This thesis is concerned with the theory of invariant bilinear differential pairings on parabolic geometries. It introduces the concept formally with the help of the jet bundle formalism and provides a detailed analysis. More precisely, after introducing the most important notations and definitions, we first of all give an algebraic description for pairings on homogeneous spaces and obtain a first existence theorem. Next, a classification of first order invariant bilinear differential pairings is given under exclusion of certain degenerate cases that are related to the existence of invariant linear differential operators. Furthermore, a concrete formula for a large class of invariant bilinear differential pairings of arbitrary order is given and many examples are computed. The general theory of higher order invariant bilinear differential pairings turns out to be much more intricate and a general construction is only possible under exclusion of finitely many degenerate cases whose significance in general remains elusive (although a result for projective geometry is included). The construction relies on so-called splitting operators examples of which are described for projective geometry, conformal geometry and CR geometry in the last chapter. / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1339548 / Thesis (Ph.D.) - University of Adelaide, School of Mathematical Sciences, 2008

Orientador: Jayme Vaz Junior / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-16T08:39:55Z (GMT). No. of bitstreams: 1 Mattos_EduardoSouza_M.pdf: 1032396 bytes, checksum: fd915adc5546adcea3d86c90b4fda15b (MD5) Previous issue date: 2010 / Resumo: Atualmente, o estudo das Álgebras de Clifford é utilizado em inúmeras áreas de pesquisa. Uma delas é na área de Visão Computacional. O objetivo central dessa dissertação consiste em exibir noções sobre Álgebras de Clifford e sua utilização na formulação dos conceitos e definições de operações entre objetos da Geometria Projetiva e na formulação algébrica de câmeras virtuais, que é um dos assuntos tratados na área de Visão Computacional. Para isso são expostos de forma gradual e coerente os principais aspectos teóricos necessários para atingir os objetivos citados. Como resultado, as Álgebras de Clifford proporcionam uma excelente descrição da Geometria Projetiva e das câmeras virtuais / Abstract: Currently, the study of Clifford algebras are used in many research areas. One is in the area of Computer Vision. The main objective of this dissertation is to display notions of Clifford algebras and their use in formulating the concepts and definitions of transactions between objects of Projective Geometry and algebraic formulation of virtual cameras, which is one of the topics covered in Computer Vision. For it is exposed gradually and consistently the main theoretical aspects needed to achieve the goals mentioned. As a result, Clifford algebras provide an excellent description of Projective Geometry and virtual cameras / Mestrado / Matematica Aplicada / Mestre em Matemática Aplicada

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-04-11T11:01:56Z No. of bitstreams: 1 marinadutravieira.pdf: 2289869 bytes, checksum: b8e82f26da6a00278d8c816af95a5769 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-04-11T11:47:24Z (GMT) No. of bitstreams: 1 marinadutravieira.pdf: 2289869 bytes, checksum: b8e82f26da6a00278d8c816af95a5769 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-04-11T11:47:37Z (GMT) No. of bitstreams: 1 marinadutravieira.pdf: 2289869 bytes, checksum: b8e82f26da6a00278d8c816af95a5769 (MD5) / Made available in DSpace on 2017-04-11T11:47:37Z (GMT). No. of bitstreams: 1 marinadutravieira.pdf: 2289869 bytes, checksum: b8e82f26da6a00278d8c816af95a5769 (MD5) Previous issue date: 2016-12-22 / O presente texto estrutura estudos realizados em torno da Geometria Projetiva. O trabalho traz resultados de um estudo histórico sobre a Geometria Projetiva e uma revisão bibliográfica sobre o ensino de Geometria no Brasil. O objetivo é enfatizar o papel de práticas curriculares alternativas, inclusive as que premiam o uso de recursos da tecnologia computacional. A partir daí, é elaborada uma pesquisa que propõe um trabalho didático que une conceitos projetivos e geometria feita com a mediação de softwares gráficos. Assim, constitui-se uma questão: COMO A GEOMETRIA PROJETIVA PODE SER UMA PRESENÇA CURRICULAR, A PARTIR DE SUA PRESENÇA NA FORMAÇÃO DO LICENCIANDO EM MATEMÁTICA? São esboçadas ideias metodológicas dentro do escopo da Fenomenologia, com as quais apronta-se uma pesquisa de campo, com posteriores tratamentos de dados e análises abarcando a experiência de licenciandos sobre atividades especialmente desenhadas. As análises permitem discussões que estabelecem uma síntese sobre a questão constituída. Nosso estudo levantou possibilidades para a inclusão da Geometria Projetiva em práticas curriculares em escolas. / This dissertation structures a study on Projective Geometry, presenting results of a historical study on Projective Geometry and a bibliographical revision on the teaching of Geometry in Brazil. The objective is to emphasize alternative curricular practices, including those rewarding the use of computational technology resources. Hence, this study suggests a didactic intervention that unites projective concepts and geometry made with the mediation of graphic software. Thus, an issue arises: HOW CAN PROJECTIVE GEOMETRY BE A CURRICULAR PRESENCE, SINCE ITS PRESENCE IN THE TRAINING OF LICENSING IN MATHEMATICS? Methodological ideas are outlined within the scope of the Phenomenology, from which a field research is then elaborated and with later data processing and analysis covering the experience of subjects graduated on specially designed activities. The assessments made allow conclusions that establish a synthesis on the indicated issue. Our study highlights possibilities on how Projective Geometry may be applied in curricular practices in schools.

