Chou Yun-Sum, Bailey. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 89-92). / Abstracts in English and Chinese. / List of Symbol / Chapter Chapter 1 --- Introduction / Chapter 1.1 --- The Goal: Euclidean Reconstruction --- p.1 / Chapter 1.2 --- Historical background --- p.2 / Chapter 1.3 --- Scope of the thesis --- p.2 / Chapter 1.4 --- Thesis Outline --- p.3 / Chapter Chapter 2 --- An introduction to stereo vision and 3D shape reconstruction / Chapter 2.1 --- Homogeneous Coordinates --- p.4 / Chapter 2.2 --- Camera Model / Chapter 2.2.1 --- Pinhole Camera Model --- p.5 / Chapter 2.3 --- Camera Calibration --- p.11 / Chapter 2.4 --- Geometry of Binocular System --- p.14 / Chapter 2.5 --- Stereo Matching --- p.15 / Chapter 2.5.1 --- Accuracy of Corresponding Point --- p.17 / Chapter 2.5.2 --- The Stereo Matching Approach --- p.18 / Chapter 2.5.2.1 --- Intensity-based stereo matching --- p.19 / Chapter 2.5.2.2 --- Feature-based stereo matching --- p.20 / Chapter 2.5.3 --- Matching Constraints --- p.20 / Chapter 2.6 --- 3D Reconstruction --- p.22 / Chapter 2.7 --- Recent development on self calibration --- p.24 / Chapter 2.8 --- Summary of the Chapter --- p.25 / Chapter Chapter 3 --- Camera Calibration / Chapter 3.1 --- Introduction --- p.26 / Chapter 3.2 --- Camera Self-calibration --- p.27 / Chapter 3.3 --- Self-calibration under general camera motion --- p.27 / Chapter 3.3.1 --- The absolute Conic Based Techniques --- p.28 / Chapter 3.3.2 --- A Stratified approach for self-calibration by Pollefeys --- p.33 / Chapter 3.3.3 --- Pollefeys self-calibration with Absolute Quadric --- p.34 / Chapter 3.3.4 --- Newsam's self-calibration with linear algorithm --- p.34 / Chapter 3.4 --- Camera Self-calibration under specially designed motion sequence / Chapter 3.4. 1 --- Hartley's self-calibration by pure rotations --- p.35 / Chapter 3.4.1.1 --- Summary of the Algorithm / Chapter 3.4.2 --- Pollefeys self-calibration with variant focal length --- p.36 / Chapter 3.4.2.1 --- Summary of the Algorithm / Chapter 3.4.3 --- Faugeras self-calibration of a 1D Projective Camera --- p.38 / Chapter 3.5 --- Summary of the Chapter --- p.39 / Chapter Chapter 4 --- Self-calibration under Planar motions / Chapter 4.1 --- Introduction --- p.40 / Chapter 4.2 --- 1D Projective Camera Self-calibration --- p.41 / Chapter 4.2.1 --- 1-D camera model --- p.42 / Chapter 4.2.2 --- 1-D Projective Camera Self-calibration Algorithms --- p.44 / Chapter 4.2.3 --- Planar motion detection --- p.45 / Chapter 4.2.4 --- Self-calibration under horizontal planar motions --- p.46 / Chapter 4.2.5 --- Self-calibration under three different planar motions --- p.47 / Chapter 4.2.6 --- Result analysis on self-calibration Experiments --- p.49 / Chapter 4.3 --- Essential Matrix and Triangulation --- p.51 / Chapter 4.4 --- Merge of Partial 3D models --- p.51 / Chapter 4.5 --- Summary of the Reconstruction Algorithms --- p.53 / Chapter 4.6 --- Experimental Results / Chapter 4.6.1 --- Experiment 1 : A Simulated Box --- p.54 / Chapter 4.6.2 --- Experiment 2 : A Real Building --- p.57 / Chapter 4.6.3 --- Experiment 3 : A Sun Flower --- p.58 / Chapter 4.7 --- Conclusion --- p.59 / Chapter Chapter 5 --- Building Reconstruction using a linear camera self- calibration technique / Chapter 5.1 --- Introduction --- p.60 / Chapter 5.2 --- Metric Reconstruction from Partially Calibrated image / Chapter 5.2.1 --- Partially Calibrated Camera --- p.62 / Chapter 5.2.2 --- Optimal Computation of Fundamental Matrix (F) --- p.63 / Chapter 5.2.3 --- Linearly Recovering Two Focal Lengths from F --- p.64 / Chapter 5.2.4 --- Essential Matrix and Triangulation --- p.66 / Chapter 5.3 --- Experiments and Discussions --- p.67 / Chapter 5.4 --- Conclusion --- p.71 / Chapter Chapter 6 --- Refine the basic model with detail depth information by a Model-Based Stereo technique / Chapter 6.1 --- Introduction --- p.72 / Chapter 6.2 --- Model Based Epipolar Geometry / Chapter 6.2.1 --- Overview --- p.74 / Chapter 6.2.2 --- Warped offset image preparation --- p.76 / Chapter 6.2.3 --- Epipolar line calculation --- p.78 / Chapter 6.2.4 --- Actual corresponding point finding by stereo matching --- p.80 / Chapter 6.2.5 --- Actual 3D point generated by Triangulation --- p.80 / Chapter 6.3 --- Summary of the Algorithms --- p.81 / Chapter 6.4 --- Experiments and discussions --- p.83 / Chapter 6.5 --- Conclusion --- p.85 / Chapter Chapter 7 --- Conclusions / Chapter 7.1 --- Summary --- p.86 / Chapter 7.2 --- Future Work --- p.88 / BIBLIOGRAPHY --- p.89

