No description available.

The ability to predict and control laminar-to-turbulent transition in high-speed flow has a substantial effect on heat transfer and skin friction, thus improving the design and operation of hypersonic vehicles. The control of transition on blunt bodies is essential to improve the performance of lifting and control surfaces. The objective of this Ph.D. research is to develop efficient and accurate algorithms for the detection of high-frequency heat flux fluctuations supported by hypersonic flow in transitional boundary layers. The focus of this research is on understanding the mathematical properties of the reconstruction such as regularity, sensitivity to noise, multi-resolution, and accuracy. This research is part of an effort to develop small-footprint heat flux sensors able to measure high-frequency fluctuations on test articles in a hypersonic wind tunnel with a small curvature radius. In the present theoretical/numerical study a multi-resolution formulation for the direct and inverse reconstruction of the heat flux from temperature sensors distributed over a multidimensional solid in a hypersonic flow was developed and validated. The solution method determines the thermal response by approximating the system Green's function with the Galerkin method and optimizes the heat flux distribution by fitting the distributed surface temperature data. Coating and glue layers are treated as separate domains for which the Green's function is obtained independently. Connection conditions for the system Green's function are derived by imposing continuity of heat flux and temperature concurrently at all interfaces. The solution heat flux is decomposed on a space-time basis with the temporal basis a multi-resolution wavelet with arbitrary scaling function. Quadrature formulas for the convolution of wavelets and the Green's function, a reconstruction approach based on isoparametric mapping of three-dimensional geometries, and a boundary wavelet approach for inverse problems were developed and verified. This approach was validated against turbulent conjugate heat transfer simulations at Mach 6 on a blunted wedge at 0 angle of attack and wind tunnel experiments of round impinging jet at Mach 0.7 It was found that multidimensional effects were important near the wedge shoulder in the short time scale, that the L-curve regularization needed to be locally corrected to analyze transitional flows and that proper regularization led to sub-cell resolution of the inverse problem. While the L2 regularization techniques are accurate they are also computationally inefficient and lack mathematical rigor. Optimal non-linear estimators were researched both as means to promote sparsity in the regularization and to pre-threshold the inverse heat conduction problem. A novel class of nonlinear estimators is presented and validated against wind tunnel experiments for a flat-faced cylinder also at Mach 6. The new approach to hypersonic heat flux reconstruction from discrete temperature data developed in this thesis is more efficient and accurate than existing techniques. / Doctor of Philosophy / The harsh environment supported by hypersonic flows is characterized by high-frequency turbulent bursts, acoustic noise, and vibrations that pollute the signals of the sensors that probe at high frequencies the state of the boundary layers developing on the walls. This research describes the search for optimal estimators of the noisy signal, i.e., those that lead to the maximum attenuation of the risk of error pollution by non-coherent scales. This research shows that linear estimators perform poorly at high-frequency and non-linear estimators can be optimized over a sparse projection of the signal in a discrete wavelet basis. Optimal non-linear estimators are developed and validated for wind tunnel experiments conducted at Mach 6 in the Advanced Propulsion and Power Laboratory at Virginia Tech.

Image segmentation is an important step in image processing, with many applications such as pattern recognition, object detection, and medical image analysis. It is a technique that separates objects of interests from the background in an image. Geometric active contour is a recent image segmentation method that overcomes previous problems with snakes. It is an attractive method for medical image segmentation as it is able to capture the object of interest in one continuous curve. The theory and implementation details of geometric active contours are discussed in this work. The robustness of the algorithm is tested through a series of tests, involving both synthetic images and medical images. Curve leaking past boundaries is a common problem in cases of non-ideal edges. Noise is also problematic for the advancement of the curve. Smoothing and parameters selection are discussed as ways to help solve these problems. This work also explores the incorporation of the multi-resolution method of Gaussian pyramids into the algorithm. Multi-resolution methods, used extensively in the areas of denoising and edge-selection, can help capture the spatial structure of an image. Results show that similar to the multi-resolution methods applied to parametric active contours, the multi-resolution can greatly increase the computation without sacrificing performance. In fact, results show that with successive smoothing and sub-sampling, performance often improves. Although smoothing and parameter adjustment help improve the performance of geometric active contours, the edge-based approach is still localized and the improvement is limited. Region-based approaches are recommended for further work on active contours.

