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Ba, Demba Elimane. "Nonlinear transform coding with lossless polar coordinates." Thesis, Massachusetts Institute of Technology, 2006. http://hdl.handle.net/1721.1/37937.
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Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.Includes bibliographical references (p. 51-52).
In conventional transform coding, the importance of preserving desirable quantization partition cell shapes prevents one from considering the use of a nonlinear change of variables. If no linear transformation of a given source would yield independent components, this means having to encode it at a rate higher than its entropy, i.e. suboptimally. This thesis proposes a new transform coding technique where the source samples are first uniformly scalar quantized and then transformed with an integer-to-integer approximation to a nonlinear transformation that would give independent components. In particular, we design a family of integer-to-integer approximations to the Cartesian-to-polar transformation and analyze its behavior for high rate transform coding. Among the benefits of such an approach is the ability to achieve redundancy reduction beyond decorrelation without limitation to orthogonal linear transformations of the original variables. A high resolution analysis is given, and for source models inspired by a sensor network application and by image compression, simulations show improvements over conventional transform coding. A comparison to state-of-the-art entropy-coded polar quantization techniques is also provided.
by Demba Elimane Ba.
S.M.
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Yao, Xueyang. "The Discrete 2D Fourier Transform In Polar Coordinates." Thesis, Université d'Ottawa / University of Ottawa, 2018. http://hdl.handle.net/10393/37656.
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The discrete Fourier transform in Cartesian coordinates has proved to be invaluable in many disciplines. However, less theory has been developed for functions that are best described in polar coordinates. In this thesis, a new discrete 2D-Fourier transform in polar coordinates is proposed and tested by numerical simulations. Guidelines for choosing sample size are developed. Furthermore, to be as useful as its Cartesian counterpart, improvements are made to reduce the computing time.
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Dovlo, Edem. "Development of a Symbolic Computer Algebra Toolbox for 2D Fourier Transforms in Polar Coordinates." Thèse, Université d'Ottawa / University of Ottawa, 2011. http://hdl.handle.net/10393/20269.
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The Fourier transform is one of the most useful tools in science and engineering and can be expanded to multi-dimensions and curvilinear coordinates. Multidimensional Fourier transforms are widely used in image processing, tomographic reconstructions and in fact any application that requires a multidimensional convolution. By examining a function in the frequency domain, additional information and insights may be obtained.
In this thesis, the development of a symbolic computer algebra toolbox to compute two dimensional Fourier transforms in polar coordinates is discussed. Among the many operations implemented in this toolbox are different types of convolutions and procedures that allow for managing the toolbox effectively. The implementation of the two dimensional Fourier transform in polar coordinates within the toolbox is shown to be a combination of two significantly simpler transforms. The toolbox is also tested throughout the thesis to verify its capabilities.
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Nunes, JoÃo Gilberto GonÃalves. "CÃnicas unificadas em coordenadas polares para uma nova abordagem no ensino mÃdio." Universidade Federal do CearÃ, 2014. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=11665.
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CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel SuperiorNeste trabalho, estudam-se de maneira sucinta as caracterÃsticas e os principais elementos algÃbricos e geomÃtricos das secÃÃes cÃnicas. Inicialmente, foram abordados os trÃs tipos gerais das secÃÃes cÃnicas, enfocando em princÃpio suas formas regulares para, em dado momento, tambÃm se discutir suas formas degeneradas. Verificou-se que, segundo um sistema cartesiano fixado, à possÃvel estabelecer uma representaÃÃo global das cÃnicas por meio de uma equaÃÃo algÃbrica do segundo grau em duas variÃveis, sendo que qualquer equaÃÃo desta forma,reciprocamente, pode ser identificada, por meio de rotaÃÃo ou translaÃÃo, com a equaÃÃo reduzida de algum tipo particular de cÃnica. Encerrando-se este trabalho, foi proposta uma abordagem inovadora para a lida no ensino mÃdio desse tÃpico de ensino-aprendizagem riquÃssimo em conceitos bÃsicos de Ãlgebra e geometria elementares, tÃo necessÃrios para uma boa formaÃÃo matemÃtica. Foi proposto que no estudo das cÃnicas se use de forma complementar a maneira alternativa de defini-las a partir de sua excentricidade, convergindo para a equaÃÃo geral unificada das cÃnicas em coordenadas polares. Essa forma generalizada e absolutamente simples de se representar as cÃnicas à tida como facilmente manipulÃvel e reflete em si mesma uma beleza singular da MatemÃtica, a Rainha das CiÃncias. Vale ressaltar que todo o enfoque dos conteÃdos aqui discutidos foi apresentado numa linguagem bastante simples e de fÃcil compreensÃo, uma vez que este trabalho se destina preferencialmente a alunos e professores da educaÃÃo bÃsica.