Made available in DSpace on 2016-02-05T18:29:18Z (GMT). No. of bitstreams: 0 Previous issue date: 2015-10-05. Added 1 bitstream(s) on 2016-02-05T18:33:04Z : No. of bitstreams: 1 000857275.pdf: 1760867 bytes, checksum: d6a76ab24ce9acf6844b3d3d0df2ebe4 (MD5) / Neste trabalho realizamos o estudo da Geometria Elíptica baseado no livro Introdução à Geometria Projetiva de Abdênago Alves de Barros e Plácido Francisco de Assis Andrade. A fim de apresentar este tema de forma didática, desenvolvemos alguns tópicos da álgebra linear e da geometria analítica que serão utilizados no decorrer deste trabalho. A Geometria Projetiva Elíptica é dividida em duas frentes: a Geometria Elíptica Dupla e a Geometria Elíptica Simples. A Geometria Elíptica Dupla tem como modelo a esfera unitária S2 e a Geometria Elíptica Simples tem como modelo o plano projetivo RP2 que pode ser visto como a esfera unitária S2 com a relação de equivalência que identifica os pontos antípodas / We have made a study of projective elliptic geometry based on the book Introdução à Geometria Projetiva of Abdênago Alves de Barros and Plácido Francisco de Assis Andrade. In order to introduce this theme in a didactic way, we developed some topics of the linear algebra and of the analytic geometry, that will be used in this work. The projective elliptic geometry is divided in two approaches the double elliptic geometry and the simple elliptic geometry. The double elliptic geometry has as model the unit sphere S2 and the simple elliptic geometry has as model the real projective plane RP2; that is, the unit sphere S2 with the equivalence relation that identi es antipodal points