Image segmentation is an important step in image processing, with many applications such as pattern recognition, object detection, and medical image analysis. It is a technique that separates objects of interests from the background in an image. Geometric active contour is a recent image segmentation method that overcomes previous problems with snakes. It is an attractive method for medical image segmentation as it is able to capture the object of interest in one continuous curve. The theory and implementation details of geometric active contours are discussed in this work. The robustness of the algorithm is tested through a series of tests, involving both synthetic images and medical images. Curve leaking past boundaries is a common problem in cases of non-ideal edges. Noise is also problematic for the advancement of the curve. Smoothing and parameters selection are discussed as ways to help solve these problems. This work also explores the incorporation of the multi-resolution method of Gaussian pyramids into the algorithm. Multi-resolution methods, used extensively in the areas of denoising and edge-selection, can help capture the spatial structure of an image. Results show that similar to the multi-resolution methods applied to parametric active contours, the multi-resolution can greatly increase the computation without sacrificing performance. In fact, results show that with successive smoothing and sub-sampling, performance often improves. Although smoothing and parameter adjustment help improve the performance of geometric active contours, the edge-based approach is still localized and the improvement is limited. Region-based approaches are recommended for further work on active contours.

Inverse problems, foundational in applied sciences, involve deducing system inputs from specific output observations. These problems find applications in diverse domains such as aerospace engineering, weather prediction, and oceanography. However, their solution often requires complex numerical simulations and substantial computational resources. Modern machine learning based approaches have emerged as an alternative and flexible methodology for solving these types of problems, however their generalization power often comes at the cost of working with large descriptive datasets, a requirement that many applications cannot afford. This thesis proposes and explores the novel Deep Multi-resolution Operator Network (DMON), inspired by the recently developed DeepONet architecture. The DMON model is designed to solve inverse problems related to chaotic non-linear systems with low-resolution data through intelligently utilizing high-resolution data from a similar system. Performance of the DMON model and the proposed selection mechanisms are evaluated on two chaotic systems, a double pendulum and turbulent flow around a cylinder, with improvements observed under idealized scenarios whereby high and low-resolution inputs are manually paired, along with minor improvements when this pairing is conducted through the proposed the latent space comparison selection mechanism. / Master of Science / In everyday life, we often encounter the challenge of determining the cause behind something we observe. For instance, meteorologists infer weather patterns based on limited atmospheric data, while doctors use X-rays and CT scans to reconstruct images representing the insides of our bodies. Solving these so called ``inverse problems'' can be difficult, particularly when the process is chaotic such as the weather, whereby small changes result in much larger ones over time. In this thesis, we propose a novel method using artificial intelligence and high-resolution simulation data to aid in solving these types of problems. Our proposed method is designed to work well even when we only have access to a small amount of information, or the information available isn't very detailed. Because of this there are potential applications of the proposed method across a wide range of fields, particularly those where acquiring detailed information is difficult, expensive, or impossible.

<p> It is possible to interpret multi-resolution analysis from both Fourier-domain and temporal/spatial domain stand-points. While a Fourier-domain interpretation helps in designing a powerful machinery for multi-resolution refinement on regular point-sets and lattices, most of its techniques cannot be directly generalized to the case of irregular sampling. Therefore, in this thesis we provide a new definition and formulation of multi-resolution refinement, based on a temporal/spatial-domain understanding, that is general enough to allow multi-resolution approximation of different spaces of functions by processing samples (or observations) that can be irregularly distributed or even obtained using different sampling methods. We then continue to provide a construction for designing and implementing classes of refinement schemes in these general settings. The framework for multi-resolution refinement that we discuss includes and extends the existing mathematical machinery for multi-resolution analysis; and the suggested construction unifies many of the schemes currently in use, and, more importantly, allows designing schemes for many new settings. </p> / Thesis / Master of Applied Science (MASc)

