Modeling of electromagnetic wave propagation in terms of Gaussian beams (GBs) has been considered in recent years. The incident radiation is expanded in terms of GBs by means of the point matching method. The simultaneous equations can be solved directly to produce excitation coefficients that generate the approximate pattern of a known antenna. Two different types of antenna patterns have been approximated in terms of GBs: a truncated antenna pattern and a hyperbolic antenna pattern. The influence of the Gaussian beam parameters on the approximation process is clarified.

This thesis presents there important results in visual object recognition based on shape. (1) A new algorithm (RAST; Recognition by Adaptive Sudivisions of Tranformation space) is presented that has lower average-case complexity than any known recognition algorithm. (2) It is shown, both theoretically and empirically, that representing 3D objects as collections of 2D views (the "View-Based Approximation") is feasible and affects the reliability of 3D recognition systems no more than other commonly made approximations. (3) The problem of recognition in cluttered scenes is considered from a Bayesian perspective; the commonly-used "bounded-error errorsmeasure" is demonstrated to correspond to an independence assumption. It is shown that by modeling the statistical properties of real-scenes better, objects can be recognized more reliably.

The topic of antenna pattern synthesis, in the context of beam shaping, is considered. One approach to this problem is to use the method of point matching. This method can be used to approximate antenna patterns with a set of uniformly spaced sources with suitable directivities. One specifies a desired antenna pattern and approximates it with a combination of beams. This approach results in a linear system of equations that can be solved for a set of beam coefficients. With suitable shifts between the matching points and between the source points, a good agreement between the assumed and the reproduced antenna patterns can be obtained along an observation line. This antenna modelling could be used in the program NERO to compute the field at the receiver antenna for a realistic 2D communication link. It is verified that the final result is not affected by the details of the antenna modelling.

The aim of this thesis is to familiarize with the issue of registration of medical image sequences. The main objective was to focus on the method of feature tracking in the image and various options of its implementation. The theoretical part describes various methods for detection of feature points and future point matching methods. In the practical part these methods were implemented in Matlab programming environment and a simple graphical user interface was created.

O registro de imagens tem um papel importante em várias aplicações, tais como reconstrução de objetos 3D, reconhecimento de padrões, imagens microscópicas, entre outras. Este registro é composto por três passos principais: (1) seleção de pontos de interesse; (2) extração de características dos pontos de interesse; (3) correspondência entre os pontos de interesse de uma imagem para a outra. Para os passos 1 e 2, algoritmos como SIFT e SURF têm apresentado resultados satisfatórios. Entretanto, para o passo 3 ocorre a presença de outliers, ou seja, pontos de interesse que foram incorretamente correspondidos. Uma única correspondência incorreta leva a um resultado final indesejável. Os algoritmos para remoção de outliers (consenso) possuem um alto custo computacional, que cresce à medida que a quantidade de outliers aumenta. Com o objetivo de reduzir o tempo de processamento necessário por esses algoritmos, o algoritmo FOMP(do inglês, Filtering out Outliers from Matched Points), foi proposto e desenvolvido neste trabalho para realizar a filtragem de outliers no conjunto de pontos inicialmente correspondidos. O método FOMP considera cada conjunto de pontos como um grafo completo, no qual os pesos são as distâncias entre os pontos. Por meio da soma de diferenças entre os pesos das arestas, o vértice que apresentar maior valor é removido. Para validar o método FOMP, foram realizados experimentos utilizando quatro bases de imagens. Cada base apresenta características intrínsecas: (a) diferenças de rotação zoom da câmera; (b) padrões repetitivos, os quais geram duplicidade nos vetores de características; (c) objetos de formados, tais como plásticos, papéis ou tecido; (d) transformações afins (diferentes pontos de vista). Os experimentos realizados mostraram que o filtro FOMP remove mais de 65% dos outliers, enquanto mantém cerca de 98%dos inliers. A abordagem proposta mantém a precisão dos métodos de consenso, enquanto reduz o tempo de processamento pela metade para os métodos baseados em grafos. / Image matching plays a major role in many applications, such as pattern recognition and microscopic imaging. It encompasses three steps: 1) interest point selection; 2) feature extraction from each point; 3) feature point matching. For steps 1 and 2, traditional interest point detectors/ extractors have worked well. However, for step 3 even a few points incorrectly matched (outliers), might lead to an undesirable result. State-of-the-art consensus algorithms present a high time cost as the number of outlier increases. Aiming at overcoming this problem, we present FOMP, a preprocessing approach, that reduces the number of outliers in the initial set of matched points. FOMP filters out the vertices that present a higher difference among their edges in a complete graph representation of the points. To validate the proposed method, experiments were performed with four image database: (a) variations of rotation or camera zoom; (b) repetitive patterns, which leads to duplicity of features vectors; (c) deformable objects, such as plastics, clothes or papers; (d) affine transformations (different viewpoint). The experimental results showed that FOMP removes more than 65% of the outliers, while keeping over 98% of the inliers. Moreover, the precision of traditional methods is kept, while reducing the processing time of graph based approaches by half.

