In this thesis, all the possible semi-prewavelets over uniform refinements of regular triangulations have been studied. A corresponding theorem is given to ensure the linear independence of a set of different pre-wavelets obtained by summing pairs of these semi-prewavelets. This provides efficient multiresolutions of the spaces of functions over various regular triangulation domains since the bases of the orthogonal complements of the coarse spaces can be constructed very easily.

Scientific visualization is an essential and indispensable tool for the systematic study of computational (CFD) datasets. There are numerous methods currently used for the unwieldy task of processing and visualizing the characteristically large datasets. Feature extraction is one such technique and has become a significant means for enabling effective visualization. This thesis proposes different modules to refine the maps which are generated from a feature detection on a dataset. The specific example considered in this work is the vortical flow in a two-dimensional oceanographic dataset. This thesis focuses on performing feature extraction by detecting the features and processing the feature maps in three different modules, namely, denoising, segmenting and ranking. The denoising module exploits a wavelet-based multiresolution analysis (MRA). Although developed for two-dimensional datasets, these techniques are directly extendable to three-dimensional cases. A comparative study of the performance of Optimal Feature-Preserving (OFP) filters and non-OFP filters for denoising is presented. A computationally economical implementation for segmenting the feature maps as well as different algorithms for ranking the regions of interest (ROI's) are also discussed in this work.

No description available.

No description available.

A height field is a set of height distance values sampled at a finite set of sample points in a two-dimensional parameter domain. A height field usually contains a lot of redundant information, much of which can be removed without a substantial degradation of its quality. A common approach to reducing the size of a height field representation is to use a piecewise polygonal surface approximation. This consists of a mesh of polygons that approximates the surfaces of the original data at a desired level of accuracy. Polygonal surface approximation of height fields has numerous applications in the fields of computer graphics and computer vision. Triangular mesh approximations are a popular means of representing three-dimensional surfaces, and multiresolution analysis (MRA) is often used to obtain compact representations of dense input data, as well as to allow surface approximations at varying spatial resolution. Multiresolution approaches, particularly those moving from coarse to fine resolutions, can often improve the computational efficiency of mesh generation as well as can provide easy control of level of details for approximations. This dissertation concerns the use of wavelet-based MRA methods to produce a triangular-mesh surface approximation from a single height field dataset. The goal of this study is to obtain a fast surface approximation for a set of height data, using a small number of approximating elements to satisfy a given error criterion. Typically, surface approximation techniques attempt to balance error of fit, number of approximating elements, and speed of computation. A novel aspect of this approach is the direct evaluation of wavelet coefficients to assess surface shape characteristics within each triangular element at a given scale. Our approach hierarchically subdivides and refines triangles as the resolution level increases. / Ph. D.

This study assessed the utility of an object-oriented approach to deciduous and coniferous forest volume and above ground biomass estimation, based solely on small-footprint, multiple return lidar data. The study area is located in Appomattox Buckingham State Forest in the Piedmont physiographic province of Virginia, U.S.A, at 78°41’ W, 37°25’ N. Vegetation is composed of various coniferous, deciduous, and mixed forest stands. The eCognition segmentation algorithm was used to derive objects from a lidar-based canopy height model (CHM). New segment selection criteria, based on between- and within-segment CHM variance, and average field plot size, were developed. Horizontal point samples were used to measure in-field volume and biomass, for 2-class (deciduous-coniferous) and 3-class (deciduous-coniferous-mixed) forest schemes. Per-segment lidar distributional parameters, e.g., mean, range, and percentiles, were extracted from the lidar data and used as input to volume and biomass regression analysis. Discriminant classification was performed using lidar point height and CHM distributions. There was no evident difference between the two-class and three-class approaches, based on similar adjusted R2 values. Two-class forest definition was preferred due to its simplicity. Two-class adjusted R2 and root mean square error (RMSE) values for deciduous volume (0.59; 51.15 m3/ha) and biomass (0.58; 37.41 Mg/ha) were improvements over those found in another plot-based study for the same study area. Although coniferous RMSE values for volume (38.03 m3/ha) and biomass (17.15 Mg/ha) were comparable to published results, adjusted R2 values (0.66 and 0.59) were lower. This was attributed to more variability and a narrower range (6.94 - 350.93 m3/ha) in measured values. Classification accuracy for discriminant classification based on lidar point height distributions (89.2%) was a significant improvement over CHM-based classification (79%). A lack of modeling and classification differences between average segment sizes was attributed to the hierarchical nature of the segmentation algorithm. However, segment-based modeling was distinctly better than modeling based on existing forest stands, with values of 0.42 and 62.36 m3/ha (volume) and 0.46 and 41.18 Mg/ha (biomass) for adjusted R2 and RMSE, respectively. Modeling results and classification accuracies indicated that an object-oriented approach, based solely on lidar data, has potential for full-scale forest inventory applications. / Ph. D.

