Scattered data collected at sample points may be used to determine simple functions to best fit the data. An ideal choice for these simple functions is bivariate splines. Triangulation of the sample points creates partitions over which the bivariate splines may be defined. But the optimality of the approximation is dependent on the choice of triangulation. An algorithm, referred to as an Edge Swapping Algorithm, has been developed to transform an arbitrary triangulation of the sample points into an optimal triangulation for representation of the scattered data. A Matlab package has been completed that implements this algorithm for any triangulation on a given set of sample points.

Zugl.: München, Techn. Univ., Diss., 2009

München, Techn. University, Diss., 2009.

No description available.

Analysis and visualization of dynamic scenes is often constrained by the amount of spatio-temporal information available from the environment. In most scenarios, we have to account for incomplete information and sparse motion data, requiring us to employ interpolation and approximation methods to fill for the missing information. Scattered data interpolation and approximation techniques have been widely used for solving the problem of completing surfaces and images with incomplete input data. We introduce approaches for such data interpolation and approximation from limited sensors, into the domain of analyzing and visualizing dynamic scenes. Data from dynamic scenes is subject to constraints due to the spatial layout of the scene and/or the configurations of video cameras in use. Such constraints include: (1) sparsely available cameras observing the scene, (2) limited field of view provided by the cameras in use, (3) incomplete motion at a specific moment, and (4) varying frame rates due to different exposures and resolutions. In this thesis, we establish these forms of incompleteness in the scene, as spatio-temporal uncertainties, and propose solutions for resolving the uncertainties by applying scattered data approximation into a spatio-temporal domain. The main contributions of this research are as follows: First, we provide an efficient framework to visualize large-scale dynamic scenes from distributed static videos. Second, we adopt Radial Basis Function (RBF) interpolation to the spatio-temporal domain to generate global motion tendency. The tendency, represented by a dense flow field, is used to optimally pan and tilt a video camera. Third, we propose a method to represent motion trajectories using stochastic vector fields. Gaussian Process Regression (GPR) is used to generate a dense vector field and the certainty of each vector in the field. The generated stochastic fields are used for recognizing motion patterns under varying frame-rate and incompleteness of the input videos. Fourth, we also show that the stochastic representation of vector field can also be used for modeling global tendency to detect the region of interests in dynamic scenes with camera motion. We evaluate and demonstrate our approaches in several applications for visualizing virtual cities, automating sports broadcasting, and recognizing traffic patterns in surveillance videos.

