Submitted by Kamila Costa (kamilavasconceloscosta@gmail.com) on 2015-06-17T20:37:08Z No. of bitstreams: 1 Dissertação-Andrea M da Mota.pdf: 827395 bytes, checksum: 3b513795b0e557b49dc4814527d37611 (MD5) / Approved for entry into archive by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2015-06-19T14:12:03Z (GMT) No. of bitstreams: 1 Dissertação-Andrea M da Mota.pdf: 827395 bytes, checksum: 3b513795b0e557b49dc4814527d37611 (MD5) / Approved for entry into archive by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2015-06-19T14:14:29Z (GMT) No. of bitstreams: 1 Dissertação-Andrea M da Mota.pdf: 827395 bytes, checksum: 3b513795b0e557b49dc4814527d37611 (MD5) / Made available in DSpace on 2015-06-19T14:14:29Z (GMT). No. of bitstreams: 1 Dissertação-Andrea M da Mota.pdf: 827395 bytes, checksum: 3b513795b0e557b49dc4814527d37611 (MD5) Previous issue date: 2014-09-15 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The objective of this notes is to prove in detail a theorem, due to Ernst Heintze and Hermann Karcher, establishing an upper bound for the volume of compact domains in a connected closed hypersurface immersed in Euclidean space E. As application we will give an alternative proof of the Alexandrov’s theorem, which states that the Euclidean spheres are the only embedded closed hypersurfaces of constant mean curvature in E. / O objetivo deste trabalho é demonstrar em detalhes um teorema devido a Ernst Heintze e Hermann Karcher que estabelece uma cota superior para o volume de domínios compactos em uma hipersuperfície conexa, fechada e mergulhada no espaço euclidiano E. Como aplicação será dada uma prova alternativa do Teorema de Alexandrov, que caracteriza as esferas euclidianas como as únicas hipersuperfícies conexas, fechadas e mergulhadas de curvatura média constante em E.

Este trabalho mostra que a suavização Gaussiana pode exercer outra função além da filtração. Considerando-se imagens binárias, este processo pode funcionar como uma espécie de marcador, que modifica as feições das fronteiras entre duas regiões homogêneas contrastantes. Tais feições são pontos de concavidades, de convexidades ou de bordas em linha reta. Ou seja, toda a informação necessária para se caracterizar a forma bidimensional de uma região. A quantidade de suavização realizada em cada ponto depende da configuração preto/branco que compõe a vizinhança onde este se situa. Isto significa que cada ponto sofre uma quantidade particular de modificação, a qual reflete a interface local entre o objeto e o fundo. Então, para detectar tais feições, basta quantificar a suavização em cada ponto. No entanto, a discriminação pixel a pixel exige que a distribuição Gaussiana apresente boa localização, o que só acontece em escalas muito baixas (σ≅0,5). Assim, propõe-se uma distribuição construída a partir da soma de duas Gaussianas. Uma é bem estreita para garantir a boa localização e a outra possui abertura irrestrita para representar a escala desejada. Para confirmar a propriedade de marcação dessa distribuição, são propostos três detectores de corners de contorno, os quais são aplicados à detecção de pontos dominantes. O primeiro utiliza a entropia de Shannon para quantificar a suavização em cada ponto. O segundo utiliza as probabilidades de objeto e de fundo contidos na vizinhança observada. O terceiro utiliza a diferença entre Gaussianas (DoG) para determinar a quantidade suavizada, porém com a restrição de que uma das versões da imagem tenha suavização desprezível, para garantir a boa localização. Este trabalho se fundamenta na física da luz e na visão biológica. Os ótimos resultados apresentados sugerem que a detecção de curvaturas do sistema visual pode ocorrer na retina. / This work shows that the Gaussian smoothing can have additional function to filtration. Considering the binary images, this process can operate as a kind of marker that changes the features of the boundaries between two contrasting homogeneous regions. These features are points of concavities, convexities or straight edges, which are all the necessary information to characterize the two-dimensional shape of a region. The amount of smoothing performed at each point depends on the black/white configuration that composes the neighborhood where the point is located. This means that each point suffers a particular modification, which reflects the local interface between object and background. Thus, to detect such features, one must quantify the smoothing at each point. However, pixel-wise discrimination requires that the Gaussian distribution does not suffer flattening, which occurs in very low scales (σ≅0.5), only. Thus, it is proposed a distribution built from the sum of two Gaussians. One must be very narrow to ensure good localization, and the other is free to represent the desired scale. To confirm the property of marking, three boundary based corner detectors are proposed, which are applied to the detection of dominant points. The first uses the Shannon\'s entropy to quantify the smoothing at each point. The second uses the probabilities of object and background contained in the local neighborhood. The third uses the difference of Gaussians (DoG) to determine the amount of smoothing. This Work relies on the physics of light and biological vision. The presented results are good enough to suggest that the curvature detection, in visual system, occurs in the retina.