A expressividade é um elemento chave para o transporte de emoções em música, e seu modelamento, vital para a concepção de sistemas de síntese mais realistas. Gestos musicais executados durante a interpretação usualmente portam a informação responsável pela expressividade percebida, e podem ser rastreados por meio de padrões sônicos a eles associados em diversas escalas de resolução. Um conjunto relevante de gestos musicais expressivos foi estudado através de uma análise em multiresolução utilizando-se a transformada wavelet. A escolha deve-se principalmente à capacidade natural desta ferramenta em realizar análises de tempo-escala/frequência, e suas semelhanças com o processamento dos estágios primários do sistema auditivo. Vinte e sete eventos musicais foram capturados em interpretações de violino e flauta, e analisados com o objetivo de avaliar a aplicabilidade desta ferramenta na identificação e segregação de padrões sônicos associados a gestos musicais expressivos. Os algoritmos wavelet foram implementados na plataforma MATLAB utilizando-se bancos de filtros organizados em esquema piramidal. Rotinas para análises gráfica e sônica e uma interface ao usuário foram também implementadas. Verificou-se que as wavelets permitem a identificação de padrões sônicos associados a gestos expressivos exibindo diferentes propriedades em níveis diferentes da análise. A técnica mostrou-se útil para isolar ruídos oriundos de fontes diversas, extrair transientes associados a gestos súbitos e/ou intensos, e para segregar a estrutura harmônica de tons musicais, entre outras potencialidades não menos importantes. Particularidades da técnica e efeitos secundários observados são discutidos, e os padrões sônicos observados nos níveis wavelets são correlacionados com os gestos musicais que lhes deram origem. São propostos trabalhos futuros objetivando a investigação de certos eventos musicais e fenômenos verificados, bem como o estudo de implementações alternativas. / Expressiveness is a key element for emotion transportation in music, and its modeling necessary to conceive more realistic synthesis systems. Musical gestures executed during a performance carry the information answering for expressiveness, and may be tracked by means of sonic patterns associated to them within several resolution scales. A relevant set of musical gestures was studied through a multiresolution analysis using the wavelet transform. The choice for this tool is mainly due to its natural ability to perform time-scale/frequency analysis, and for its similarities with early auditory processing stages. Twenty seven musical events were captured from violin and flute performances, and analyzed in order to evaluate the applicability of this tool for identification and segregation of sonic patterns associated with expressive musical gestures. The wavelet algorithms were implemented on the MATLAB platform, employing filter banks organized in a pyramidal scheme. Graphical and sonic analysis routines and a user interface were carried out over the same platform. It was verified that wavelets enable the identification of sonic patterns associated to musical gestures revealing different properties on different levels of the analysis. The technique showed up useful to isolate noise from different sources, extract transients associated to sudden and/or intense gestures, and segregate the tonal harmonic structure, among other important features. Particularities of the technique and secondary effects observed are discussed, and sonic patterns on wavelet levels are correlated with the musical gestures which produced them. Future works are proposed addressing further investigation of certain musical events and phenomena observed, as well as the study of alternative implementations.