Making a computer &lsquo / see&rsquo / is certainly one of the greatest challanges for today. Apart from possible applications, the solution may also shed light or at least give some idea on how, actually, the biological vision works. Many problems faced en route to successful algorithms require finding corresponding tokens in different views, which is termed the correspondence problem. For instance, given two images of the same scene from different views, if the camera positions and their internal parameters are known, it is possible to obtain the 3-Dimensional coordinates of a point in space, relative to the cameras, if the same point may be located in both images. Interestingly, the camera positions and internal parameters may be extracted solely from the images if a sufficient number of corresponding tokens can be found. In this sense, two subproblems, as the choice of the tokens and how to match these tokens, are examined. Due to the arbitrariness of the image pairs, invariant schemes for extracting and matching interest points, which were taken as the tokens to be matched, are utilised. In order to appreciate the ideas of the mentioned schemes, topics as scale-space, rotational and affine invariants are introduced. The geometry of the problem is briefly reviewed and the epipolar constraint is imposed using statistical outlier rejection methods. Despite the satisfactory matching performance of simple correlation-based matching schemes on small-baseline pairs, the simulation results show the improvements when the mentioned invariants are used on the cases for which they are strictly necessary.

O registro de imagens tem um papel importante em várias aplicações, tais como reconstrução de objetos 3D, reconhecimento de padrões, imagens microscópicas, entre outras. Este registro é composto por três passos principais: (1) seleção de pontos de interesse; (2) extração de características dos pontos de interesse; (3) correspondência entre os pontos de interesse de uma imagem para a outra. Para os passos 1 e 2, algoritmos como SIFT e SURF têm apresentado resultados satisfatórios. Entretanto, para o passo 3 ocorre a presença de outliers, ou seja, pontos de interesse que foram incorretamente correspondidos. Uma única correspondência incorreta leva a um resultado final indesejável. Os algoritmos para remoção de outliers (consenso) possuem um alto custo computacional, que cresce à medida que a quantidade de outliers aumenta. Com o objetivo de reduzir o tempo de processamento necessário por esses algoritmos, o algoritmo FOMP(do inglês, Filtering out Outliers from Matched Points), foi proposto e desenvolvido neste trabalho para realizar a filtragem de outliers no conjunto de pontos inicialmente correspondidos. O método FOMP considera cada conjunto de pontos como um grafo completo, no qual os pesos são as distâncias entre os pontos. Por meio da soma de diferenças entre os pesos das arestas, o vértice que apresentar maior valor é removido. Para validar o método FOMP, foram realizados experimentos utilizando quatro bases de imagens. Cada base apresenta características intrínsecas: (a) diferenças de rotação zoom da câmera; (b) padrões repetitivos, os quais geram duplicidade nos vetores de características; (c) objetos de formados, tais como plásticos, papéis ou tecido; (d) transformações afins (diferentes pontos de vista). Os experimentos realizados mostraram que o filtro FOMP remove mais de 65% dos outliers, enquanto mantém cerca de 98%dos inliers. A abordagem proposta mantém a precisão dos métodos de consenso, enquanto reduz o tempo de processamento pela metade para os métodos baseados em grafos. / Image matching plays a major role in many applications, such as pattern recognition and microscopic imaging. It encompasses three steps: 1) interest point selection; 2) feature extraction from each point; 3) feature point matching. For steps 1 and 2, traditional interest point detectors/ extractors have worked well. However, for step 3 even a few points incorrectly matched (outliers), might lead to an undesirable result. State-of-the-art consensus algorithms present a high time cost as the number of outlier increases. Aiming at overcoming this problem, we present FOMP, a preprocessing approach, that reduces the number of outliers in the initial set of matched points. FOMP filters out the vertices that present a higher difference among their edges in a complete graph representation of the points. To validate the proposed method, experiments were performed with four image database: (a) variations of rotation or camera zoom; (b) repetitive patterns, which leads to duplicity of features vectors; (c) deformable objects, such as plastics, clothes or papers; (d) affine transformations (different viewpoint). The experimental results showed that FOMP removes more than 65% of the outliers, while keeping over 98% of the inliers. Moreover, the precision of traditional methods is kept, while reducing the processing time of graph based approaches by half.

