A number of missions to comets and asteroids have been undertaken by major space organizations driving a need to accurately characterize their gravitational fields. This is complicated however by their irregular shapes. To accurately and safely navigate spacecraft in these environments, a simple point-mass gravity model is insufficient and instead higher-fidelity models are required. Several such models exist for this purpose but all posess drawbacks. Moreover, there are some applications for which the currently available models are not particular well suited. In this dissertation, numerical quadrature and curvilinear meshing techniques are applied to the small body gravity problem. The goal of this work is to to create a gravitational model suitable for integating large numbers of low altitude trajectories and rapidly characterizing the near-surface potential field. In total three new models are developed. The first applies two-dimensional quadrature formulas to calculate the gravitational field of an arbitrary triangular surface mesh. The second extends this result to curvilinear surface meshes that more accurately approximate the surface topology. The third applies three-dimensional quadrature to curvilinear tetrahedral meshes to generate accurate distributions of point-masses. The accuracy of the new models is fully characterized and simple relations are presented for predicting the error of integrated trajectories. The efficiency of the models is then compared to other high-fidelity models currently in use. The new models perform well between the body's circumsphere and a thin layer that surrounds the surface.

nÃo hà / O presente estudo tem por objetivo analisar as relaÃÃes comerciais entre o estado do Cearà e os demais estados da federaÃÃo do Brasil no ano de 2010. O caminho traÃado para a anÃlise aborda a tÃcnica do modelo gravitacional como referencial analÃtico, com vistas a elaborar um modelo empÃrico para a estimaÃÃo dos determinantes do fluxo das exportaÃÃes interestaduais das empresas enquadradas na atividade de indÃstria de transformaÃÃo. Para tal, foi estimado o Modelo Gravitacional por meio do mÃtodo dos MÃnimos Quadrados OrdinÃrios (MQO) utilizando as movimentaÃÃes comerciais das exportaÃÃes interestaduais do CearÃ, o Produto Interno Bruto (PIB) dos estados e a distÃncia entre Fortaleza e as capitais dos demais estados brasileiros. Os dados relativos Ãs exportaÃÃes foram extraÃdos dos registros da Secretaria de Estado da Fazenda do Cearà (Sefaz-Ce), atravÃs do sistema informatizado da nota fiscal eletrÃnica (NFE). Os resultados empÃricos obtidos na anÃlise indicam que apenas a variÃvel distÃncia apresentou significÃncia estatÃstica e o sinal està de acordo com o previsto na literatura dos modelos gravitacionais. / The present study aims to analyze the trade relations between the state of Cearà and the other States of the Federation of Brazil in the year 2010. The path traced for analysis discusses the technique of the gravitational model as a reference analytical, with a view to develop an empirical model to estimate the determinants of the flow of interstate exports from companies classified in the activity of manufacturing industry. To this end, it was estimated the gravitational model through the Ordinary Least Squares method (OLS) using the commercial transactions of the interstate exports of CearÃ, the Gross Domestic Product (GDP) of the states and the distance between Fortaleza and the capitals of other Brazilian states. The data on exports were extracted of the records of the Department of Finance of Cearà (Sefaz-Ce), through the computerized system of electronic invoice (NFE). The empirical results obtained from the analysis indicate that only the variable distance was statistically significant and the signal is in accordance with the provisions in the literature from gravitational models.

nÃo hà / A anÃlise de imagens à um importante campo da visÃo computacional cujo propÃsito à extrair informaÃÃes significativas de imagens. Entre os vÃrios atributos relevantes que podem ser analisados, a textura à um dos mais importantes por ser uma fonte rica de informaÃÃes. O objetivo desta tese à desenvolver novos mÃtodos de anÃlise de textura (nÃveis de cinza e coloridas) baseados em modelos gravitacionais simplicados e caminhos mais curtos em grafos, que propiciem vetores de caracterÃsticas mais discriminativos do que os mÃtodos jà estabelecidos pela literatura. A primeira abordagem converte uma imagem em um sistema gravitacional simplificado cujo processo de colapso à explorado por meio de descritores de dimensÃo fractal e lacunaridade. A segunda abordagem converte os pixels de uma imagem em vÃrtices de um grafo ponderado nÃo-orientado e explora os caminhos mais curtos entre pares de vÃrtices em diferentes escalas e orientaÃÃes. Adicionalmente, nesta tese à proposto o estudo dessas abordagens na anÃlise de imagens de folhas de plantas para facilitar o moroso processo de taxonomia vegetal (problema este especialmente relevante para os botÃnicos) e de imagens mÃdicas para identificaÃÃo/classificaÃÃo de patologias, auxiliando o diagnÃstico mÃdico. Os experimentos sÃo realizados nas bases de imagens: Brodatz, UIUC, VisTex, USPTex, Outex, texturas foliares, parÃnquima paliÃÃdico, pap-smear e de tecido mamÃrio. Os resultados mais significativos de classificaÃÃo sÃo obtidos das bases UIUC, USPTex e parÃnquima paliÃÃdico, com taxas de acertos de 55,00%, 96,57% e 91,56% (menores taxas) obtidas pelos mÃtodos propostos, respectivamente. Essas taxas de acertos sÃo quase sempre superiores aos resultados obtidos pelos mÃtodos usados para comparaÃÃo, demonstrando que os mÃtodos propostos abrem promissoras fontes de pesquisa para os estudos de anÃlise de texturas em nÃveis de cinza e coloridas. / Image analysis is an important field of computer vision whose role is to extract significant information from images. Among several relevant attributes, texture is one of the most important because it is a rich source of information. This thesis aims to develop novel texture analysis methods (for grayscale and color images) based on simplified gravitational systems and shortest paths in graphs which provide feature vectors more discriminative than the methods already established in literature. The first approach converts an image into a simplified gravitational system whose collapse process is explored by using fractal dimension and lacunarity descriptors. The second approach converts the pixels of an image into vertices of a non-oriented weighted graph and explores the shortest paths between pairs of vertices in different scales and orientations. Additionally, this thesis proposes to apply these approaches to plant leaf identification (a relevant problem for botanists), and medical image identification/classication, increasing the confidence of medical diagnosis. The experiments are performed on the following image databases: Brodatz,UIUC, VisTex, USPTex, Outex, leaf textures, palisade parenchyma, pap-smear and breast tissues. The most significant comparison results are obtained from UIUC, USPTex and palisade parenchyma, with success rates of 55,00%, 96,57% and 91,56% (lower success rates) obtained by the proposed methods, respectively. These success rates are almost always superior to the results obtained by the methods used for comparison. This demonstrates that the proposed methods open promising sources of research in grayscale and color texture analysis.

In this thesis work the accuracy of the spherical harmonic synthesis and analysis are investigated, by simulated numerical studies.The main idea is to investigate the loss of accuracy, in the geopotential coeffcients, by the following testing method. We start with a synthesis calculation, using the coefficients(EGM2008), to calculate geoid heights on a regular grid. Those geoid heights are then used in an analysis calculation to obtain a new set of coeffcients, which are in turn used to derive a new set of geoid heights. The difference between those two sets of geoid heights will be analyzed to assess the accuracy of the synthesis and analysis calculations.The tests will be conducted with both point-values and area-means in the blocks in the grid. The area-means are constructed in some different ways and will also be compared to the mean value from 10000 point values as separate tests. Numerical results from this investigation show there are signifi…cant systematic errors in the geoid heights computed by spherical harmonic synthesis and analysis, sometimes reaching as high as several meters. Those big errors are most common at the polar regions and at the mid-latitude regions.