In this work, the features and the main algebraic and geometric elements of conic sections were succinctly studied. lnitially, the three general types of the conic sections were discussed, focusing at first on their regular forms and then, in certain moment, discussing about their degenerate forms. It was found that, according to a fixed Cartesian system, it is possible to establish a global representation of the conics through a two-variable algebraic quadratic equation, in a way that, in any equation of this form, reciprocally, can be identified by means of rotation or translation, with the reduced equation of any particular type of conic. At the end of this work, it was proposed an innovative approach of this rich teaching-leaming topic in basic concepts of elementary algebra and geometry to be applied in high school, as required for good mathematical training. lt was proposed that the study of conic would be used complementing the alternativa way to define them from their eccentricity, converging to a unified general equation of the conics in polar coordinates. This generalized way and absolutely simple to represent the conical is seen as easily manipulated and reflects on itself a singular beauty of mathematics, The Queen of Sciences. lt is worth to emphasize that the focus of the content discussed was presented in a very simple, easy to understand language, once this work is preferably intended for students and teachers of basic education.
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White, Edward C. Jr. "Polar - legendre duality in convex geometry and geometric flows." Thesis, Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/24689.
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Барило, Олександр Борисович, Александр Борисович Барило, Oleksandr Borysovych Barylo, and К. В. Алтиннікова. "Особливості обробки електронограм у полярних координатах." Thesis, Видавництво СумДУ, 2010. http://essuir.sumdu.edu.ua/handle/123456789/4416.
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Silva, Diego Maradona Félix da. "A hipérbole e suas aplicações." Universidade Federal de Goiás, 2013. http://repositorio.bc.ufg.br/tede/handle/tede/3442.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
The Hyperbole and its Applications begins with a brief historical background on the origins of the conic sections analysis, followed by a proposition of a new approach to the conic sections studies in High School, due to the large amount of important applications these studies have in everyday life. The rst chapter of the research presents the primary concepts necessary to a good hyperbole study understanding. After presenting this concepts the research focuses in the evidence of the hyperbole concept, its most important elements, the rotary axis and the hyperbole properties. Among these properties, the main object of this study is the re ective hyperbole property, since it can be applied to many elds of study such as Astronomy, in the Telescopes and even Navigations. Some other properties are brie y mentioned during this work and others have a more detailed approach. Finally, a largely used new coordinates system is presented - the Polar Coordinate System. The research purpose is to infer, by the use of this new system, the equations of the ellipse, parable and hyperbole.
A Hipérbole e suas Aplicações inicia-se com um breve contexto histórico sobre o qual se originou o estudo das cônicas e propõe uma abordagem diferenciada para o estudo de cônicas no Ensino Médio devido a grande quantidade de aplicações importantes das propriedades das cônicas no cotidiano. O primeiro capítulo do trabalho trata-se dos conceitos preliminares para um bom estudo da hipérbole. Logo em seguida apresentamos o conceito de hipérbole, seus principais elementos, rotação de eixos e propriedades da hipérbole. Dentre essas propriedades, o principal objeto de estudo será a propriedade re etora da hipérbole, pois é esta que tem aplicações nos mais variados ramos da ciência tal como Astronomia, nos telescópios e na navegação. Algumas aplicações serão citadas brevemente e outras abordadas com mais detalhes. Finalizando, apresentaremos um novo sistema de coordenadas também muito utilizado: o sistema de Coordenadas Polares e adotando esse novo sistema, deduzir as equações da elipse, parábola e hipérbole.
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Stanque, Edson Luis. "DIVISÃO DE POLÍGONOS IRREGULARES DO ELIPSÓIDE BIAXIAL NA SUPERFÍCIE DA PROJEÇÃO AZIMUTAL EQUIVALENTE DE LAMBERT." Universidade Federal de Santa Maria, 2007. http://repositorio.ufsm.br/handle/1/9485.