In this thesis, a pipeline for structure-from-motion with mixed camera types is described and methods for the steps of this pipeline to make it effective and automatic are proposed. These steps can be summarized as calibration, feature point matching, epipolar geometry and pose estimation, triangulation and bundle adjustment. We worked with catadioptric omnidirectional and perspective cameras and employed the sphere camera model, which encompasses single-viewpoint catadioptric systems as well as perspective cameras. For calibration of the sphere camera model, a new technique that has the advantage of linear and automatic parameter initialization is proposed. The projection of 3D points on a catadioptric image is represented linearly with a 6x10 projection matrix using lifted coordinates. This projection matrix is computed with an adequate number of 3D-2D correspondences and decomposed to obtain intrinsic and extrinsic parameters. Then, a non-linear optimization is performed to refine the parameters. For feature point matching between hybrid camera images, scale invariant feature transform (SIFT) is employed and a method is proposed to improve the SIFT matching output. With the proposed approach, omnidirectional-perspective matching performance significantly increases to enable automatic point matching. In addition, the use of virtual camera plane (VCP) images is evaluated, which are perspective images produced by unwarping the corresponding region in the omnidirectional image. The hybrid epipolar geometry is estimated using random sample consensus (RANSAC) and alternatives of pose estimation methods are evaluated. A weighting strategy for iterative linear triangulation which improves the structure estimation accuracy is proposed. Finally, multi-view structure-from-motion (SfM) is performed by employing the approach of adding views to the structure one by one. To refine the structure estimated with multiple views, sparse bundle adjustment method is employed with a modification to use the sphere camera model. Experiments on simulated and real images for the proposed approaches are conducted. Also, the results of hybrid multi-view SfM with real images are demonstrated, emphasizing the cases where it is advantageous to use omnidirectional cameras with perspective cameras.

Atmospheric nucleation is a process of phase transformation like liquid water transforming into solid or gas phase water, which serves as a significant impact on many atmospheric and technological processes. During the process of the atmospheric nucleation, certain 3D molecular models for atmospheric nucleation will be generated, which are main mixtures of water molecules and hexanol molecules. Analyzing these 3D molecular models can promote the understanding for the nucleation and growth of the particles and phases in a multi-component mixture, as well as for the changes in climate and weather. Therefore, the research for atmospheric nucleation can be transformed into the research for the 3D molecular visualizations and comparisons, which are the similarity calculations. Unfortunately, the research on understanding atmospheric nucleation processes is restricted due to the lack of efficient visual data exploration tools. In this paper, the issue of lacking efficient data visualization tools is tackled by implementing our own application to visualize the atmospheric nucleation. The similarity calculation for these 3D molecules is implemented in order to analyze and compare the atmospheric nucleation processes and molecular models. Admittedly, there are various 3D molecular similarity calculation algorithms, such as clique-detection algorithms and point matching, etc; however, these algorithms are specifically utilized in the fields of protein amino-acids and pharmacophore. Due to the large scale of the atmospheric nucleation data, GPU (Graphical Processing Units) is employed in order to significantly reduce the computation times. This is achieved by utilizing CUDA (Compute Uniform Device Architecture) technology which allows us to execute our algorithm in a parallel method. Furthermore, in this research, the knowledge of hypertree visualization is intended to be utilized to enhance the previously developed web-based visualization and analysis tool that allows remote users to effectively mine the wealth of particle-based nucleation simulation data. The research goal is to speed up knowledge discovery and improve users' productivity through effective data visualization technique and more friendly user interface design. Meanwhile, a feasible parallel computing solution is developed to overcome the slow response due to expensive large data pre-processing. The core research of my thesis is to calculate the similarity between the distinct 3D molecules.