Orientador: Alice Kimie Miwa Libardi / Banca: Eliris Cristina Rizziolli / Banca: Marta Cilene Gadotti / Banca: Northon Canevari Leme Penteado / Resumo: Neste trabalho realizamos o estudo da Geometria Elíptica baseado no livro "Introdução à Geometria Projetiva" de Abdênago Alves de Barros e Plácido Francisco de Assis Andrade. A fim de apresentar este tema de forma didática, desenvolvemos alguns tópicos da álgebra linear e da geometria analítica que serão utilizados no decorrer deste trabalho. A Geometria Projetiva Elíptica é dividida em duas frentes: a Geometria Elíptica Dupla e a Geometria Elíptica Simples. A Geometria Elíptica Dupla tem como modelo a esfera unitária S2 e a Geometria Elíptica Simples tem como modelo o plano projetivo RP2 que pode ser visto como a esfera unitária S2 com a relação de equivalência que identifica os pontos antípodas / Abstract: We have made a study of projective elliptic geometry based on the book "Introdução à Geometria Projetiva" of Abdênago Alves de Barros and Plácido Francisco de Assis Andrade. In order to introduce this theme in a didactic way, we developed some topics of the linear algebra and of the analytic geometry, that will be used in this work. The projective elliptic geometry is divided in two approaches the double elliptic geometry and the simple elliptic geometry. The double elliptic geometry has as model the unit sphere S2 and the simple elliptic geometry has as model the real projective plane RP2; that is, the unit sphere S2 with the equivalence relation that identi es antipodal points / Mestre

Girard Desargues (1951-1662) was a key figure in the transformation of architectural geometry from its ancient and venerated status as transcendental knowledge and supreme reality to a mere technological instrument for the control of building construction practice. As a friend of Rene Descartes and Marin Mersenne, Desargues participated in the development of the mechanistic worldview which accompanied the emergence of experimental science and the renewed interest in mathematics and geometry as axiomatic, deductive systems. This dissertation examines in detail Desargues' methods of stereotomy (the geometrical basis of architectural stone cutting) and his system of perspective construction without vanishing points beyond the picturespace. Desargues' theorem and other key discoveries for which he is still known in the history of mathematics are discussed as they bear upon his methods of stereotomy and perspective. Desargues' stereotomy is almost certainly the first attempt at a universal descriptive geometry such as Gaspard Monge finally developed after the French revolution. Desargues' work in this area may thus be seen as a precocious foreshadowing of the engineering geometry in common use today. The writings of Desargues have been consulted in the original French. Extensive passages are quoted and translated, and a number of illustrations from the original texts are reproduced. Supplementary illustrations are also provided. Appendices list the known architectural works of Desargues, his writings and those of his friend and student Bosse which bear upon the exposition of Desargues' methods. / Ph. D.

[Truncated abstract] Image transition effects are commonly used on television and human computer interfaces. The transition between images creates a perception of continuity which has aesthetic value in special effects and practical value in visualisation. The work in this thesis demonstrates that better image transition effects are obtained by incorporating properties of projective geometry into image transition algorithms. Current state-of-the-art techniques can be classified into two main categories namely shape interpolation and warp generation. Many shape interpolation algorithms aim to preserve rigidity but none preserve it with perspective effects. Most warp generation techniques focus on smoothness and lack the rigidity of perspective mapping. The affine transformation, a commonly used mapping between triangular patches, is rigid but not able to model perspective effects. Image transition techniques from the view interpolation community are effective in creating transitions with the correct perspective effect, however, those techniques usually require more feature points and algorithms of higher complexity. The motivation of this thesis is to enable different views of a planar surface to be interpolated with an appropriate perspective effect. The projective geometric relationship which produces the perspective effect can be specified by two quadrilaterals. This problem is equivalent to finding a perspectively appropriate interpolation for projective transformation matrices. I present two algorithms that enable smooth perspective transition between planar surfaces. The algorithms only require four point correspondences on two input images. ...The second algorithm generates transitions between shapes that lie on the same plane which exhibits a strong perspective effect. It recovers the perspective transformation which produces the perspective effect and constrains the transition so that the in-between shapes also lie on the same plane. For general image pairs with multiple quadrilateral patches, I present a novel algorithm that is transitionally symmetrical and exhibits good rigidity. The use of quadrilaterals, rather than triangles, allows an image to be represented by a small number of primitives. This algorithm uses a closed form force equilibrium scheme to correct the misalignment of the multiple transitional quadrilaterals. I also present an application for my quadrilateral interpolation algorithm in Seitz and Dyer's view morphing technique. This application automates and improves the calculation of the reprojection homography in the postwarping stage of their technique. Finally I unify different image transition research areas into a common framework, this enables analysis and comparison of the techniques and the quality of their results. I highlight that quantitative measures can greatly facilitate the comparisons among different techniques and present a quantitative measure based on epipolar geometry. This novel quantitative measure enables the quality of transitions between images of a scene from different viewpoints to be quantified by its estimated camera path.