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This dissertation supplies the methodology of the measure (area) in the Earth model adopted for Geodesy. This model is the ellipsoid of revolution, in which the system of Cartesian coordinates, the curvilinear coordinate system and the polar coordinate system are described. The coordinate nature in the development of the surface measure calculation is discussed. The following demonstrations are illustrated: the ellipse equation, the eccentricity of the ellipse, the meridian section curvature radius equation, the meridian transversal section curvature radius equation and elliptic integral. It define algebraic geodesic line and geometrically. The juridical basis are the article 3º of Brazilian Federal Law 10.267/2001, which modify article 176 of the Brazilian Federal Law 6.015/1973 (Public Record Law) and adds to this article the paragraphs 3º and 4º, the paragraph 3º of article 225 of the Brazilian Law 6.015/1973 and the article 971 of the Código de Processo Civil (CPC), which require the coordinates of the corners of the real property on the Brazilian Geodetic System (SGB). The partitioning of the regular ellipsoid quadrilateral and the partitioning of the irregular ellipsoid quadrilateral located in the real property Pó de Serra is presented. To become this partitioning, it was used surface of the Lambert azimuthal equal-area projection, i. e., the curvilinear geodetic coordinates in plane coordinates has been transformed. The surface partitioning was determined using the method area equation of the Gauss trapezes connected with the equation of the straight line. The direct problem of the Lambert azimuthal equal-area projection and the inverse problem supply the methodology that become feasible the juridical exigence (articles 176 and 225 of Brazilian Federal Law 6.015/1973 and article 971 of the CPC). The methodology to the geodetic coordinates system with the purpose to calculate the partitioned areas of surface on the ellipsoid can be applied. The calculation of surface measure supplies the effective practice of the mencioned juridical basis.O propósito deste trabalho é fornecer os fundamentos de cálculo de medida de superfície (área) no modelo de Terra adotado pela Geodésia. Esse modelo é o elipsóide de revolução ao qual se vincula o sistema de coordenadas cartesianas, o sistema de coordenadas curvilíneas e o sistema de coordenadas polares. Discute a natureza das coordenadas no desenvolvimento do cálculo da medida de superfície. Efetuam-se as seguintes demonstrações: equação da elipse, equação da excentricidade da elipse, equação do raio de curvatura da seção meridiana, equação do raio de curvatura da seção transversal meridiana e integral elíptica. Define linha geodésica algébrica e geometricamente. Apresentam-se os instrumentos legais que são o artigo 3º da Lei 10.267/2001, o qual altera o artigo 176, inciso II da Lei 6.015/1973 (Lei de Registros Públicos) e acrescenta a este artigo os parágrafos 3º e 4º, o parágrafo 3º do artigo 225 da Lei 6.015/1973 e o artigo 971 do Código de Processo Civil (CPC), os quais vinculam as coordenadas dos vértices do imóvel ao Sistema Geodésico Brasileiro (SGB). Efetuam-se a divisão do quadrilátero elipsóidico regular e também do quadrilátero elipsóidico irregular localizado na gleba Pó de Serra. Para se fazer esta divisão, usou-se a superfície da projeção azimutal equivalente de Lambert, ou seja, as coordenadas elipsóidicas curvilíneas foram transformadas em coordenadas planas desse sistema de projeção. A divisão destas superfícies foi efetuada pelo método da equação da área dos trapézios de Gauss em conjunto com a equação da reta. Os problemas direto e inverso da projeção azimutal equivalente de Lambert fornecem a metodologia que tornam exeqüíveis os dispositivos legais (artigos 176 e 225 da Lei 6.015/1973 e artigo 971 do CPC). A metodologia de cálculo proposto pode ser aplicada ao sistema de coordenadas geodésicas com a finalidade de calcular as áreas de uma divisão de superfície no elipsóide. Os fundamentos do cálculo de medida de superfície instrumentalizam o efetivo cumprimento dos dispositivos legais retrocitados.
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Sousa, Segundo Jos? S?vio Alves de. "Um m?todo para determina??o da profundidade combinando vis?o est?reo e autocalibra??o para aplica??o em rob?tica m?vel." Universidade Federal do Rio Grande do Norte, 2007. http://repositorio.ufrn.br:8080/jspui/handle/123456789/15209.
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Previous issue date: 2007-04-30Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior
This work proposes a method to determine the depth of objects in a scene using a combination between stereo vision and self-calibration techniques. Determining the rel- ative distance between visualized objects and a robot, with a stereo head, it is possible to navigate in unknown environments. Stereo vision techniques supply a depth measure by the combination of two or more images from the same scene. To achieve a depth estimates of the in scene objects a reconstruction of this scene geometry is necessary. For such reconstruction the relationship between the three-dimensional world coordi- nates and the two-dimensional images coordinates is necessary. Through the achievement of the cameras intrinsic parameters it is possible to make this coordinates systems relationship. These parameters can be gotten through geometric camera calibration, which, generally is made by a correlation between image characteristics of a calibration pattern with know dimensions. The cameras self-calibration allows the achievement of their intrinsic parameters without using a known calibration pattern, being possible their calculation and alteration during the displacement of the robot in an unknown environment. In this work a self-calibration method based in the three-dimensional polar coordinates to represent image features is presented. This representation is determined by the relationship between images features and horizontal and vertical opening cameras angles. Using the polar coordinates it is possible to geometrically reconstruct the scene. Through the proposed techniques combination it is possible to calculate a scene objects depth estimate, allowing the robot navigation in an unknown environment