A expressividade é um elemento chave para o transporte de emoções em música, e seu modelamento, vital para a concepção de sistemas de síntese mais realistas. Gestos musicais executados durante a interpretação usualmente portam a informação responsável pela expressividade percebida, e podem ser rastreados por meio de padrões sônicos a eles associados em diversas escalas de resolução. Um conjunto relevante de gestos musicais expressivos foi estudado através de uma análise em multiresolução utilizando-se a transformada wavelet. A escolha deve-se principalmente à capacidade natural desta ferramenta em realizar análises de tempo-escala/frequência, e suas semelhanças com o processamento dos estágios primários do sistema auditivo. Vinte e sete eventos musicais foram capturados em interpretações de violino e flauta, e analisados com o objetivo de avaliar a aplicabilidade desta ferramenta na identificação e segregação de padrões sônicos associados a gestos musicais expressivos. Os algoritmos wavelet foram implementados na plataforma MATLAB utilizando-se bancos de filtros organizados em esquema piramidal. Rotinas para análises gráfica e sônica e uma interface ao usuário foram também implementadas. Verificou-se que as wavelets permitem a identificação de padrões sônicos associados a gestos expressivos exibindo diferentes propriedades em níveis diferentes da análise. A técnica mostrou-se útil para isolar ruídos oriundos de fontes diversas, extrair transientes associados a gestos súbitos e/ou intensos, e para segregar a estrutura harmônica de tons musicais, entre outras potencialidades não menos importantes. Particularidades da técnica e efeitos secundários observados são discutidos, e os padrões sônicos observados nos níveis wavelets são correlacionados com os gestos musicais que lhes deram origem. São propostos trabalhos futuros objetivando a investigação de certos eventos musicais e fenômenos verificados, bem como o estudo de implementações alternativas. / Expressiveness is a key element for emotion transportation in music, and its modeling necessary to conceive more realistic synthesis systems. Musical gestures executed during a performance carry the information answering for expressiveness, and may be tracked by means of sonic patterns associated to them within several resolution scales. A relevant set of musical gestures was studied through a multiresolution analysis using the wavelet transform. The choice for this tool is mainly due to its natural ability to perform time-scale/frequency analysis, and for its similarities with early auditory processing stages. Twenty seven musical events were captured from violin and flute performances, and analyzed in order to evaluate the applicability of this tool for identification and segregation of sonic patterns associated with expressive musical gestures. The wavelet algorithms were implemented on the MATLAB platform, employing filter banks organized in a pyramidal scheme. Graphical and sonic analysis routines and a user interface were carried out over the same platform. It was verified that wavelets enable the identification of sonic patterns associated to musical gestures revealing different properties on different levels of the analysis. The technique showed up useful to isolate noise from different sources, extract transients associated to sudden and/or intense gestures, and segregate the tonal harmonic structure, among other important features. Particularities of the technique and secondary effects observed are discussed, and sonic patterns on wavelet levels are correlated with the musical gestures which produced them. Future works are proposed addressing further investigation of certain musical events and phenomena observed, as well as the study of alternative implementations.

