l’enroulement des SLEs, nous avons montré comment adapter la relation de KPZ à la famille ci-dessus de processus d’explorations du champ libre. On peut interpréter ces résultats aussi comme une description de la géométrie du champ libre près des ces lignes d’exploration. / In this thesis we study the geometry of the Gaussian free field (GFF). After a gentle general introduction, we describe what we call the Hodge decomposition of the white noise – a way to represent the white noise vector field as a sum of a gradient and a rotation of independent GFFs. This decomposition gives rise to the Donsker invariance principle for the GFF.Next, we revisit from a slightly different angle the theory of so-called local sets of the GFF, introduced by Schramm and Sheffield. These random sets allow one to study the geometry of the GFF in a Markovian way. We also go a step further in describing the behaviour of the field near the boundary of possibly several local sets. The first chapter ends with a study of boundary oscillations of the GFF.The GFF is only a generalized function, yet it comes out that one can still make sense of it as a „random landscape“. In particular, Schramm and Sheffield gave meaning to the level lines of the GFF in terms of a coupling with SLE_4 process. In chapter 2 we study this coupling and describe the existent proofs and a non-proof of measurability of the SLE_4 process in this coupling. The rest of this chapter contains one of the most technical parts of the thesis – we obtain fine estimates on the winding of the SLE curves, conditioned to pass closely by a fixed point.This technical work is put in use in chapter 3, where we study the so called KPZ relation. In this context, the KPZ formula relates fractal dimensions of sets under the Euclidean geometry and under the „quantum geometry“ given by the exponential of the GFF. So far the KPZ formula was derived for planar sets independent of the quantum geometry. Here, we determine the KPZ formulas for sets that are naturally coupled with the quantum geometry – for the flow and level lines of the GFF. The family of KPZ formulas obtained resemble but still differ from the KPZ formula for independent sets.

We study constraints imposed on a general unitary two-dimensional conformal field theory by modular invariance. We begin with a review of previous bounds on the conformal dimension Delta1 of the lowest primary operator assuming unitarity, a discrete spectrum, modular invariance, cL, cR > 1, and no extended chiral algebra. We then obtain bounds on the conformal dimensions Delta2, Delta3 using no additional assumptions. We also show that in order to find a bound for Delta4 or higher Deltan, we need to assume a larger minimum value for ctot that grows logarithmically with n. We next extend the previous results to remove the requirement that our two-dimensional conformal field theories have no extended chiral algebra. We then show that modular invariance also implies an upper bound on the total number of states of positive energy less than ctot=24 (or equivalently, states of conformal dimension between ctot=24 and ctot=12), in terms of the number of negative energy states. Finally, we consider the case where the CFT has a gravitational dual and investigate the gravitational interpretation of our results. Using the AdS3/CFT2 correspondence, we obtain an upper bound on the lightest few massive excitations (both with and without the constraint of no chiral primary operators) in a theory of 3D matter and gravity with Lambda < 0. We show our results are consistent with facts and expectations about the spectrum of BTZ black holes in 2+1 gravity. We then discuss the upper and lower bounds on number of states and primary operators in the dual gravitational theory, focusing on the case of AdS3 pure gravity.