O trabalho apresentado por essa dissertação busca contribuir com a atenuação do problema da correspondência em visão estéreo a partir de uma abordagem local de soluções. São usadas duas estratégias como solução às ambigüidades e às oclusões da cena: a análise multi-resolução das imagens empregando a estrutura piramidal, e a força de agrupamento perceptual, conhecida como Gestalt theory na psicologia. Inspirado no sistema visual humano, a visão estéreo é uma área de grande interesse em visão computacional, e está relacionada à recuperação de informações tridimensionais de uma cena a partir de imagens da mesma. Para isso, as imagens são capturadas em posições diferentes para o futuro relacionamento das várias projeções de um mesmo ponto 3D. Apesar de ser estudada há quase quatro décadas, ela ainda apresenta problemas de difícil solução devido às dificuldades relacionadas às distorções produzidas pela mudança da perspectiva de visualização. Dentre esses problemas destacam-se os relacionados à oclusão de pontos e também à ambigüidade gerada pela repetição ou ausência de textura nas imagens. Esses por sua vez compõem a base do problema estéreo, chamado de problema da correspondência. Os resultados obtidos são equivalentes aos obtidos por técnicas globais, com a vantagem de requerer menor complexidade computacional. O uso da teoria de agrupamento perceptual faz desse trabalho um método moderno de estimação de disparidades, visto que essa técnica é alvo de atenção especial em recentes estudos na área de visão computacional. / This work aims to give a contribution to the correspondence problem using a local approach. Two strategies are used as solution to ambiguities and occlusions: the multi-resolution analysis with irnages pyramids and the other is the perceptual grouping weight, called Gestalt theory in the psychology. Inspired by human vision system, the stereo vision is an very important area in computer vision. It is related with the 3D information recovery from a pair of images. The images are captured frorn different positions to hereafter association of the 3D point projections. Although it has being studied for quite a long time, stereo vision presents some difficult problems, related to the change of visualisation perspective. Among the different problems originated from point of view changes, occlusions and ambiguities have special attention and compose the foundation of stereo problem, named correspondence problem. The results obtained were closer to the ones generated by global techniques, with the advantage of requiring less computational complexity. The use of Gestalt theory makes this a modern disparity estimation method, as this theory has been received special attention in computer vision researchs.

Multi-resolution visualization (MRV) systems are widely used for handling large amounts of information. These systems look different but they share many common features. The visualization research community lacks a general framework that summarizes the common features among the wide variety of MRV systems in order to help in MRV system design, analysis, and enhancement. This dissertation proposes such a general framework. This framework is based on the definition that a MRV system is a visualization system that visually represents perceptions in different levels of detail and allows users to interactively navigate among the representations. The visual representations of a perception are called a view. The framework is composed of two essential components: view simulation and interactive visualization. View simulation means that an MRV system simulates views of non-existing perceptions through simplification on the data structure or the graphics generation process. This is needed when the perceptions provided to the MRV system are not at the user's desired level of detail. The framework identifies classes of view simulation approaches and describes them in terms of simplification operators and operands (spaces). The simplification operators are further divided into four categories, namely sampling operators, aggregation operators, approximation operators, and generalization operators. Techniques in these categories are listed and illustrated via examples. The simplification operands (spaces) are also further divided into categories, namely data space and visualization space. How different simplification operators are applied to these spaces is also illustrated using examples. Interactive visualization means that an MRV system visually presents the views to users and allows users to interactively navigate among different views or within one view. Three types of MRV interface, namely the zoomable interface, the overview + context interface, and the focus + detail interface, are presented with examples. Common interaction tools used in MRV systems, such as zooming and panning, selection, distortion, overlap reduction, previewing, and dynamic simplification are also presented. A large amount of existing MRV systems are used as examples in this dissertation, including several MRV systems developed by the author based on the general framework. In addition, a case study that analyzes and suggests possible improvements for an existing MRV system is described. These examples and the case study reveal that the framework covers the common features of a wide variety of existing MRV systems, and helps users analyze and improve existing MRV systems as well as design new MRV systems.