Os centros operacionais e de pesquisa em previsão numérica do tempo geralmente trabalham com uma grande quantidade de dados complexos multivariados, tendo que interpretá-los num curto espaço de tempo. Técnicas de visualização científica podem ser utilizadas para ajudar a entender o comportamento atmosférico. Este trabalho descreve a arquitetura e as facilidades apresentadas pelo sistema VisualMet, que foi implementado com base em um estudo das tarefas desenvolvidas pelos meteorologistas responsáveis pelo 8º Distrito de Meteorologia, em Porto Alegre. Este centro coleta dados meteorológicos três vezes ao dia, de 32 estações locais, e recebe dados similares do Instituto Nacional de Meteorologia, localizado em Brasília, e do National Meteorological Center, localizado nos Estados Unidos. Tais dados são resultados de observações de variáveis tais como temperatura, pressão, velocidade do vento e tipos de nuvens. As tarefas dos meteorologistas e as classes de dados foram observadas e analisadas para definir as características do sistema. A arquitetura e a implementação do VisualMet seguem, respectivamente, uma abordagem orientada a ferramentas e o paradigma de programação orientada a objetos. Dados obtidos das estações meteorológicas são instancias de uma classe chamada "Entidade". Três outras classes de objetos representando ferramentas que suportam as tarefas dos meteorologistas foram modeladas. Os objetos no sistema são apresentados ao usuário através de duas janelas, "Base de Entidades" e " Base de Ferramentas". A implementação da "Base de Ferramentas" inclui ferramentas de mapeamento (para produzir mapas de contorno, mapas de ícones e gráficos), ferramentas de armazenamento (para guardar e recuperar imagens geradas pelo sistema) e uma ferramenta de consulta (para ler valores de variáveis de estações selecionadas). E dada especial atenção a ferramenta de mapa de contorno, onde foi utilizado o método Multiquádrico para interpolação de dados. O trabalho apresenta ainda um estudo sobre métodos de interpolação de dados esparsos, antes de descrever detalhadamente os resultados obtidos com a ferramenta de mapa de contorno. Estes resultados (imagens) são discutidos e comparados com mapas gerados manualmente por meteorologistas do 8º Distrito de Meteorologia. Possíveis extensões do presente trabalho são também abordadas. / The weather forecast centers deal with a great volume of complex multivariate data, which usually have to be understood within short time. Scientific visualization techniques can be used to support both daily forecasting and meteorological research. This work reports the architecture and facilities of a system, named VisualMet, that was implemented based on a case study of the tasks accomplished by the meteorologists responsible for the 8th Meteorological District, in the South of Brazil. This center collects meteorological data three times a day from 32 local stations and receives similar data from both the National Institute of Meteorology, located in Brasilia, and National Meteorological Center, located in the United States of America. Such data result from observation of variables like temperature, pressure, wind velocity, and type of clouds. The tasks of meteorologists and the classes of application data were observed to define system requirements. The architecture and implementation of Visual- Met follow the tool-oriented approach and object-oriented paradigm, respectively. Data taken from meteorological stations are instances of a class named Entity. Three other classes of tools which support the meteorologists' tasks are modeled. Objects in the system are presented to the user through two windows, "Entities Base" and "Tools Base". Current implementation of the "Tools Base" contains mapping tools (to produce contour maps, icons maps and graphs), recording tools (to save and load images generated by the system) and a query tool (to read variables values of selected stations). The results of applying the multiquadric method to interpolate data for the construction of contour maps are also discussed. Before describing the results obtained with the multiquadric method, this work also presents a study on interpolation methods for scattered data. The results (images) obtained with the contour map tool are discussed and compared with the maps drawn by the meteorologists of the 8th Meteorological District. Possible extensions to this work are also presented.

In this work the problem of calibrating Flush Air Data Sensing (FADS) has been addressed. The inverse problem of extracting freestream wind speed and angle of attack from pressure measurements has been solved. The aim of this work was to develop machine learning and statistical tools to optimize design and calibration of FADS systems. Experimental and Computational Fluid Dynamics (EFD and CFD) solve the forward problem of determining the pressure distribution given the wind velocity profile and bluff body geometry. In this work three ways are presented in which machine learning techniques can improve calibration of FADS systems. First, a scattered data approximation scheme, called Sequential Function Approximation (SFA) that successfully solved the current inverse problem was developed. The proposed scheme is a greedy and self-adaptive technique that constructs reliable and robust estimates without any user-interaction. Wind speed and direction prediction algorithms were developed for two FADS problems. One where pressure sensors are installed on a surface vessel and the other where sensors are installed on the Runway Assisted Landing Site (RALS) control tower. Second, a Tikhonov regularization based data-model fusion technique with SFA was developed to fuse low fidelity CFD solutions with noisy and sparse wind tunnel data. The purpose of this data model fusion approach was to obtain high fidelity, smooth and noiseless flow field solutions by using only a few discrete experimental measurements and a low fidelity numerical solution. This physics based regularization technique gave better flow field solutions compared to smoothness based solutions when wind tunnel data is sparse and incomplete. Third, a sequential design strategy was developed with SFA using Active Learning techniques from the machine learning theory and Optimal Design of Experiments from statistics for regression and classification problems. Uncertainty Sampling was used with SFA to demonstrate the effectiveness of active learning versus passive learning on a cavity flow classification problem. A sequential G-optimal design procedure was also developed with SFA for regression problems. The effectiveness of this approach was demonstrated on a simulated problem and the above mentioned FADS problem.