Thesis (MScEng)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: In this study we consider the lack of rotational invariance of three different population based optimization methods, namely the particle swarm optimization (PSO) algorithm, the differential evolution (DE) algorithm and the continuous-parameter genetic algorithm (CPGA). We then propose rotationally invariant versions of these algorithms. We start with the PSO. The so-called classical PSO algorithmis known to be variant under rotation, whereas the linear PSO is rotationally invariant. This invariance however, comes at the cost of lack of diversity, which renders the linear PSO inferior to the classical PSO. The previously proposed so-called diverse rotationally invariant (DRI) PSO is an algorithm that aims to combine both diversity and invariance. This algorithm is rotationally invariant in a stochastic sense only. What is more, the formulation depends on the introduction of a random rotation matrix S, but invariance is only guaranteed for ‘small’ rotations in S. Herein, we propose a formulation which is diverse and strictly invariant under rotation, if still in a stochastic sense only. To do so, we depart with the linear PSO, and then we add a self-scaling random vector with a standard normal distribution, sampled uniformly from the surface of a n-dimensional unit sphere. For the DE algorithm, we show that the classic DE/rand/1/bin algorithm, which uses constant mutation and standard crossover, is rotationally variant. We then study a previously proposed rotationally invariant DE formulation in which the crossover operation takes place in an orthogonal base constructed using Gramm-Schmidt orthogonalization. We propose two new formulations by firstly considering a very simple rotationally invariant formulation using constant mutation and whole arithmetic crossover. This rudimentary formulation performs badly, due to lack of diversity. We then introduce diversity into the formulation using two distinctly different strategies. The first adjusts the crossover step by perturbing the direction of the linear combination between the target vector and the mutant vector. This formulation is invariant in a stochastic sense only. We add a self-scaling random vector to the unaltered whole arithmetic crossover vector. This formulation is strictly invariant, if still in a stochastic sense only. In this study we consider the lack of rotational invariance of three different population based optimization methods, namely the particle swarm optimization (PSO) algorithm, the differential evolution (DE) algorithm and the continuous-parameter genetic algorithm (CPGA). We then propose rotationally invariant versions of these algorithms. We start with the PSO. The so-called classical PSO algorithmis known to be variant under rotation, whereas the linear PSO is rotationally invariant. This invariance however, comes at the cost of lack of diversity, which renders the linear PSO inferior to the classical PSO. The previously proposed so-called diverse rotationally invariant (DRI) PSO is an algorithm that aims to combine both diversity and invariance. This algorithm is rotationally invariant in a stochastic sense only. What is more, the formulation depends on the introduction of a random rotation matrix S, but invariance is only guaranteed for ‘small’ rotations in S. Herein, we propose a formulation which is diverse and strictly invariant under rotation, if still in a stochastic sense only. To do so, we depart with the linear PSO, and then we add a self-scaling random vector with a standard normal distribution, sampled uniformly from the surface of a n-dimensional unit sphere. For the DE algorithm, we show that the classic DE/rand/1/bin algorithm, which uses constant mutation and standard crossover, is rotationally variant. We then study a previously proposed rotationally invariant DE formulation in which the crossover operation takes place in an orthogonal base constructed using Gramm-Schmidt orthogonalization. We propose two new formulations by firstly considering a very simple rotationally invariant formulation using constant mutation and whole arithmetic crossover. This rudimentary formulation performs badly, due to lack of diversity. We then introduce diversity into the formulation using two distinctly different strategies. The first adjusts the crossover step by perturbing the direction of the linear combination between the target vector and the mutant vector. This formulation is invariant in a stochastic sense only. We add a self-scaling random vector to the unaltered whole arithmetic crossover vector. This formulation is strictly invariant, if still in a stochastic sense only. For the CPGA we show that a standard CPGA using blend crossover and standard mutation, is