Este trabalho prop?e um m?todo para determinar a profundidade de objetos em cena utilizando uma combina??o das t?cnicas de vis?o est?reo e autocalibra??o. Determinando a dist?ncia relativa entre objetos visualizados e um rob? m?vel, dotado de uma cabe?a est?reo, ? poss?vel efetuar sua navega??o em ambientes desconhecidos. As t?cnicas de vis?o est?reo fornecem uma medida de profundidade a partir da combina??o de duas ou mais imagens de uma mesma cena. Para a obten??o de estimativas da profundidade dos objetos presentes nesta cena ? necess?rio uma reconstru??o da geometria da mesma. Para tal reconstru??o ? necess?rio o relacionamento das coordenadas tridimensionais do mundo com as coordenadas bidimensionais das imagens. Atrav?s da obten??o dos par?metros intr?nsecos das c?meras ? poss?vel fazer o relacionamento entre os sistemas de coordenadas. Estes par?metros podem ser obtidos atrav?s da calibra??o geom?trica das c?meras, a qual ? geralmente feita atrav?s da visualiza??o de um objeto padr?o de calibra??o com dimens?es conhecidas. A autocalibra??o das c?meras permite a obten??o dos par?metros intr?nsecos das mesmas sem a utiliza??o de um padr?o conhecido de calibra??o, sendo poss?vel a obten??o e a altera??o destes durante o deslocamento do rob? m?vel em um ambiente desconhecido. ? apresentado neste trabalho um m?todo de autocalibra??o baseado na representa??o de caracter?sticas da imagem por coordenadas polares tridimensionais. Estas s?o determinadas relacionando-se caracter?sticas das imagens com os ?ngulos de abertura horizontal e vertical das c?meras. Utilizando-se estas coordenadas polares ? poss?vel efetuar uma reconstru??o geom?trica da cena de forma precisa. Atrav?s desta combina??o das t?cnicas proposta ? poss?vel obter-se uma estimativa da profundidade de objetos cena, permitindo a navega??o de um rob? m?vel aut?nomo em um ambiente desconhecido
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MIYABO, Susumu, Toru NAKAMURA, Yasushi ISHII, Toshihiro MISAWA, Joan Dae LEE, Hisatoshi MAEDA, 進. 宮保, et al. "極座標による心筋Tｌ-201Bull's-eye表示の試み." 日本核医学会, 1988. http://hdl.handle.net/2237/19427.
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Мартиненко, Сергій Сергійович, Сергей Сергеевич Мартыненко, Serhii Serhiiovych Martynenko, and М. С. Руденко. "Оптимізація радіуса кола зчитування полярної системи координат при розпізнаванні біологічних об`єктів." Thesis, Видавництво СумДУ, 2010. http://essuir.sumdu.edu.ua/handle/123456789/4427.
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Naser, Inam. "Rotated Polar Coordinate system, its Solid Vector Mathematical Operations, and 3-D Unsharp Masking and Gradient-Based Laplacian Spatial Filters of a Field of Vectors for Geometrical Edges Detection." University of Cincinnati / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1592135647774656.
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Soares, Vanessa Ribeiro. "Batalha naval e suas aplicações." Universidade Federal de Goiás, 2016. http://repositorio.bc.ufg.br/tede/handle/tede/5909.
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This work has the purpose contribute to the improvement in some teaching contents of analytic geometry and trigonometry in high school . The content work was based on the National Curriculum Parameters, highlighting de nitions, theorems and properties necessary for the development of student learning. The theme was chosen after a practical experience involving the Naval Battle game in order to reduce the students' di culties. The playful work, as the game, has a practical application that does the student become familiar with the content. That's an interesting way to propose problems and solutions involving the content. Thus becomes something attractive to the student and encourages creativity in nding problems solutions.
O trabalho tem como objetivo contribuir para o aprimoramento no ensino de alguns conteúdos de Geometria Analítica e Trigonometria no Ensino Médio. Dentro dos Parâmetros Curriculares Nacionais, trabalhamos o conteúdo destacando de nições, teoremas e propriedades necessárias para o desenvolvimento de aprendizagem do aluno. O tema foi escolhido depois de uma experiência prática envolvendo o jogo Batalha Naval a m de diminuir as di culdades dos alunos. O trabalho lúdico, como o jogo, tem uma aplicação prática que faz o aluno se familiarizar com os conceitos. É uma forma interessante de propor problemas e soluções envolvendo o conceitos. Assim se torna algo atrativo para o aluno e favorece a criatividade na busca de soluções para os problemas.
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Zhang, Huaijian. "Boundary Integral Techniques in Three Dimensions for Deep Water Waves." The Ohio State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=osu1306712208.
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Calisti, Matteo. "Misure di Hausdorff e formula dell'area in R^n." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2018. http://amslaurea.unibo.it/17037/.