A camera calibration procedure corresponds to determine the digital geometric and optical characteristics of the camera from a known initial data set. This problem can be divided into three steps: a) acquisition of initial data; b) calibration process itself; and c) optimization. This work presents the development of a calibration tool based on a generic architecture for any calibration approach. For this aim, the presented system allows the personalization of each calibration step. In the proposed tool new calibration procedures are introduced dynamically, allowing a better integration between the modules of the system. / Fundação de Amparo a Pesquisa do Estado de Alagoas / Um processo de calibração de câmera consiste no problema de determinar as características geométricas digitais e ópticas da câmera a partir de um conjunto de dados iniciais. Este problema pode ser dividido em três etapas: aquisição de dados iniciais, o processo de calibração em si e otimização. Este trabalho propõe o desenvolvimento de uma ferramenta de calibração baseada em uma arquitetura genérica para qualquer processo de calibração. Para este propósito, o sistema apresentado neste trabalho permite a personalização de cada etapa da calibração. A inclusão de novos métodos de calibração é realizada de forma dinâmica, permitindo assim maior integração e flexibilidade entre os módulos do sistema.

Text in Afrikaans / Real empowerment of school learners requires preparing them for the age of technology. This empowerment can be achieved by developing their higher-order thinking skills. This is clearly the intention of the proposed South African FET National Curriculum Statements Grades 10 to 12 (Schools). This research shows that one method of developing higher-order thinking skills is to adopt an integrated curriculum approach. The research is based on the assumption that an integrated curriculum approach will produce learners with a more integrated knowledge structure which will help them to solve problems requiring higher-order thinking skills. These assumptions are realistic because the empirical results of several comparative research studies show that an integrated curriculum helps to improve learners' ability to use higher-order thinking skills in solving nonroutine problems. The curriculum mentions four kinds of integration, namely integration across different subject areas, integration of mathematics with the real world, integration of algebraic and geometric concepts, and integration into and the use of dynamic geometry software in the learning and teaching of geometry. This research shows that from a psychological, pedagogical, mathematical and historical perspective, the theme conic sections can be used as an integrating factor in the new proposed FET mathematics curriculum. Conics are a powerful tool for making the new proposed curriculum more integrated. Conics can be used as an integrating factor in the FET band by means of mathematical exploration, visualisation, relating learners' experiences of various parts of mathematics to one another, relating mathematics to the rest of the learners' experiences and also applying conics to solve real-life problems. / Mathematical Sciences / D.Phil. (Wiskundeonderwys)

Text in Afrikaans / Real empowerment of school learners requires preparing them for the age of technology. This empowerment can be achieved by developing their higher-order thinking skills. This is clearly the intention of the proposed South African FET National Curriculum Statements Grades 10 to 12 (Schools). This research shows that one method of developing higher-order thinking skills is to adopt an integrated curriculum approach. The research is based on the assumption that an integrated curriculum approach will produce learners with a more integrated knowledge structure which will help them to solve problems requiring higher-order thinking skills. These assumptions are realistic because the empirical results of several comparative research studies show that an integrated curriculum helps to improve learners' ability to use higher-order thinking skills in solving nonroutine problems. The curriculum mentions four kinds of integration, namely integration across different subject areas, integration of mathematics with the real world, integration of algebraic and geometric concepts, and integration into and the use of dynamic geometry software in the learning and teaching of geometry. This research shows that from a psychological, pedagogical, mathematical and historical perspective, the theme conic sections can be used as an integrating factor in the new proposed FET mathematics curriculum. Conics are a powerful tool for making the new proposed curriculum more integrated. Conics can be used as an integrating factor in the FET band by means of mathematical exploration, visualisation, relating learners' experiences of various parts of mathematics to one another, relating mathematics to the rest of the learners' experiences and also applying conics to solve real-life problems. / Mathematical Sciences / D.Phil. (Wiskundeonderwys)