In this thesis we prove the genericity of the set of metrics on a manifold with boundary M^{n+1}, such that all free boundary constant mean curvature (CMC) embeddings \\varphi: \\Sigma^n \\to M^{n+1}, being \\Sigma a manifold with boundary, are non-degenerate (Bumpy Metrics), (Theorem 2.4.1). We also give sufficient conditions to obtain a free boundary CMC deformation of a CMC inmersion (Theorems 3.2.1 and 3.2.2), and a stability criterion for this type of immersions (Theorem 3.3.3 and Corollary 3.3.5). In addition, given a one-parametric family, {\\varphi _t : \\Sigma \\to M} , of free boundary CMC immersions, we give criteria for the existence of smooth bifurcated branches of free boundary CMC immersions for the family {\\varphi_t}, via the implicit function theorem when the kernel of the Jacobi operator J is non-trivial, (Theorems 4.2.3 and 4.3.2), and we study stability and instability problems for hypersurfaces in this bifurcated branches (Theorems 5.3.1 and 5.3.3). / Nesta tese, provamos a genericidade do conjunto de métricas em uma variedade com fronteira M^{n+1}, de modo que todos os mergulhos de curvatura média constante (CMC) e fronteira livre \\varphi : \\Sigma^n \\to M^{n+1}, sendo \\Sigma uma variedade com fronteira, sejam não-degenerados (Métricas Bumpy), (Teorema 2.4.1). Nós também fornecemos condições suficientes para obter uma deformação CMC e fronteira livre de uma imersão CMC (Teoremas 3.2.1 and 3.2.2), e um critério de estabilidade para este tipo de imersões (Teorema 3.3.3 and Corolario 3.3.5). Além disso, dada uma família 1-paramétrica, {\\varphi _t : \\Sigma \\to M} , de imersões de CMC e fronteira livre, damos os critérios para a existência de ramos de bifurcação suaves de imersões CMC e fronteira livre para a familia {\\varphi_t}, por meio de o teorema da função implícita quando o kernel do operador Jacobi J é não-trivial, (Teoremas 4.2.3 and 4.3.2), e estudamos o problema da estabilidade e instabilidade para hipersuperfícies em naqueles ramos de bifurcação (Teoremas 5.3.1 and 5.3.3).

A identificação de observações influentes e/ou aberrantes de um conjunto de dados é conhecida como uma parte das análises de diagnóstico. Esta técnica de diagnóstico têm como uma das finalidades verificar a robustez de um modelo estatístico, pois a não identificação dos dados influentes pode afetar a análise ou obter resultados incorretos. As metodologias comumente utilizadas para o diagnóstico de observações influentes em modelos de regressão são métodos de influência global (Belsey et al., 1980). Cook (1986) introduziu um método geral para avaliar a influência local de pequenas perturbações no modelo estatístico ou nos dados, usando diferentes tipos de perturbações. Como complemento às técnicas de detecção de observações discrepantes, é proposto o método procura \\forward\", por Atkinson e Riani (2000), que é uma metodologia para detectar observações atípicas mascaradas. Neste trabalho, propomos o uso da influência local com procura \"forward\" na obtenção de observações mascaradas influentes considerando modelos de regressão linear. / The identification of influential and/or atypical observations in a data set is known as a part of the diagnostic analysis. One of the purposes of the diagnostic analysis is to verify the robustness of a statistical model, as the non-identification of influential observations can affect the analysis or may cause the obtainment of incorrect results. The most commonly used methodology for the diagnostic of influential observations in regression models are the global influence (Belsey et al., 1980). Cook (1986) introduced a general method to evaluate the local influence of small perturbations in the statistical model or in the data set using different perturbation schemes. As a complement to the techniques of detection atypical observations, it is proposed the forward search procedure by Atkinson e Riani (2000), which is a methodology to detect the masked atypical observations in a data set. In this work we propose the use of the local influence approach together with the forward search to obtain the masked influential observations in linear regression models.