Os centros operacionais e de pesquisa em previsão numérica do tempo geralmente trabalham com uma grande quantidade de dados complexos multivariados, tendo que interpretá-los num curto espaço de tempo. Técnicas de visualização científica podem ser utilizadas para ajudar a entender o comportamento atmosférico. Este trabalho descreve a arquitetura e as facilidades apresentadas pelo sistema VisualMet, que foi implementado com base em um estudo das tarefas desenvolvidas pelos meteorologistas responsáveis pelo 8º Distrito de Meteorologia, em Porto Alegre. Este centro coleta dados meteorológicos três vezes ao dia, de 32 estações locais, e recebe dados similares do Instituto Nacional de Meteorologia, localizado em Brasília, e do National Meteorological Center, localizado nos Estados Unidos. Tais dados são resultados de observações de variáveis tais como temperatura, pressão, velocidade do vento e tipos de nuvens. As tarefas dos meteorologistas e as classes de dados foram observadas e analisadas para definir as características do sistema. A arquitetura e a implementação do VisualMet seguem, respectivamente, uma abordagem orientada a ferramentas e o paradigma de programação orientada a objetos. Dados obtidos das estações meteorológicas são instancias de uma classe chamada "Entidade". Três outras classes de objetos representando ferramentas que suportam as tarefas dos meteorologistas foram modeladas. Os objetos no sistema são apresentados ao usuário através de duas janelas, "Base de Entidades" e " Base de Ferramentas". A implementação da "Base de Ferramentas" inclui ferramentas de mapeamento (para produzir mapas de contorno, mapas de ícones e gráficos), ferramentas de armazenamento (para guardar e recuperar imagens geradas pelo sistema) e uma ferramenta de consulta (para ler valores de variáveis de estações selecionadas). E dada especial atenção a ferramenta de mapa de contorno, onde foi utilizado o método Multiquádrico para interpolação de dados. O trabalho apresenta ainda um estudo sobre métodos de interpolação de dados esparsos, antes de descrever detalhadamente os resultados obtidos com a ferramenta de mapa de contorno. Estes resultados (imagens) são discutidos e comparados com mapas gerados manualmente por meteorologistas do 8º Distrito de Meteorologia. Possíveis extensões do presente trabalho são também abordadas. / The weather forecast centers deal with a great volume of complex multivariate data, which usually have to be understood within short time. Scientific visualization techniques can be used to support both daily forecasting and meteorological research. This work reports the architecture and facilities of a system, named VisualMet, that was implemented based on a case study of the tasks accomplished by the meteorologists responsible for the 8th Meteorological District, in the South of Brazil. This center collects meteorological data three times a day from 32 local stations and receives similar data from both the National Institute of Meteorology, located in Brasilia, and National Meteorological Center, located in the United States of America. Such data result from observation of variables like temperature, pressure, wind velocity, and type of clouds. The tasks of meteorologists and the classes of application data were observed to define system requirements. The architecture and implementation of Visual- Met follow the tool-oriented approach and object-oriented paradigm, respectively. Data taken from meteorological stations are instances of a class named Entity. Three other classes of tools which support the meteorologists' tasks are modeled. Objects in the system are presented to the user through two windows, "Entities Base" and "Tools Base". Current implementation of the "Tools Base" contains mapping tools (to produce contour maps, icons maps and graphs), recording tools (to save and load images generated by the system) and a query tool (to read variables values of selected stations). The results of applying the multiquadric method to interpolate data for the construction of contour maps are also discussed. Before describing the results obtained with the multiquadric method, this work also presents a study on interpolation methods for scattered data. The results (images) obtained with the contour map tool are discussed and compared with the maps drawn by the meteorologists of the 8th Meteorological District. Possible extensions to this work are also presented.