rotationally variant. To construct a rotationally invariant CPGA it is possible to modify the crossover operation to be rotationally invariant. This however, again results in loss of diversity. We introduce diversity in two ways: firstly using a modified mutation scheme, and secondly, following the same approach as in the PSO and the DE, by adding a self-scaling random vector to the offspring vector. This formulation is strictly invariant, albeit still in a stochastic sense only. Numerical results are presented for the variant and invariant versions of the respective algorithms. The intention of this study is not the contribution of yet another competitive and/or superior population based algorithm, but rather to present formulations that are both diverse and invariant, in the hope that this will stimulate additional future contributions, since rotational invariance in general is a desirable, salient feature for an optimization algorithm. / AFRIKAANSE OPSOMMING: In hierdie studie bestudeer ons die gebrek aan rotasionele invariansie van drie verskillende populasiegebaseerde optimeringsmetodes, met name die partikel-swerm optimerings (PSO) algoritme, die differensi¨ele evolusie (DE) algoritme en die kontinue-parameter genetiese algoritme (KPGA). Ons stel dan rotasionele invariante weergawes van hierdie algoritmes voor. Ons beginmet die PSO. Die sogenaamde klassieke PSO algoritme is bekend dat dit variant is onder rotasie, terwyl die lineˆere PSO rotasioneel invariant is. Hierdie invariansie lei tot ’n gebrek aan diversiteit in die algoritme, wat beteken dat die lineˆere PSO minder goed presteer as die klassieke PSO. Die voorheen voorgestelde sogenaamde diverse rotasionele invariante (DRI) PSO is ’n algoritme wat beoog om beide diversiteit en invariansie te kombineer. Hierdie algoritme is slegs rotasioneel invariant in ’n stogastiese sin. Boonop is die formulering afhanklik van ’n willekeurige rotasie matriks S, maar invariansie is net gewaarborg vir ’klein’ rotasies in S. In hierdie studie stel ons ’n formulering voor wat divers is en streng invariant onder rotasie, selfs al is dit steeds net in ’n stogastiese sin. In hierdie formulering, vertrek ons met die lineˆere PSO, en voeg dan ’n self-skalerende ewekansige vektor met ’n standaard normaalverdeling by, wat eenvormig van die oppervlakte van ’n n-dimensionele eenheid sfeer geneem word. Vir die DE algoritme toon ons aan dat die klassieke DE/rand/1/bin algoritme, wat gebruik maak van konstante mutasie en standaard kruising rotasioneel variant is. Ons bestudeer dan ’n voorheen voorgestelde rotasionele invarianteDE formulering waarin die kruisingsoperasie plaasvind in ’n ortogonale basis wat gekonstrueer wordmet behulp van die Gramm-Schmidt ortogonalieseringsproses. Verder stel ons dan twee nuwe formulerings voor deur eerstens ’n baie eenvoudige rotasionele invariante formulering te oorweeg, wat konstante mutasie en volledige rekenkundige kruising gebruik. Hierdie elementˆere formulering onderpresteer as gevolg van die afwesigheid van diversiteit. Ons voeg dan diversiteit by die formulering toe, deur gebruik te maak van twee afsonderlike strategie ¨e. Die eerste verander die kruisings stap deur die rigting van die lineˆere kombinasie tussen die teiken vektor en die mutasie vektor te perturbeer. Hierdie formulering is slegs invariant in ’n stogastiese sin. In die ander formulering, soos met die nuwe rotasionele invariante PSO, voeg ons bloot ’n self-skalerende ewekansige vektor by die onveranderde volledige rekenkundige kruisingsvektor. Hierdie formulering is streng invariant onder rotasie, selfs al is dit steeds net in ’n stogastiese sin. Vir die KPGA wys ons dat die standaard KPGA wat gemengde kruising en standaard mutasies gebruik, rotasioneel variant is. Om ’n rotasionele invariante KPGA te konstrueer is dit moontlik om die kruisingsoperasie aan te pas. Dit veroorsaak weereens ’n verlies aan diversiteit. Ons maak die algoritmes divers op twee verskillende maniere: eerstens deur gebruik te maak van ’n gewysigde mutasie skema, en tweedens deur die selfde aanslag te gebruik as in die PSO en die DE, deur ’n self-skalerende ewekansige vektor by die nageslag vektor te voeg. Hierdie formulering is streng invariant onder rotasie, selfs al is dit steeds net in ’n stogastiese sin. Numeriese resultate word vir die variante en invariante weergawe van die onderskeie algoritmes verskaf. Die doel van hierdie studie is nie die bydrae van bloot nog ’n kompeterend en/of beter populasiegebaseerde optimeringsmetode nie, maar eerder om formulerings voor te lê wat beide divers en invariant is, met die hoop dat dit in die toekoms bykomende bydraes sal stimuleer, omdat rotasionele invariansie in die algemeen ’n aantreklike, belangrike kenmerk is vir ’n optimerings algoritme.