The objective of this dissertation is to provide a new design approach to a fully automated book reader for individuals with visual impairment and blindness that is portable and cost effective. This approach relies on the geometry of the design setup and provides the mathematical foundation for integrating, in a unique way, a 3-D space surface map from a low-resolution time of flight (ToF) device with a high-resolution image as means to enhance the reading accuracy of warped images due to the page curvature of bound books and other magazines. The merits of this low cost, but effective automated book reader design include: (1) a seamless registration process of the two imaging modalities so that the low resolution (160 x 120 pixels) height map, acquired by an Argos3D-P100 camera, accurately covers the entire book spread as captured by the high resolution image (3072 x 2304 pixels) of a Canon G6 Camera; (2) a mathematical framework for overcoming the difficulties associated with the curvature of open bound books, a process referred to as the dewarping of the book spread images, and (3) image correction performance comparison between uniform and full height map to determine which map provides the highest Optical Character Recognition (OCR) reading accuracy possible. The design concept could also be applied to address the challenging process of book digitization. This method is dependent on the geometry of the book reader setup for acquiring a 3-D map that yields high reading accuracy once appropriately fused with the high-resolution image. The experiments were performed on a dataset consisting of 200 pages with their corresponding computed and co-registered height maps, which are made available to the research community (cate-book3dmaps.fiu.edu). Improvements to the characters reading accuracy, due to the correction steps, were quantified and measured by introducing the corrected images to an OCR engine and tabulating the number of miss-recognized characters. Furthermore, the resilience of the book reader was tested by introducing a rotational misalignment to the book spreads and comparing the OCR accuracy to those obtained with the standard alignment. The standard alignment yielded an average reading accuracy of 95.55% with the uniform height map (i.e., the height values of the central row of the 3-D map are replicated to approximate all other rows), and 96.11% with the full height maps (i.e., each row has its own height values as obtained from the 3D camera). When the rotational misalignments were taken into account, the results obtained produced average accuracies of 90.63% and 94.75% for the same respective height maps, proving added resilience of the full height map method to potential misalignments.

Stress-strain relations for unconfined and confined concrete are proposed to overcome some shortcomings of existing commonly used models. Specifically, existing models are neither easy to invert nor integrate to obtain equivalent rectangular stress-block parameters for hand analysis and design purposes. The stress?strain relations proposed are validated for a whole range of concrete strengths and confining stresses. Then, closed form expressions are derived for the equivalent rectangular stress-block parameters. The efficacy of the results is demonstrated for hand analysis applied for deriving the moment-curvature performance of a confined concrete column. Results are compared with those obtained from a computational fiber-element using the proposed stress-strain model and another widely used model; good agreement between the two is observed. The model is then utilized in the development of a new structural system that utilizes the positive attributes of timber and concrete to form a parallel. Timber has the advantage of being a light weight construction material, easy to handle, is environmentally friendly. However, large creep deflections and significant issues with sound transmission (the footfall problem) generally limit timber use to small spans and low rise buildings. Concrete topping on timber sub-floors mitigate some of these issues, but even with well engineered wood systems, the spans are relatively short. In this study, a new structural system called structural boxed-concrete, which utilizes the positive attributes of both timber and reinforced concrete to form a parallel system (different from timber-concrete composite system) is explored. A stress-block approach is developed to calculate strength and deformation. An analytical stress-block based moment-curvature analysis is performed on the timber-boxed concrete structural elements. Results show that the structural timber-boxed concrete members may have better strength and ductility capacities when compared to an equivalent ordinary reinforced concrete member.

