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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[pt] A presente dissertação analisa a relação interdisciplinar entre a matemática e as artes, dando especial destaque ao Teorema de Desargues como uma ponte entre estas áreas. Destaca-se a importância atual da interdisciplinaridade na educação, embasada pela Base Nacional Comum Curricular (BNCC), que dá destaque à integração de tecnologia e conhecimento em múltiplas áreas do currículo escolar. O Teorema de Desargues é abordado como um conceito que rompe os limites da matemática, alcançando também os campos da arte e da tecnologia. A Geometria Projetiva é contextualizada historicamente, apresentando seus primeiros passos e progresso ao longo do tempo. Revela Girard Desargues como um como precursor de ideias nesse contexto, contribuindo tanto para o avanço da matemática quanto para a expressão artística. A dissertação enfatiza a aplicação prática do Teorema de Desargues no contexto educacional, propondo atividades significativas e atrativas para os alunos no contexto escolar. Apresenta o produto educacional desenvolvido pelos autores como uma fonte valiosa de sugestões para educadores que pretendem se dedicar à interdisciplinaridade. A dissertação promove uma abordagem educacional que estimula o diálogo entre disciplinas, destacando a conexão entre matemática, geometria projetiva, arte e tecnologia, para isso utiliza o Teorema de Desargues desempenhando um papel central nesse processo. / [en] The present dissertation examines the interdisciplinary relationship between mathematics and the arts, with special emphasis on Desargues Theorem as a bridge between these fields. It highlights the current importance of interdisciplinarity in education, supported by the National Common Curricular Base (BNCC), which emphasizes the integration of technology and knowledge across multiple areas of the school curriculum. Desargues Theorem is approached as a concept that transcends the boundaries of mathematics, also reaching into the realms of art and technology. Projective Geometry is historically contextualized, tracing its origins and development over time. Girard Desargues is revealed as a precursor of ideas in this context, contributing to both the advancement of mathematics and artistic expression. The dissertation emphasizes the practical application of Desargues Theorem in the educational context, proposing meaningful and engaging activities for students in the school setting. It presents the educational product developed by the authors as a valuable source of suggestions for educators looking to dedicate themselves to interdisciplinarity. The dissertation promotes an educational approach that encourages dialogue between disciplines, highlighting the connection between mathematics, projective geometry, art, and technology, utilizing Desargues Theorem as a central element in this process.

Ce travail montre l'unité de l'œuvre de Pascal dans ce qui concerne la « comparabilité des incomparables » : la comparaison, langagière ou mathématique, qui se fait entre des choses qui ne pourraient pas en principe être rapprochées. Il s'agit de faire une approche historique et linguistique pour poser des questions philosophiques par rapport à la comparaison, notamment sur le rôle de principe que l'infini y joue selon Pascal. Nous identifions la comparaison des incomparables sous trois formes.La première partie de ce travail est consacrée à formuler une forme rhétorique d'analogie que nous nommons l'« analogie de disproportion » (nous inspirant de Secretan 1998). Si l'analogie est généralement dite faire une comparaison entre deux rapports, chacun desquels existe entre des choses homogènes, l'analogie de disproportion permet en revanche de montrer une ressemblance entre des rapports d'hétérogénéité, entre des disproportions ou entre des distances infinies: deux choses sont aussi différentes entre elles que deux autres. Pascal étant un auteur qui souligne surtout les disproportions, nous montrons qu'il compare ces disproportions, notamment pour délimiter à l'homme ce qu'il ne peut pas connaître parfaitement.La deuxième partie analyse la pratique mathématique de Pascal « en poids, nombre et mesure » : il s'agit de montrer que dans la méthode des indivisibles des Lettres de A. Dettonville, dans le Traité du triangle arithmétique et dans la comparaison du courbe et du droit, toujours l'infini (ou plutôt l'indéfini) intervient comme un facteur qui permet la comparabilité de ce qui semblait être incomparable. La troisième partie fait une discussion proprement philosophique sur l'infiniment petit et l'infiniment grand, prenant en compte la pratique mathématique de Pascal analysée dans la deuxième partie. Il est question de discuter sur la nature des « indivisibles », des « différences » et des « distances infinies ». Nous proposons que l'« infini » dans la pratique mathématique de Pascal relève plutôt de l'« indéfini », reliant cela à une distinction entre le sens absolu et le sens relatif des mots. Une exception dans la pratique mathématique de Pascal est la géométrie projective, où il faut accepter des éléments à distance infinie. La « rencontre » des deux infinis, finalement, permet de montrer la réciprocité de l'infini de grandeur et de l'infini de petitesse. Une discussion est faite à ce propos, reliant la proportion inverse entre les deux infinis à la grandeur et la petitesse de l'homme et au caractère paradoxal de certaines vérités selon Pascal, lesquelles sont résolues dans la personne du Christ. On conclut que Pascal propose non pas une connaissance directe de l'infini, mais plutôt une approche à la relation que l'homme, être fini, possède avec l'infini / This thesis shows the unity of Pascal's work in what concerns the "comparability of incomparables'': the comparison, either in mathematics our natural language, between things which could not in principle be brought together. The approach is both a historical and a linguistic one, and it aims to recovery some important questions regarding the philosophical nature of comparisons, more specifically, the role of the infinite in Pascal's thought. The comparison of incomparables may be identified in three different formsIn the first part, we formulate a rhetorical form of analogy that we call an "analogy of disproportion'' (inspired by Secretan 1998). If the analogy is generally said to make a comparison between two relations, each of which exists between homogeneous things, the analogy of disproportion, on the other hand, shows a resemblance between relations of heterogeneity, between disproportions or between infinite distances: two things may be as different from each other as any two other things. Even if disproportions are a central theme to Pascal, he did not shy away of comparing such disproportions -- in particular to delimit what man cannot know perfectly.The second part analyzes the mathematical practice of Pascal "in weight, number and measure'': it is necessary to show that in the method of indivisibles of the Lettres de A. Dettonville, in the Traité du Triangle Arithmétique and in the comparison of the curved and the straight lines, always the infinite (or rather the indefinite) intervenes as a factor that allows the comparability of what would seem to be incomparable. The third part makes a philosophical discussion on the infinitely small and the infinitely large, taking into account Pascal's mathematical practice, which was analyzed in the second part. We discuss the nature of "indivisibles'', "differences'' and "infinite distances''. We suggest that the "infinite'' in Pascal's mathematical practice is rather an "indefinite'', linking it to a distinction between the absolute and the relative meaning of words. An exception in Pascal's mathematical practice is his projective geometry, where it is necessary to accept elements at an infinite distance. The "encounter'' of the two infinites makes it possible to show the reciprocity of the infinity of greatness and the infinity of smallness. Finally, we analyze the inverse proportionality between the two infinites with regard to the greatness and the wretchedness of man and to the paradoxical nature of certain truths according to Pascal, which are concealed in the person of the Christ. The conclusion is that Pascal arrives not at a direct knowledge of the infinite, but to an approach to the relation that man, a finite being, has with the infinite

We describe a new direct method for estimating structure and motion from image intensities of multiple views. We extend the direct methods of Horn- and-Weldon to three views. Adding the third view enables us to solve for motion, and compute a dense depth map of the scene, directly from image spatio -temporal derivatives in a linear manner without first having to find point correspondences or compute optical flow. We describe the advantages and limitations of this method which are then verified through simulation and experiments with real images.