Capes / Na busca por uma melhor representação da realidade tridimensional, as Geometrias não- Euclidianas oferecem uma alternativa ao euclidianismo clássico e um dos destaques e a Geometria Projetiva. Assim, o objetivo deste trabalho e, através de ilustrações, contribuir para a assimilação de definições como perspectiva, projeção e o principio da dualidade. E, a partir de resultados importantes como o Teorema de Desargues, o Teorema de Pappus e o Teorema de Pascal, queremos facilitar a compreensão e a visualização de algumas das técnicas de perspectiva que podem ser adaptadas para o uso na sala de aula pelos professores da Educação B ́ sica. A aplicação de uma oficina de Geometria Projetiva em uma turma do 6o ano do Ensino Fundamental e a avaliação dos resultados revelaram que o tema pode ser desenvolvido de maneira promissora com os estudantes na Educação B ́ sica, obtendo uma melhor compreensão do objeto real e associando-o ao conteúdo matemático envolvido. / In search for a better representation of three-dimensional reality, non-Euclidean Geometries offer an alternative to the classic euclidianism and the Projective Geometry is one of the highlights. The purpose of this word is contribute to the assimilation of definitions such as perspective, projection, and the principle of duality, through illustrations. And, from important results as Desargues’ Theorem, Pappus’ Theorem and Pascal’s Theorem, we want to facilitate understanding and viewing some of the perspective techniques that can be adapted for use in classroom by Basic Education teachers. The application of a workshop of Projective Geometry in a class of 6th grade of elementary school and the evaluation of the results revealed that the theme can be developed in a promising way with students in basic education, getting a better comprehension of the real object and associating it to the mathematical content involved.

Capes / Na busca por uma melhor representação da realidade tridimensional, as Geometrias não- Euclidianas oferecem uma alternativa ao euclidianismo clássico e um dos destaques e a Geometria Projetiva. Assim, o objetivo deste trabalho e, através de ilustrações, contribuir para a assimilação de definições como perspectiva, projeção e o principio da dualidade. E, a partir de resultados importantes como o Teorema de Desargues, o Teorema de Pappus e o Teorema de Pascal, queremos facilitar a compreensão e a visualização de algumas das técnicas de perspectiva que podem ser adaptadas para o uso na sala de aula pelos professores da Educação B ́ sica. A aplicação de uma oficina de Geometria Projetiva em uma turma do 6o ano do Ensino Fundamental e a avaliação dos resultados revelaram que o tema pode ser desenvolvido de maneira promissora com os estudantes na Educação B ́ sica, obtendo uma melhor compreensão do objeto real e associando-o ao conteúdo matemático envolvido. / In search for a better representation of three-dimensional reality, non-Euclidean Geometries offer an alternative to the classic euclidianism and the Projective Geometry is one of the highlights. The purpose of this word is contribute to the assimilation of definitions such as perspective, projection, and the principle of duality, through illustrations. And, from important results as Desargues’ Theorem, Pappus’ Theorem and Pascal’s Theorem, we want to facilitate understanding and viewing some of the perspective techniques that can be adapted for use in classroom by Basic Education teachers. The application of a workshop of Projective Geometry in a class of 6th grade of elementary school and the evaluation of the results revealed that the theme can be developed in a promising way with students in basic education, getting a better comprehension of the real object and associating it to the mathematical content involved.