Shear-wall dominant multi-story reinforced concrete structures, constructed by using a special tunnel form technique are commonly built in countries facing a substantial seismic risk, such as Chile, Japan, Italy and Turkey. In 1999, two severe urban earthquakes struck Kocaeli and D&uuml / zce provinces in Turkey with magnitudes (Mw) 7.4 and 7.1, respectively. These catastrophes caused substantial structural damage, casualties and loss of lives. In the aftermath of these destructive earthquakes, neither demolished nor damaged shear-wall dominant buildings constructed by tunnel form techniques were reported. In spite of their high resistance to earthquake excitations, current seismic code provisions including the Uniform Building Code and the Turkish Seismic Code present limited information for their design criteria. This study presents experimental investigation of the panel unit having H-geometry. To investigate the seismic behavior of panel buildings, two prototype test specimens which have H wall design were tested at the Structural Mechanics Laboratory at METU. The experimental work involves the testing of two four-story, 1/5-scale reinforced concrete panel form building test specimens under lateral reversed loading, simulating the seismic forces and free vibration tests. Free vibration tests before and after cracking were done to assess the differences between the dynamic properties of uncracked and cracked test specimens. A moment-curvature program named Waller2002 for shear walls is developed to include the effects of steel strain hardening, confinement of concrete and tension strength of concrete. The moment-curvature relationships of panel form test specimens showed that walls with very low longitudinal steel ratios exhibit a brittle flexural failure with very little energy absorption. Shear walls of panel form test specimens have a reinforcement ratio of 0.0015 in the longitudinal and vertical directions. Under gradually increasing reversed lateral loading, the test specimens reached ultimate strength, as soon as the concrete cracked, followed by yielding and then rupturing of the longitudinal steel. The displacement ductility of the panel form test specimens was found to be very low. Thus, the occurrence of rupture of the longitudinal steel, as also observed in analytical studies, has been experimentally verified. Strength, stiffness, energy dissipation and story drifts of the test specimens were examined by evaluating the test results.

This thesis proposes machine learning algorithms for processing geometry by example. Each algorithm takes as input a collection of shapes along with exemplar values of target properties related to shape processing tasks. The goal of the algorithms is to output a function that maps from the shape data to the target properties. The learned functions can be applied to novel input shape data in order to synthesize the target properties with style similar to the training examples. Learning such functions is particularly useful for two different types of geometry processing problems. The first type of problems involves learning functions that map to target properties required for shape interpretation and understanding. The second type of problems involves learning functions that map to geometric attributes of animated shapes required for real-time rendering of dynamic scenes. With respect to the first type of problems involving shape interpretation and understanding, I demonstrate learning for shape segmentation and line illustration. For shape segmentation, the algorithms learn functions of shape data in order to perform segmentation and recognition of parts in 3D meshes simultaneously. This is in contrast to existing mesh segmentation methods that attempt segmentation without recognition based only on low-level geometric cues. The proposed method does not require any manual parameter tuning and achieves significant improvements in results over the state-of-the-art. For line illustration, the algorithms learn functions from shape and shading data to hatching properties, given a single exemplar line illustration of a shape. Learning models of such artistic-based properties is extremely challenging, since hatching exhibits significant complexity as a network of overlapping curves of varying orientation, thickness, density, as well as considerable stylistic variation. In contrast to existing algorithms that are hand-tuned or hand-designed from insight and intuition, the proposed technique offers a largely automated and potentially natural workflow for artists. With respect to the second type of problems involving fast computations of geometric attributes in dynamic scenes, I demonstrate algorithms for learning functions of shape animation parameters that specifically aim at taking advantage of the spatial and temporal coherence in the attribute data. As a result, the learned mappings can be evaluated very efficiently during runtime. This is especially useful when traditional geometric computations are too expensive to re-estimate the shape attributes at each frame. I apply such algorithms to efficiently compute curvature and high-order derivatives of animated surfaces. As a result, curvature-dependent tasks, such as line drawing, which could be previously performed only offline for animated scenes, can now be executed in real-time on modern CPU hardware.