Ma thèse étudie le problème de la reconnaissance des objets et des textures. Dans ce cadre, il est nécessaire de construire des représentations de signaux avec des propriétés d'invariance et de stabilité qui ne sont pas satisfaites par des approches linéaires. Les opérateurs de Scattering itèrent des décompositions en ondelettes et rectifications avec des modules complexes. Ces opérateurs définissent une transformée non-linéaire avec des propriétés remarquables ; en particulier, elle est localement invariante par translation et Lipschitz continue par rapport à l'action des difféomorphismes. De plus, les opérateurs de Scattering définissent une représentation des processus stationnaires qui capture les moments d'ordre supérieur, et qui peut être estimée avec faible variance à partir d'un petit nombre de réalisations. Dans cette thèse, nous obtenons des nouvelles propriétés mathématiques de la représentation en scattering, et nous montrons leur efficacité pour la reconnaissance des objets et textures. Grâce à sa continuité Lipschitz par rapport à l'action des difféomorphismes, la transformée en scattering est capable de linéariser les petites déformations. Cette propriété peut être exploitée en pratique avec un classificateur génératif affine, qui nous permet d'obtenir l'état de l'art sur la reconnaissance des chiffres manuscrites. Nous étudions ensuite les représentations en Scattering des textures dans le cadre des images et du son. Nous montrons leur capacité à discriminer des phénomènes non-gaussiens avec des estimateurs à faible variance, ce qui nous permet d'obtenir de l'état de l'art pour la reconnaissance des textures. Finalement, nous nous intéressons aux propriétés du Scattering pour l'analyse multifractale. Nous introduisons une renormalisation des coéfficients en Scattering qui permet d'identifier de façon efficace plusieurs paramètres multifractales; en particulier, nous obtenons une nouvelle caractérisation de l'intermittence à partir des coefficients de Scattering ré-normalisés, qui peuvent s'estimer de façon consistante.

We present an algorithm for the calculation of scalar and tensor one- and two-loop integrals that contribute to the virtual corrections of 2 →2 partonic scattering. First, the tensor integrals are related to scalar integrals that contain an irreducible propagator-like structure in the numerator. Then, we use Integration by Parts and Lorentz Invariance recurrence relations to build a general system of equations that enables the reduction of any scalar integral (with and without structure in the numerator) to a basis set of master integrals. Their expansions in e = 2-D/2 have already been calculated and we present a summary of the techniques that have been used to this end, as well as a compilation of the expansions we need in the different physical regions. We then apply this algorithm to the direct evaluation of the Feynman diagrams contributing to the O(α4/8) one- and two-loop matrix-elements for massless like and unlike quark-quark, quark-gluon and gluon-gluon scattering. The analytic expressions we provide are regularised in Convensional Dimensional Regularisation and renormalised in the MS scheme. Finally, we show that the structure of the infrared divergences agrees with that predicted by the application of Catani's formalism to the analysis of each partonic scattering process. The results presented in this thesis provide the complete calculation of the one- and two-loop matrix-elements for 2 2 processes needed for the next-to-next-to-leading order contribution to inclusive jet production at hadron colliders.

Underwater video is used by marine biologists to observe, identify, and quantify living marine resources. Video sequences are typically analyzed manually, which is a time consuming and laborious process. Automating this process will significantly save time and cost. This work proposes a technique for automatic fish classification in underwater video. The steps involved are background subtracting, fish region tracking and classification using features. The background processing is used to separate moving objects from their surrounding environment. Tracking associates multiple views of the same fish in consecutive frames. This step is especially important since recognizing and classifying one or a few of the views as a species of interest may allow labeling the sequence as that particular species. Shape features are extracted using Fourier descriptors from each object and are presented to nearest neighbor classifier for classification. Finally, the nearest neighbor classifier results are combined using a probabilistic-like framework to classify an entire sequence. The majority of the existing pattern matching techniques focus on affine invariance, mainly because rotation, scale, translation and shear are common image transformations. However, in some situations, other transformations may be modeled as a small deformation on top of an affine transformation. The proposed algorithm complements the existing Fourier transform-based pattern matching methods in such a situation. First, the spatial domain pattern is decomposed into non-overlapping concentric circular rings with centers at the middle of the pattern. The Fourier transforms of the rings are computed, and are then mapped to polar domain. The algorithm assumes that the individual rings are rotated with respect to each other. The variable angles of rotation provide information about the directional features of the pattern. This angle of rotation is determined starting from the Fourier transform of the outermost ring and moving inwards to the innermost ring. Two different approaches, one using dynamic programming algorithm and second using a greedy algorithm, are used to determine the directional features of the pattern.