O trabalho apresentado por essa dissertação busca contribuir com a atenuação do problema da correspondência em visão estéreo a partir de uma abordagem local de soluções. São usadas duas estratégias como solução às ambigüidades e às oclusões da cena: a análise multi-resolução das imagens empregando a estrutura piramidal, e a força de agrupamento perceptual, conhecida como Gestalt theory na psicologia. Inspirado no sistema visual humano, a visão estéreo é uma área de grande interesse em visão computacional, e está relacionada à recuperação de informações tridimensionais de uma cena a partir de imagens da mesma. Para isso, as imagens são capturadas em posições diferentes para o futuro relacionamento das várias projeções de um mesmo ponto 3D. Apesar de ser estudada há quase quatro décadas, ela ainda apresenta problemas de difícil solução devido às dificuldades relacionadas às distorções produzidas pela mudança da perspectiva de visualização. Dentre esses problemas destacam-se os relacionados à oclusão de pontos e também à ambigüidade gerada pela repetição ou ausência de textura nas imagens. Esses por sua vez compõem a base do problema estéreo, chamado de problema da correspondência. Os resultados obtidos são equivalentes aos obtidos por técnicas globais, com a vantagem de requerer menor complexidade computacional. O uso da teoria de agrupamento perceptual faz desse trabalho um método moderno de estimação de disparidades, visto que essa técnica é alvo de atenção especial em recentes estudos na área de visão computacional. / This work aims to give a contribution to the correspondence problem using a local approach. Two strategies are used as solution to ambiguities and occlusions: the multi-resolution analysis with irnages pyramids and the other is the perceptual grouping weight, called Gestalt theory in the psychology. Inspired by human vision system, the stereo vision is an very important area in computer vision. It is related with the 3D information recovery from a pair of images. The images are captured frorn different positions to hereafter association of the 3D point projections. Although it has being studied for quite a long time, stereo vision presents some difficult problems, related to the change of visualisation perspective. Among the different problems originated from point of view changes, occlusions and ambiguities have special attention and compose the foundation of stereo problem, named correspondence problem. The results obtained were closer to the ones generated by global techniques, with the advantage of requiring less computational complexity. The use of Gestalt theory makes this a modern disparity estimation method, as this theory has been received special attention in computer vision researchs.

The low-level interpretation of images provides constraints on 3D surface shape at multiple resolutions, but typically only at scattered locations over the visual field. Subsequent visual processing can be facilitated substantially if the scattered shape constraints are immediately transformed into visible-surface representations that unambiguously specify surface shape at every image point. The required transformation is shown to lead to an ill-posed surface reconstruction problem. A well-posed variational principle formulation is obtained by invoking 'controlled continuity,' a physically nonrestrictive (generic) assumption about surfaces which is nonetheless strong enough to guarantee unique solutions. The variational principle, which admits an appealing physical interpretation, is locally discretized by applying the finite element method to a piecewise, finite element representation of surfaces. This forms the mathematical basis of a unified and general framework for computing visible-surface representations. The computational framework unifies formal solutions to the key problems of (i) integrating multiscale constraints on surface depth and orientation from multiple visual sources, (ii) interpolating these scattered constraints into dense, piecewise smooth surfaces, (iii) discovering surface depth and orientation discontinuities and allowing them to restrict interpolation appropriately, and (iv) overcoming the immense computational burden of fine resolution surface reconstruction. An efficient surface reconstruction algorithm is developed. It exploits multiresolution hierarchies of cooperative relaxation processes and is suitable for implementation on massively parallel networks of simple, locally interconnected processors. The algorithm is evaluated empirically in a diversity of applications.