[pt] Esta tese apresenta um estudo sobre métodos semianalíticos para modelagem de guias de ondas com contornos complexos. Os campos eletromagnéticos dentro de meios não homogêneos e anisotrópicos são resolvidos por meio de harmônicos cilíndricos como base para outras abordagens numéricas, como o método de perturbação regular (RPM), o método de perturbação de material em cavidade (CMPM) e o método de casamento de pontos (PMM). As novas soluções semianalíticas que exploramos aqui podem ser empregadas para a análise de comunicação sem fio ao longo de túneis, bem como para a modelagem de sensores realistas de perfilagem durante a perfuração em problemas geofísicos de baixa frequência. Estudamos o potencial do RPM ao combiná-lo com os princípios da transformação óptica (TO) para analisar um guia de onda coaxial excêntrico preenchido com materiais anisotrópicos. Além disso, estendemos o CMPM clássico proposto por Harrington para lidar com meios anisotrópicos para resolver os números de onda de corte dos campos modais no mesmo guia de onda de maneira aproximada, mas numericamente eficiente. Outra solução de perturbação é proposta combinando as correções de baixa ordem do RPM no CMPM para fornecer correções de alta ordem para os números de onda de corte dos modos suportados pelo guia. Uma formulação matemática de um método semianalítico baseado em PMM para resolver guias de onda preenchidos com meios anisotrópicos e com camadas arbitrárias também é apresentada. Uma versão melhorada deste método é introduzida para modelar estruturas guiadas cilíndricas de múltiplas camadas não circulares. Essas soluções baseadas em casamento de pontos representam boas alternativas para abordagens de força bruta, como métodos de elementos finitos e de diferenças finitas. / [en] This thesis presents a study on semi-analytic methods for modeling waveguides with complex-shaped boundaries. The electromagnetic fields inside inhomogeneous and anisotropic media are solved via cylindrical harmonics as a basis for other numerical approaches, including the regular perturbation method (RPM), the cavity-material perturbation method (CMPM), and the point-matching method (PMM). The novel semi-analytic solutions we have explored here can be employed for the analysis of wireless communication along tunnels and boreholes as well as for the modeling of realistic logging-whiledrilling (LWD) sensors and their environments at low-frequency geophysical problems. We studied the potential of the RPM when combining it with the transformation optics (TO) principles to analyze an eccentric coaxial waveguide filled with anisotropic materials. Furthermore, we have extended the classical CMPM proposed by Harrington to handling anisotropic media for solving the cutoff wavenumbers of the modal fields in the same eccentric coaxial waveguide in an approximated but numerically efficient manner. Another perturbation solution is proposed here and combines the low-order corrections from RPM into the CMPM for providing high-order corrections to the cutoff wavenumbers of the modes supported in this guide. A mathematical formulation of a semi-analytic point-matching method for solving more complex anisotropic-filled waveguides with an arbitrary number of layers is also presented. An improved version of this method is introduced for modeling noncircular multi-layered cylindrical guided structures. Such point-matching-based solutions represent good alternatives to brute-force approaches such as finiteelement and finite-difference methods and motivate further investigations. We present a series of validation results showing the accuracy, efficiency, and potential limitations of the explored methods.