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Advisor(s)
Abstract(s)
O progresso nas mais vastas áreas de tecnologia tem crescido intensamente nos últimos anos.
Áreas como a aeronáutica, a meteorologia, a modelação geológica, a geologia, os padrões climáticos, os espectros estelares, ou distribuições de genes humanos, confrontam-se regularmente
com problemas de reconstrução de superfícies nas mais variadas aplicações. Os dados numéricos reais são usualmente difíceis de analisar. Qualquer função que efectivamente correlacione
os dados reais é difícil de obter e de difícil interacção. Existem muitos métodos para reconstruir
a superfície contínua a partir de dados dispersos ou regularmente espaçados no domínio. Nesta
dissertação, a ideia da teoria básica de aproximação multiquádrica de Hardy para reconstrução
de superfícies foi desenvolvida para aproximar um determinado conjunto de dados. Este método faz parte de uma classe de métodos conhecidos como métodos de funções de base radial,
e mostramos a sua superioridade em termos de precisão e suavidade pretendidas, ainda como a
redução do número total de dados necessários para a reconstrução da superfície. Os exemplos
de aplicação nesta dissertação são para elevação digital do terreno (DEM), reconstrução de superfícies 3D, mas este método é facilmente estendido para outras áreas em qualquer dimensão.
Discutimos a sua implementação, o seu desempenho e providenciamos simulações numéricas.
Progress in the wider areas of technology has grown strongly in recent years. Areas such as aeronautics, meteorology, geological modeling, geology, climate patterns, stellar spectra, or human gene distributions, are regularly confronted with problems of surface reconstruction in various applications. The real numerical data is usually difficult to analyze. Any function that effectively correlate the actual data is difficult to obtain and of difficult interaction. There are many methods to reconstruct a continuous surface from scattered data or regularly spaced in the domain. In this thesis, the idea of the basic theory of Hardy multiquadric approach to surface reconstruction has been developed to approximate a given data set. This method is part of a class of methods known as methods of radial basis functions and we show its superiority in terms of accuracy and smoothness desired, and even with the reduced total number of data needed for reconstruction of the surface. The applications examples in this thesis are to digital terrain elevation (DEM), 3D surface reconstruction, but this method is easily extended to other areas in any dimension. We discuss its implementation, its performance and provide numerical simulations.
Progress in the wider areas of technology has grown strongly in recent years. Areas such as aeronautics, meteorology, geological modeling, geology, climate patterns, stellar spectra, or human gene distributions, are regularly confronted with problems of surface reconstruction in various applications. The real numerical data is usually difficult to analyze. Any function that effectively correlate the actual data is difficult to obtain and of difficult interaction. There are many methods to reconstruct a continuous surface from scattered data or regularly spaced in the domain. In this thesis, the idea of the basic theory of Hardy multiquadric approach to surface reconstruction has been developed to approximate a given data set. This method is part of a class of methods known as methods of radial basis functions and we show its superiority in terms of accuracy and smoothness desired, and even with the reduced total number of data needed for reconstruction of the surface. The applications examples in this thesis are to digital terrain elevation (DEM), 3D surface reconstruction, but this method is easily extended to other areas in any dimension. We discuss its implementation, its performance and provide numerical simulations.
Description
Keywords
Reconstrução de superfícies Superfície - Multiquádrica Funções multiquádrica de Hardy Funções de Franke