Os centros operacionais e de pesquisa em previsão numérica do tempo geralmente trabalham com uma grande quantidade de dados complexos multivariados, tendo que interpretá-los num curto espaço de tempo. Técnicas de visualização científica podem ser utilizadas para ajudar a entender o comportamento atmosférico. Este trabalho descreve a arquitetura e as facilidades apresentadas pelo sistema VisualMet, que foi implementado com base em um estudo das tarefas desenvolvidas pelos meteorologistas responsáveis pelo 8º Distrito de Meteorologia, em Porto Alegre. Este centro coleta dados meteorológicos três vezes ao dia, de 32 estações locais, e recebe dados similares do Instituto Nacional de Meteorologia, localizado em Brasília, e do National Meteorological Center, localizado nos Estados Unidos. Tais dados são resultados de observações de variáveis tais como temperatura, pressão, velocidade do vento e tipos de nuvens. As tarefas dos meteorologistas e as classes de dados foram observadas e analisadas para definir as características do sistema. A arquitetura e a implementação do VisualMet seguem, respectivamente, uma abordagem orientada a ferramentas e o paradigma de programação orientada a objetos. Dados obtidos das estações meteorológicas são instancias de uma classe chamada "Entidade". Três outras classes de objetos representando ferramentas que suportam as tarefas dos meteorologistas foram modeladas. Os objetos no sistema são apresentados ao usuário através de duas janelas, "Base de Entidades" e " Base de Ferramentas". A implementação da "Base de Ferramentas" inclui ferramentas de mapeamento (para produzir mapas de contorno, mapas de ícones e gráficos), ferramentas de armazenamento (para guardar e recuperar imagens geradas pelo sistema) e uma ferramenta de consulta (para ler valores de variáveis de estações selecionadas). E dada especial atenção a ferramenta de mapa de contorno, onde foi utilizado o método Multiquádrico para interpolação de dados. O trabalho apresenta ainda um estudo sobre métodos de interpolação de dados esparsos, antes de descrever detalhadamente os resultados obtidos com a ferramenta de mapa de contorno. Estes resultados (imagens) são discutidos e comparados com mapas gerados manualmente por meteorologistas do 8º Distrito de Meteorologia. Possíveis extensões do presente trabalho são também abordadas. / The weather forecast centers deal with a great volume of complex multivariate data, which usually have to be understood within short time. Scientific visualization techniques can be used to support both daily forecasting and meteorological research. This work reports the architecture and facilities of a system, named VisualMet, that was implemented based on a case study of the tasks accomplished by the meteorologists responsible for the 8th Meteorological District, in the South of Brazil. This center collects meteorological data three times a day from 32 local stations and receives similar data from both the National Institute of Meteorology, located in Brasilia, and National Meteorological Center, located in the United States of America. Such data result from observation of variables like temperature, pressure, wind velocity, and type of clouds. The tasks of meteorologists and the classes of application data were observed to define system requirements. The architecture and implementation of Visual- Met follow the tool-oriented approach and object-oriented paradigm, respectively. Data taken from meteorological stations are instances of a class named Entity. Three other classes of tools which support the meteorologists' tasks are modeled. Objects in the system are presented to the user through two windows, "Entities Base" and "Tools Base". Current implementation of the "Tools Base" contains mapping tools (to produce contour maps, icons maps and graphs), recording tools (to save and load images generated by the system) and a query tool (to read variables values of selected stations). The results of applying the multiquadric method to interpolate data for the construction of contour maps are also discussed. Before describing the results obtained with the multiquadric method, this work also presents a study on interpolation methods for scattered data. The results (images) obtained with the contour map tool are discussed and compared with the maps drawn by the meteorologists of the 8th Meteorological District. Possible extensions to this work are also presented.

In the representation of scattered data by smooth pp (:= piecewise polynomial) functions, perhaps the most important problem is to find an optimal triangulation of the given sample sites (called vertices). Of course, the notion of optimality depends on the desirable properties in the approximation or modeling problems. In this paper, we are concerned with optimal approximation order with respect to the given order r of smoothness and degree k of the polynomial pieces of the smooth pp functions. We will only consider C1 pp approximation with r = 1 and k = 4. The main result in this paper is an efficient method for triangulating any finitely many arbitrarily scattered sample sites, such that these sample sites are the only vertices of the triangulation, and that for any discrete data given at these sample sites, there is a C1 piecewise quartic polynomial on this triangulation that interpolates the given data with the fifth order of approximation.