Neste trabalho, discutem-se aspectos das transformações conformes na eletrodinâmica clássica com ênfase na invariância e nas leis de conservação. Inicialmente, abordaram-se aspectos gerais das transformações conformes e fez-se um resumo histórico da evolução dessas transformações. Procurou-se fazer uma apresentação didática, revisando-se a formulação Lagrangiana e o Teorema de Noether para campos aplicado à eletrodinâmica. Estudaram-se as transformações conformes no espaço plano, onde se mostrou que para dimensões maiores ou iguais a três o número de transformações é finito. A partir das equações de Maxwell em coordenadas curvilíneas, chegou-se à condição para que essas equações mantivessem sua forma cartesiana. Com essa condição, mostrou-se que a eletrodinâmica clássica é invariante para o grupo de transformações conformes. Foram discutidas as leis de conservação associadas à invariância conforme da eletrodinâmica clássica a partir do teorema de Noether. Das simetrias por translações no espaço-tempo, obtiveram-se as leis de conservação do momento linear e da energia. Das simetrias associadas às rotações, obtiveram-se seis quantidades conservadas: três delas ligadas à conservação do momento angular e, com relação às três restantes, observou-se, a partir de analogias com a mecânica, que estavam associadas ao movimento do centro de energia do campo. Para a interpretação da grandeza conservada por simetria de escala, verificou-se, também a partir de uma analogia mecânica, que essa simetria somente é verificada para partículas não massivas ou para partículas massivas a altas energias. Finalmente, para as transformações conformes especiais, verificou-se que as leis de conservação resultantes são consequências das leis anteriores de conservação para o campo eletromagnético, e neste caso, essa simetria também somente se manifesta para partículas de massa nula ou para altas energias. / In this work, aspects of conformal transformations in classical electrodynamics are discussed with emphasis on the invariance and conservation laws. Initially, a general view of conformal transformations was shown and a summary of the historical evolution of those transformations was presented. The work was approached didactically, and Noethers theorem based on the electrodynamics Lagrangian formulation was revised. The conformal transformations were studied in plane spaces and it was shown that, for dimensions greater than or equal to three, the number of transformations is finite. Starting from Maxwells equations in curvilinear coordinates, a condition for maintaining those equations in Cartesian form was established. With that condition, it was shown that the classical electrodynamics laws are invariant for the group of conformal transformations. The conservation laws associated with the conformal invariance of classical electrodynamics were discussed, based on Noethers theorem. From the space-time translation symmetry, the laws of conservation of linear momentum and of energy were obtained. From rotational symmetry, six conserved quantities were obtained: three of them associated with angular momentum and the remaining three, observed, starting from analogies with mechanics, were associated with the movement of the center of energy of the field. For the interpretation of the quantity conserved by scale symmetry, it was verified, also from a mechanical analogy, that that symmetry is only valid for null mass particles or for high energies. Finally, for the special conformal transformations, it was verified that the resultant laws of conservation are consequences of the previous laws, and in that case, symmetry is also valid only for particles of null mass or for high energies.