This thesis proposes machine learning algorithms for processing geometry by example. Each algorithm takes as input a collection of shapes along with exemplar values of target properties related to shape processing tasks. The goal of the algorithms is to output a function that maps from the shape data to the target properties. The learned functions can be applied to novel input shape data in order to synthesize the target properties with style similar to the training examples. Learning such functions is particularly useful for two different types of geometry processing problems. The first type of problems involves learning functions that map to target properties required for shape interpretation and understanding. The second type of problems involves learning functions that map to geometric attributes of animated shapes required for real-time rendering of dynamic scenes. With respect to the first type of problems involving shape interpretation and understanding, I demonstrate learning for shape segmentation and line illustration. For shape segmentation, the algorithms learn functions of shape data in order to perform segmentation and recognition of parts in 3D meshes simultaneously. This is in contrast to existing mesh segmentation methods that attempt segmentation without recognition based only on low-level geometric cues. The proposed method does not require any manual parameter tuning and achieves significant improvements in results over the state-of-the-art. For line illustration, the algorithms learn functions from shape and shading data to hatching properties, given a single exemplar line illustration of a shape. Learning models of such artistic-based properties is extremely challenging, since hatching exhibits significant complexity as a network of overlapping curves of varying orientation, thickness, density, as well as considerable stylistic variation. In contrast to existing algorithms that are hand-tuned or hand-designed from insight and intuition, the proposed technique offers a largely automated and potentially natural workflow for artists. With respect to the second type of problems involving fast computations of geometric attributes in dynamic scenes, I demonstrate algorithms for learning functions of shape animation parameters that specifically aim at taking advantage of the spatial and temporal coherence in the attribute data. As a result, the learned mappings can be evaluated very efficiently during runtime. This is especially useful when traditional geometric computations are too expensive to re-estimate the shape attributes at each frame. I apply such algorithms to efficiently compute curvature and high-order derivatives of animated surfaces. As a result, curvature-dependent tasks, such as line drawing, which could be previously performed only offline for animated scenes, can now be executed in real-time on modern CPU hardware.

Vascular diseases are among the leading causes of death in Canada and around the globe. A major underlying cause of most such medical conditions is atherosclerosis, a gradual accumulation of plaque on the walls of blood vessels. Particularly vulnerable to atherosclerosis is the carotid artery, which carries blood to the brain. Dangerous narrowing of the carotid artery can lead to embolism, a dislodgement of plaque fragments which travel to the brain and are the cause of most strokes. If this pathology can be detected early, such a deadly scenario can be potentially prevented through treatment or surgery. This not only improves the patient's prognosis, but also dramatically lowers the overall cost of their treatment. Medical imaging is an indispensable tool for early detection of atherosclerosis, in particular since the exact location and shape of the plaque need to be known for accurate diagnosis. This can be achieved by locating the plaque inside the artery and measuring its volume or texture, a process which is greatly aided by image segmentation. In particular, the use of ultrasound imaging is desirable because it is a cost-effective and safe modality. However, ultrasonic images depict sound-reflecting properties of tissue, and thus suffer from a number of unique artifacts not present in other medical images, such as acoustic shadowing, speckle noise and discontinuous tissue boundaries. A robust ultrasound image segmentation technique must take these properties into account. Prior to segmentation, an important pre-processing step is the extraction of a series of features from the image via application of various transforms and non-linear filters. A number of such features are explored and evaluated, many of them resulting in piecewise smooth images. It is also proposed to decompose the ultrasound image into several statistically distinct components. These components can be then used as features directly, or other features can be obtained from them instead of the original image. The decomposition scheme is derived using Maximum-a-Posteriori estimation framework and is efficiently computable. Furthermore, this work presents and evaluates an algorithm for segmenting the carotid artery in 3D ultrasound images from other tissues. The algorithm incorporates information from different sources using an energy minimization framework. Using the ultrasound image itself, statistical differences between the region of interest and its background are exploited, and maximal overlap with strong image edges encouraged. In order to aid the convergence to anatomically accurate shapes, as well as to deal with the above-mentioned artifacts, prior knowledge is incorporated into the algorithm by using weak geometric priors. The performance of the algorithm is tested on a number of available 3D images, and encouraging results are obtained and discussed.