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La misura di Lebesgue permette di misurare il volume degli oggetti n-dimensionali di R^n, ma tutti quelli di dimensione inferiore s come le superfici sono sottoinsiemi di R^n di misura di Lebesgue nulla. Non potendo definire una nozione, ad esempio, di "area" attraverso suddivisioni successive come per la lunghezza di una curva si ricorre alla teoria della misura definendo la misura di Hausdorff s-dimensionale. Viene dapprima esposta la teoria della misura nella sua generalità, con alcune proprietà delle misure astratte e della sigma-algebra di Borel, una loro classificazione e alcuni teoremi di ricoprimento (in particolare quello di Vitali) a cui si farà ricorso dopo. Successivamente vengono introdotte la premisura e misura di Hausdorff H^s, alcune sue prime proprietà e la dimensione di Hausdorff dim_H. Viene studiato il comportamento di H^s e dim_H sotto l'effetto di funzioni lipschitziane e bilipschitziane con studio della dimensione di Hausdorff dell'insieme di Cantor e un breve accenno ai frattali e la loro relazione con le funzioni bilipschitziane. Un tema centrale per poter introdurre la formula di area è la simmetrizzazione di Steiner: ne vengono dimostrate le proprietà principali e attraverso di essa si dimostra la disuguaglianza isodiametrica e l'uguaglianza tra le misure di Hausdorff e di Lebesgue, quando s=n. Infine si dimostra la formula dell'area dapprima per insiemi piatti e poi per insiemi parametrizzabili e nell'Appendice si giustifica l'utilizzo della costante di normalizzazione nella definizione di H^s.
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Masuku, Mthokozisi. "Matrix polar coordinates." Thesis, 2011. http://hdl.handle.net/10539/9240.
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Matrix models feature prominently when studying string theory. In this project
we extend well known single matrix model results to two matrix models. The
two matrix model is represented using polar coordinates and then used to compute
the kinetic piece of the quantum mechanical Hamiltonian operator of two,
space indexed, hermitian matrices with a radially invariant potential. As an
extension of these matrix polar coordinates, we determine the form(s) of the
Laplacian(s) that act on invariant states. The radially dependent Hamiltonian
operator is shown to be equivalent to a system of non interacting (2+1) dimensional
fermions. Further on, we consider the integral of the two matrix model
in polar coordinates to show the standard solution which emulates the Wigner
distribution in the free case, when g2Y M = 0. Also in the large N limit we
find that the polar coordinate matrix model, when solved using perturbation
theory, agrees with the well known result of perturbation theory up to order
λ, where λ is the ’t Hooft coupling constant.
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Liu, Hung-Liang, and 劉烘良. "Contouring Control of Biaxial Systems Based on Polar Coordinates." Thesis, 2000. http://ndltd.ncl.edu.tw/handle/06570481064191014189.
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碩士國立中正大學
機械系
88
This thesis is concerned with the contouring control of a biaxial system. Due to the complicated relationship between contour error and system states, the design of contouring controllers is in general very difficult, and can not be applied to nonlinear plants. The polar coordinate system is adopted in this study to simplify the contour error model. Based on this, we transform the contouring control problem into a stabilization problem and employ the technique of feedback stabilization for controller design. This method not only integrates the effects of commonly used feedback, feedforward and cross-coupled control, but is also applicable to nonlinear plants. In addition, a feedforward friction compensator is incorporated to eliminate part of the friction (static and Coulomb friction), leaving the rest as external disturbance. The sliding mode control is utilized to improve the robustness to system uncertainly as needed. Both numerical simulations and experimental results verify the analysis.
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Ying-Chi, Lee, and 李英吉. "An Investigation of the Bi-Polar Coordinates Beam Propagation Method." Thesis, 2000. http://ndltd.ncl.edu.tw/handle/87512927428159882354.
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碩士國立臺灣大學
電機工程學研究所
88
The bi-polar coordinates beam propagation method (BPC-BPM) is investigated. It not only supports flexible division of waveguides but also simulates mesh shapes more accurately. For special waveguides such as taper, sector, etc., the conventional beam propagation method (BPM) can only approximate them by staircases. As computation is concerned with the conventional BPM, refractive index parameters have to be calculated step by step. Whereas with the BPC-BPM, the same refractive index parameters are used for all steps. In this paper, we also study the dispersion characteristics of BPC-BPM and found that the proposed BPC-BPM shows convergent characteristics during Pade iteration.
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Yu-WenCheng and 鄭鈺雯. "Quality Evaluation on Object Coordinates Determined by FORMOSAT-2 Stereo Pairs in Polar Area." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/78020885973277368474.