In dieser Arbeit werden Algorithmen für die Berechnung elektronischer Korrelations- und Anregungsenergien mittels der Coupled-Cluster Methode auf adaptiven Gittern entwickelt und implementiert. Die jeweiligen Funktionen und Operatoren werden adaptiv durch Multiskalenanalyse dargestellt, was eine Basissatz unabängige Beschreibung mit kontrollierter numerischer Genauigkeit ermöglicht. Gleichungen für die Coupled-Cluster Methode werden in einem verallgemeinerten Rahmen, unabhängig von virtuellen Orbitalen und globalen Basissätzen, neu formuliert. Hierzu werden die amplitudengewichteten Anregungen in virtuelle Orbitale ersetzt durch Anregungen in n-Elektronenfunktionen, welche durch Gleichungen im n-Elektronen Ortsraum bestimmt sind. Die erhaltenen Gleichungen können, analog zur Basissatz abh¨angigen Form, mit leicht angepasster Interpretation diagrammatisch dargestellt werden. Aufgrund des singulären Coulomb Potentials werden die Arbeitsgleichungen mit einem explizit korrelierten Ansatz regularisiert. Coupled-Cluster singles mit genäherten doubles (CC2) und ähnliche Modelle werden, für geschlossenschalige Systeme und in regularisierter Form, in die MADNESS Bibliothek (eine allgemeine Bibliothek zur Darstellung von Funktionen und Operatoren mittels Multiskalenanalyse) implementiert. Mit der vorgestellten Methode können elektronische CC2 Paarkorrelationsenergien und Anregungsenergien mit bestimmter numerischer Genauigkeit unabhängig von globalen Basissätzen berechnet werden, was anhand von kleinen Molekülen verifiziert wird / In this work algorithms for the computation of electronic correlation and excitation energies with the Coupled-Cluster method on adaptive grids are developed and implemented. The corresponding functions and operators are adaptively represented with multiresolution analysis allowing a basis-set independent description with controlled numerical accuracy. Equations for the coupled-cluster model are reformulated in a generalized framework independent of virtual orbitals and global basis-sets. For this, the amplitude weighted excitations into virtuals are replaced by excitations into n-electron functions which are determined by projected equations in the n-electron position space. The resulting equations can be represented diagrammatically analogous to basis-set dependent approaches with slightly adjusted rules of interpretation. Due to the singular Coulomb potential, the working equations are regularized with an explicitly correlated ansatz. Coupled-cluster singles with approximate doubles (CC2) and similar models are implemented for closed-shell systems and in regularized form into the MADNESS library (a general library for the representation of functions and operators with multiresolution analysis). With the presented approach electronic CC2 pair-correlation energies and excitation energies can be computed with definite numerical accuracy and without dependence on global basis sets, which is verified on small molecules.

Geographic object-based image analysis (GEOBIA) is an innovative image classification technique that treats spatial features in an image as objects, rather than as pixels; thus resembling closer to that of human perception of the geographic space. However, the process of a GEOBIA application allows for multiple interpretations. Particularly sensitive parts of the process include image segmentation and training data selection. The multiresolution segmentation algorithm (MSA) is commonly applied. The performance of segmentation depends primarily on the algorithms scale parameter, since scale controls the size of image objects produced. The fact that the scale parameter is unit less makes it a challenge to select a suitable one; thus, leaving the analyst to a method of trial and error. This can lead to a possible bias. Additionally, part from the segmentation, training area selection usually means that the data has to be manually collected. This is not only time consuming but also prone to subjectivity. In order to overcome these challenges, we tested a GEOBIA scheme that involved automatic methods of MSA scale parameterisation and training area selection which enabled us to more objectively classify images. Three study areas within Sweden were selected. The data used was high resolution Geografiska Sverigedata (GSD) orthophotos from the Swedish mapping agency, Lantmäteriet. We objectively found scale for each classification using a previously published technique embedded as a tool in eCognition software. Based on the orthophoto inputs, the tool calculated local variance and rate of change at different scales. These figures helped us to determine scale value for the MSA segmentation. Moreover, we developed in this study a novel method for automatic training area selection. The method is based on thresholded feature statistics layers computed from the orthophoto band derivatives. Thresholds were detected by Otsu’s single and multilevel algorithms. The layers were run through a filtering process which left only those fit for use in the classification process. We also tested the transferability of classification rule-sets for two of the study areas. This test helped us to investigate the degree to which automation can be realised. In this study we have made progress toward a more objective way of object-based image classification, realised by automating the scheme. Particularly noteworthy is the algorithm for automatic training area selection proposed, which compared to manual selection restricts human intervention to a minimum. Results of the classification show overall well delineated classes, in particular, the border between open area and forest contributed by the elevation data. On the other hand, there still persists some challenges regarding separating between deciduous and coniferous forest. Furthermore, although water was accurately classified in most instances, in one of the study areas, the water class showed contradictory results between its thematic and positional accuracy; hence stressing the importance of assessing the result based on more than the thematic accuracy. From the transferability test we noted the importance of considering the spatial/spectral characteristics of an area before transferring of rule-sets as these factors are a key to determine whether a transfer is possible.