Height estimation of objects can be implemented both for soft-biometrics and as an object tracking feature. In first case we can eliminate some possible subjects having considerably different height than the observed one, and focus on determining more distinctive remote identification features, like colour, face or ear, and search for similar subjects in a smaller set of possible candidates. For object tracking it can be used for temporal and spatial correspondence analysis as well or simultaneously for both in case of having different cameras. In this thesis we propose a novel method for automatic estimation of height using an uncalibrated camera. Nowadays such cameras can be found in any corner for different purposes like as for security reasons. A crucial moment in height estimation is finding vanishing points. In the method we use RANSAC to estimate best vanishing point from several estimated candidate points. The method has the new advantages that from different frames and their respective height estimations, automatically determines certain reasonable heights depending on height measurements distribution. With spreading of camera implementation in common applications, we believe this new software can be widely applied in as many fields as it can be imagined.

Pas de résumé / In this thesis, we study the problem of registering 2D image sets and 3D point clouds under threedifferent acquisition set-ups. The first set-up assumes that the image sets are captured using 2Dcameras that are fully calibrated and coupled, or rigidly attached, with a 3D sensor. In this context,the point cloud from the 3D sensor is registered directly to the asynchronously acquired 2D images.In the second set-up, the 2D cameras are internally calibrated but uncoupled from the 3D sensor,allowing them to move independently with respect to each other. The registration for this set-up isperformed using a Structure-from-Motion reconstruction emanating from images and planar patchesrepresenting the point cloud. The proposed registration method is globally optimal and robust tooutliers. It is based on the theory Sum-of-Squares polynomials and a Branch-and-Bound algorithm.The third set-up consists of uncoupled and uncalibrated 2D cameras. The image sets from thesecameras are registered to the point cloud in a globally optimal manner using a Branch-and-Prunealgorithm. Our method is based on a Linear Matrix Inequality framework that establishes directrelationships between 2D image measurements and 3D scene voxels.

In this technical note we use insights from the theory of projective geometry to provide novel and non-algebraic proofs of convergence of continuous-time fictitious play for a class of games. As a corollary we obtain a kind of equilibrium selection result, whereby continuous-time fictitious play converges to a particular equilibrium contained in a continuum of equivalent equilibria for symmetric 4x4 zero-sum games.

This thesis is dedicated photogrammetric image analysis that makes it possible from your photos with the help selected methods to determine the location and dimensions of objects recorded on them. There are explained the basics of photogrammetry and its current application. Chapters focused on digital imaging describing its characteristics, treatment options and key points findability for the scene calibration. For a comprehensive view are in this thesis introduced examples of existing software, its possibilities and use in practice.

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A synthetic approach to the construction of projective geometry, its methods and selected results are given in the proposed thesis. The main historical drawbacks of the original proof of Chasles's theorem for non-developable ruled surfaces and von Staudt's formalization of projective geometry are commented. The corre- sponding theoretical background is elaborated on visual demonstrations with the accent to interrelations of classical synthetic, axiomatic and analytic points of view. Synthetic methods of projective geometry and their mixture with analytic methods are described on examples including numerous alternative proofs and generalizations of some theorems. A method of four-dimensional visualization is introduced in details. Elementary constructions of images of points, lines, planes and 3-spaces are followed by models of polychora, their sections and shadows. Chasles's theorem is proven for non-developable ruled quadrics on synthetic vi- sualizations, then generalized and proven within the pure projective framework for algebraic surfaces. The synthetic classification of regular quadrics is derived from descriptive geometry constructions of sections of four-dimensional cones and analytically verified in the projective extension of the real space. An integral part of the thesis is a...