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碩士國立成功大學
測量及空間資訊學系碩博士班
98
FORMOSAT-2 satellite developed by Taiwan has high spatial resolution (2m panchromatic images) and high temporal resolution (revisit time interval of one day). In this study, the data process programs developed are adopted to use FORMOSAT-2 images to get polar terrain features and determine the terrain surface changes. By means of analyzing the data quality index including accuracy, reliability and conditional number, the quality of object coordinates determined by FORMOSAT-2 images is examined and analyzed. The inherent problems and limitations to the determination of accurate DSM in polar area are also discussed, and some solutions are given. In the process of simulated frame images in the polar region, if the baseline length of images is increased from 100km to 800km, the horizontal and vertical accuracy is increased about 2m and 35m, respectively. The internal reliability value of horizontal coordinates is decreased 1m and external reliability value is decreased 1, and also, the internal and external reliability values of vertical coordinate are decreased 106 and 54, respectively. They show that the observation errors can be found more easily and they have less effect on the determination of correct function values of unknowns when the baseline length is increased. Compared to the results determined by two images taken on the same orbit, four images taken on two neighboring orbits have better accuracy with the standard deviation decrease of about 31m and 40m on horizontal and vertical coordinates, respectively. In addition, the internal and external reliability values of horizontal coordinates are decreased 3 and 3, and the internal and external reliability values of vertical coordinate are decreased 7 and 4, respectively. In the test areas in polar region, no ground control points are available. Therefore, three stereo models are computed respectively by using stereo pairs taken on three days, where 11 and 23 points determined from the stereo pairs taken on first day are selected and used as GCPs and check points in the computations of the stereo pairs on the second and third day. The model on the second day has the RMSD on X, Y and Z with ±15.57m, ±8.90m and ±28.18m, respectively. The RMSD on X, Y and Z of the points on the model of the third day is ±46.70m, ±18.9m and ±43.48m, respectively. Because the check points and ground control points in polar areas can not be acquired, the DSMs determined by real FORMOSAT-2 images are compared by means of relative registration of any two DSMs. Although the real volume can not be measured in the polar area, the fast-change in the terrain suface of polar region can still be detected by registration of any two DSMs determined by FORMOSAT-2 images taken on different days.
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Huang, Ying-Chen, and 黃英誠. "A Cost Efficient Design of Polar Coordinates Based MIMO STBC FEQ for IEEE 802.16 OFDM System." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/44288938673019508115.
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碩士國立中央大學
電機工程研究所
95
Wireless communication has been one of the most popular fields due to its enormously potential opportunities. Among the techniques involved in such an area, the Multiple-Input Multiple-Output (MIMO) has emerged as one of the hotest issues discussed recently in virtue of its high transmission rate as well as fine transmission quality. Many groups worldwide are dedicated their vigor to the improvement in such a technique. In this thesis the discussions of physical-layer techniques with respect to the space-time coding for MIMO-OFDM system in IEEE 802.16 are addressed. To resolve the higher hardware implementation cost in MIMO compared with the Single-Input Single-Output (SISO), a coordinate transformation has been employed to translate the STBC decoding of Cartesian coordinates into the decoding of polar coordinates. In addition, a new LMS channel tracking algorithm, aimed at the effect of channel time variations, is proposed to conduct tracking for time-variant channel. A transmitter platform as well as a channel model was built by C programming. Simulations and actual implementations for channel estimation, STBC decoding, and LMS channel tracking algorithm have also been carried out in C and Verilog.
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KUTOVÁ, Eva. "Aplikovaná matematika --- Sbírka řešených příkladů." Master's thesis, 2010. http://www.nusl.cz/ntk/nusl-80181.
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This thesis contains solutions to chosen problems of applied mathematics. It comprises examples related to geometrical applications of the double and triple integrals´ theory, ie calculation methods of areas, volumes, mass and coordinates of gravity centres. Each problem´s solution is described in detail and supplemented with a picture. The problems are arranged according to complexity.
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Machynia, Adam. "Application of translational addition theorems to electrostatic and magnetostatic field analysis for systems of circular cylinders." 2012. http://hdl.handle.net/1993/5291.
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Analytic solutions to the static and stationary boundary value field problems relative to an arbitrary configuration of parallel cylinders are obtained by using translational addition theorems for scalar Laplacian polar functions, to express the field due to one cylinder in terms of the polar coordinates of the other cylinders such that the boundary conditions can be imposed at all the cylinder surfaces. The constants of integration in the field expressions of all the cylinders are obtained from a truncated infinite matrix equation.
Translational addition theorems are available for scalar cylindrical and spherical wave functions but such theorems are not directly available for the general solution of the Laplace equation in polar coordinates. The purpose of deriving these addition theorems and applying them to field problems involving systems of cylinders is to obtain exact analytic solutions with controllable accuracies, thereby, yielding benchmark solutions to validate other approximate numerical methods.
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Li, Huai-Che, and 李懷哲. "Polar-Coordinate Fourier Volume Rendering." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/20744232374413003382.
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碩士國立中興大學
電機工程學系所
94
The requirement of high resolution volume visualization is rapidly increasing with the development of modern computer technology. How to handle large volumetric dataset effectively becomes a major problem in volume rendering techniques. Fourier volume rendering (FVR) shows great computational advantages then Ray-casting volume rendering algorithm that suitable for generating projection image of volume dataset interactively. In this work, we present a novel FVR algorithm based on polar coordinate for rendering volume dataset with both high speed and high image quality. Our method processes volumetric spectrum in polar coordinate instead the Cartesian coordinate in traditional FVR algorithm. By this way, the heavy computation can be leaved into pre-processing step and spectrum data can be stored into spectrum-liked data structure. In this paper, we implement both traditional FVR method and our Polar approach for comparison. In our experiment, polar approach can produce high-quality images with high rendering speed.