Reconhecimento de padrões em imagens é um problema clássico da área de visão computacional e consiste em detectar um padrão ou objeto de referência (template) em uma imagem digital. A maioria dos métodos para esta finalidade propostos na literatura simplifica as imagens por meio de operações como binarização, segmentação e detecção de bordas ou pontos de contorno, para em seguida extrair um conjunto de atributos descritores. O problema é que esta simplificação pode descartar informações importantes para descrição dos padrões, fazendo diminuir a robustez do processo de detecção. Um método eficiente deve ter a habilidade de identificar um padrão sujeito a algumas transformações geométricas como rotação, escalonamento, translação, cisalhamento e, no caso de métodos para imagens coloridas, deve ainda tratar do problema da constância da cor. Além disso, o conjunto de atributos que descrevem um padrão deve ser pequeno o suficiente para viabilizar o desenvolvimento de aplicações práticas como um sistema de visão robótica ou um sistema de vigilância. Estes são alguns dos motivos que justificam os esforços empreendidos nos inúmeros trabalhos desta natureza encontrados na literatura. Neste trabalho é proposto um método de casamento de padrões em imagens digitais, denominado Ciratefi (Circular, Radial and Template-Matching Filter), livre de segmentação e invariante sob transformações de similaridade, brilho e contraste. O Ciratefi consiste de três etapas de filtragem que sucessivamente descartam pontos na imagem analisada que não correspondem ao padrão procurado. Também foram propostas duas extensões do Ciratefi, uma que utiliza operadores morfológicos na extração dos atributos descritores, denominada Ciratefi Morfológico e outra para imagens coloridas chamada de color Ciratefi. Foram realizados vários experimentos com o intuito de comparar o desempenho do método proposto com dois dos principais métodos encontrados na literatura. Os resultados experimentais mostram que o desempenho do Ciratefi é superior ao desempenho dos métodos empregados na análise comparativa. / Pattern recognition in images is a classical problem in computer vision. It consists in detecting some reference pattern or template in a digital image. Most of the existing pattern recognition techniques usually apply simplifications like binarization, segmentation, interest points or edges detection before extracting features from images. Unfortunately, these simplification operations can discard rich grayscale information used to describe the patterns, decreasing the robustness of the detection process. An efficient method should be able to identify a pattern subject to some geometric transformations such as translation, scale, rotation, shearing and, in the case of color images, should deal with the color constancy problem. In addition, the set of features that describe a pattern should be sufficiently small to make feasible practical applications such as robot vision or surveillance system. These are some of the reasons that justify the effort for development of many works of this nature found in the literature. In this work we propose a segmentation-free template matching method named Ciratefi (Circular, Radial and Template-Matching Filter) that is invariant to rotation, scale, translation, brightness and contrast. Ciratefi consists of three cascaded filters that successively exclude pixels that have no chance of matching the template from further processing. Also we propose two extensions of Ciratefi, one using the mathematical morphology approach to extract the descriptors named Morphological Ciratefi and another to deal with color images named Color Ciratefi. We conducted various experiments aiming to compare the performance of the proposed method with two other methods found in the literature. The experimental results show that Ciratefi outperforms the methods used in the comparison analysis.

Nesta tese estudamos as propriedades críticas dos modelos anisotrópicos (isotrópicos) de Heisenberg com spin s arbitrário. O espectro das Hamiltonianas, com condições periódicas de contorno, foi calculado para redes finitas, resolvendo-se as equações do Bethe ansatz associadas. Nossos resultados indicam que a anomalia conforme destes modelos tem o valor c=3s/(1+s), independente da anisotropia, e os expoentes críticos variam continuamente com a anisotropia assim como no modelo de 8-vértices. O conteúdo de operadores destes modelos indica que a teoria de campos que governa a criticalidade destes modelos de spin é descrita por operadores formados pelo produto de um operador Gaussiano por outro com simetria Z(2s). Estudando estes modelos, com certas condições especiais de contorno, mostramos que eles são relacionados com uma nova classe de teorias unitárias recentemente propostas / This thesis is concerned with the critical properties of anisotropic (isotropic) Heisenberg chain,with arbitrary spin-s. The eigenspectrum of these Hamiltoniana, with periodic boundaries, are calculated for finite chains by solving numerically their associated Bethe ansatz equations. The results indicate that the conformal anomaly hás the value c=3s/1+s, independently of the anisotropy, and the exponentes vary continuously with the anisotropy like in the 8-vertex model. The operator content of these models indicate that the underlying field theory governing these critical spin-s models are described by composite fields formed by the product of Gaussian and Z(2s) fields. Studying these models, with some special boundary conditions, we show that they are related with a large class of unitary conformal field theories recntly introduced