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Hu, Wan-Nong, and 胡琬穠. "Spatial Modulation MIMO Detection Algorithms in Polar Coordinate." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/5zkxjd.
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碩士國立清華大學
通訊工程研究所
106
The thesis proposed 5 algorithms for spatial modulation detector in polar coordinate. There are maximum likeliood detector in polar coordinate(PML), gradient detector in polar coordinate(PGML), one-stage candidate selection(OCS), two-stage candidate selection(TCS) and modified two-stage candidate selection(MTCS). We derived the maximum likelihood detector in polar coordinate(PML) and find that the complexity is lower than in rectangular coordinate. With the mathematical proof of only single local minimum in maximum likelihood distance formula and the slope of distance is monotonically increasing from the local minimum, we reinterpret the maximum likelihood solution from minimum distance to minimum slope summation. The interpretation leads to the PGML and it has lower complexity and the performance is near optimal. From the formula of slope summation, we proposed OCS algorithm by using part of the information: phase as parameter to select candidates from all the combinations of spatial and symbol index. To enhance the power of candidate selection, we proposed the TCS algorithm by adding the magnitude information which requires more complexity. With the property of convex in phase and magnitude domain, we proposed the MTCS algorithm which reduced the complexity efficiently. In the simulation result, we can see that the BER performance of sub optimal detectors in polar coordinate are near to optimal detector and the complexity are comparable to the sub optimal detector in rectangular coordinate. Among all the detectors, MTCS algorithm has the lowest complexity.
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Li, Guo-Cai, and 李國財. "A Scalable Sensor Network Using a Polar Coordinate System." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/39249677352623650421.
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碩士東海大學
資訊工程與科學系
95
Due to the quick development of chip design and antenna manufacturing techniques, wireless facilities, such as wireless sensors, have become significantly smaller and cheaper than before. Their usage has also consequently been widely enriched, such as in the areas of healthcare and forest monitoring. A wireless sensor network (WSN) is often used to monitor a specific environment for a specific purpose. However, how to effectively utilize the limited resources in a sensor, also in a WSN, is crucial. In a WSN, geographical information is usually employed to locate a node and its surroundings. In this article, we propose a system, named Relative Position for sensor Routing using Polar-coordinates (RP2) that deploys a polar coordinate system to identify sensor positions and route network packets. A sensor ID that carries geographical metadata can be helpful in positioning a sensor.
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Pang, Jia-Lun, and 龐嘉倫. "Nonlinear Control of a Wheeled Mobile Robot Using Polar Coordinate." Thesis, 2004. http://ndltd.ncl.edu.tw/handle/47985471515109870160.
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碩士國立中興大學
電機工程學系
92
This thesis develops methodologies and techniques for control architecture design, point-to-point control as well as path following, and implementation of a vision-based wheeled mobile robot (WMR). To achieve point-to-point control, two novel kinematic point-to-point control laws in the polar coordinate have been proposed in order to achieve an asymptotical point-to-point control. Moreover, these two control approaches are extended to derive a path following control for the wheeled mobile robot. The experimental system is composed of a vision system with a host computer, an embedded digital signal process (DSP) system for the wheeled mobile robot and a wireless RS232 modem. A high-performance and computation-effective DSP-based controller is constructed for executing the developed path following and point-to-point control laws. Simulation and experimental results are included to illustrate the feasibility and effectiveness of the proposed control laws.
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Kuo, Chih-Ting, and 郭治廷. "An Improved Watermarking Approach in the Log-polar Coordinate System." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/77898745863018615798.
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碩士國立臺北大學
通訊工程研究所
98
The purpose watermarking an image is to keep hackers from unauthorized use of copyrighted contents as well as malicious modification. In many digital watermarking systems, the basic principle to retrieve the watermark is based on the knowledge of the positions for embedding the watermark. However, geometric distortions such as rotation, scaling, and translation (RST) may rearrange watermark positions, and often result in the failure of the watermark retrieval. In this thesis, the proposed scheme aims to develop a watermarking method to be resilient to rotation, scaling, and translation of the geometric distortions. Watermarking algorithm that is robust to RST distortions in this paper. The watermark data sequence is embedded into the log-polar mapping (LPM) magnitude spectrum, which is obtained by taking the Fourier transform of the cover image, and transforming the corresponding Fourier magnitudes into log-polar magnitude spectrums. For watermark detection, a function is designed to extract watermark-related magnitudes along the polar-radius axis. In the proposed approach, rotating the watermarked image results in a cyclical shift of the embedded watermark data, scaling the image results in amplification of the embedded watermark data, and translating the image has no effect on the embedded watermark data. Correlation coefficient is adopted as the detection measures. False positive results on a set of 12 images with 1000 watermarks are tested, as well as the properties of robustness are described. The experimental results have shown that the proposed scheme is robust to several attacks such as rotating, rotating with cropping, scaling, scaling with cropping, translating, translating with cropping, and JPEG compression.
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Chu, Hsuan-Lin, and 朱璿霖. "Perspective Transformed Text Recognition Using Polar Coordinate Features within Minimum Bounding Ellipse." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/28522777334463918890.
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碩士國立中興大學
資訊科學與工程學系
105
Optical Character Recognition is an important application of computer vision in recent years. In this paper, we propose a novel method to recognize the perspective transformed texts. The method consists of three main steps. First, we use linear programming to find the area of the minimum bounding ellipse. Then the ellipse is normalized and transformed to polar coordinates. Finally, feature extraction is performed based on polar coordinates and text recognition is achieved by comparing feature vectors using Cosine Similarity formula. Experimental results show that our method has very high rate in accuracy.
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LEE, WEI-CHEN, and 李偉禎. "FPGA-Based Optimal Mapping Implementation for Polar to Cartesian Coordinate Transformation In Image Processing." Thesis, 2001. http://ndltd.ncl.edu.tw/handle/60570176678627053886.
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碩士義守大學
電子工程學系
89
An axis transformation is necessary if radar data, expressed in terms of polar coordinates, is to be displayed on a raster scan display, which must use Cartesian coordinates. The transformation to Cartesian coordinates requires real multiplication by trigonometric functions. Normally, it is achieved by software. The slow operation in software is unable to meet the requirement of radar data in real time. This thesis will study the Bresenham algorithm to calculate the optimum pixel address using addition and subtraction operations in hardware. The pixel address of sample data of primary and secondary surveillance radar to be update can be implemented by hardware using ALTERA’s FPGA chip to achieve the performance of real time.
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His-Tsai, Chen, and 陳錫材. "An algorithm for querying sub-image based on the polor coordinate." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/86686924624580511467.
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碩士元智大學
資訊工程學系
90
Spatial relationship is a very important technology to deal with the image retrieval problems. For the sub-image retrieval problems, several researchers had proposed quite good methods to solve them based on the spatial relationship. However, both the processing time and required space for their algorithms are quite huge. In this paper, we adopt the polar coordinate for expressing the spatial relationships of image objects precisely and propose a very efficient algorithm for the sub-image retrieval problems. Our methods may reduce the processing time and required space quite effectively.
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CHANG, CHE-WEI, and 張哲瑋. "Developing the skull defect auto-repairmen algorism by using demon registration and polar coordinate transformation methodologies." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/w38d24.
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碩士東海大學
工業工程與經營資訊學系
105
Cranioplasty surgery ranks top two in latest nervous surgery operation statistics in the Ministry of Health and Welfare database. Except metal cranium implants, another traditional cranioplasty surgery could hand-made prosthesis by using bone cement. However, the perfect fit and artistic prosthesis is difficult to fabricate manually, especially, the random defeat occurs in different surgical cases. Via 3D image technology progress, three dimension cranium images helped surgeons to observe defeats easily and visually and establish a better and precision surgical planning before the operation. 3D printing technology mature assists the surgical planning to excuse in the operation. 3D printing mode for bone cement plastic surgery will significantly reduce the surgical time and enhance the medical quality. Based on this reason, artificial intelligent design system developed by this study would like to establish a commercial software that will design the prosthesis fit, uniform thickness and customized curve automatically. This study proposed the Demon registration algorism corresponding with transformation of polar coordinate to establish the automatic cranium defeat repair system. The result of repair algorism by using polar coordinate performed better than Cartesian coordinate in cranium defeat repair. With linear interpolation method combined with the polar coordinate algorism will significantly reduce the process time. This study will validate various clinical cases to perform the system reliability and designed prosthesis accuracy. Through the algorism development, this research would like to establish an automatic repair system to solve the surgical unmet needs of prosthesis pre-process time reduction, accurate prosthesis structure fabrication, finally enhance the medical quality in the end.
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Cheng, Yen-Chun, and 程彥鈞. "Table-Based Design of Arithmetic Function Units for Angle Rotation and Rectangular-to-Polar-Coordinate Conversion." Thesis, 2009. http://ndltd.ncl.edu.tw/handle/rpjfun.
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碩士國立中山大學
資訊工程學系研究所
97
In this thesis, an efficiency method for reducing the rotation ROM size in table-based architecture is proposed. The original rotation can be divided into two stages, coarse stage and fine stage. Our approach modifies the previous two-stage rotation method and proposes a multi-stage architecture and discuses three-stage phase calculation. The effect of table reduction is more apparently for higher accuracy requirement in the three-stage architecture. The total area of the previous two-stage architecture is larger than the proposed table-reduced three-stage architecture because the table size takes a significant ratio of the total area especially when the required bit accuracy is large. In the proposed three-stage design, there are two different types of architectures, depending on the rotation angles in the first and second rotation stages. Comparison of different types of architecture with the previous method shows that our designs indeed reduce the table size and the total area significantly.