Dissertations / Theses on the topic 'Geometry, Projective'
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1
Winroth, Harald. "Dynamic projective geometry." Doctoral thesis, Stockholm : Tekniska högsk, 1999. http://www.lib.kth.se/abs99/winr0324.pdf.
2
Wong, Tzu Yen. "Image transition techniques using projective geometry." University of Western Australia. School of Computer Science and Software Engineering, 2009. http://theses.library.uwa.edu.au/adt-WU2009.0149.
Abstract:
[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.
3
Romano, Raquel Andrea. "Projective minimal analysis of camera geometry." Thesis, Massachusetts Institute of Technology, 2002. http://hdl.handle.net/1721.1/29231.
Abstract:
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2002.Includes bibliographical references (p. 115-120).
This thesis addresses the general problem of how to find globally consistent and accurate estimates of multiple-view camera geometry from uncalibrated imagery of an extended scene. After decades of study, the classic problem of recovering camera motion from image correspondences remains an active area of research. This is due to the practical difficulties of estimating many interacting camera parameters under a variety of unknown imaging conditions. Projective geometry offers a useful framework for analyzing uncalibrated imagery. However, the associated multilinear models-the fundamental matrix and trifocal tensorare redundant in that they allow a camera configuration to vary along many more degrees of freedom than are geometrically admissible. This thesis presents a novel, minimal projective model of uncalibrated view triplets in terms of the dependent epipolar geometries among view pairs. By explicitly modeling the trifocal constraints among projective bifocal parameters-the epipoles and epipolar collineations-this model guarantees a solution that lies in the valid space of projective camera configurations. We present a nonlinear incremental algorithm for fitting the trifocally constrained epipolar geometries to observed image point matches. The minimal trifocal model is a practical alternative to the trifocal tensor for commonly found image sequences in which the availability of matched point pairs varies widely among different view pairs. Experimental results on synthetic and real image sequences with typical asymmetries in view overlap demonstrate the improved accuracy of the new trifocally constrained model.
(cont.) We provide an analysis of the objective function surface in the projective parameter space and examine cases in which the projective parameterization is sensitive to the Euclidean camera configuration. Finally, we present a new, numerically stable method for minimally parameterizing the epipolar geometry that gives improved estimates of minimal projective representations.
by Raquel A. Romano.
Ph.D.
4
Contatto, Felipe. "Vortices, Painlevé integrability and projective geometry." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/275099.
Abstract:
GaugThe first half of the thesis concerns Abelian vortices and Yang-Mills theory. It is proved that the 5 types of vortices recently proposed by Manton are actually symmetry reductions of (anti-)self-dual Yang-Mills equations with suitable gauge groups and symmetry groups acting as isometries in a 4-manifold. As a consequence, the twistor integrability results of such vortices can be derived. It is presented a natural definition of their kinetic energy and thus the metric of the moduli space was calculated by the Samols' localisation method. Then, a modified version of the Abelian–Higgs model is proposed in such a way that spontaneous symmetry breaking and the Bogomolny argument still hold. The Painlevé test, when applied to its soliton equations, reveals a complete list of its integrable cases. The corresponding solutions are given in terms of third Painlevé transcendents and can be interpreted as original vortices on surfaces with conical singularity. The last two chapters present the following results in projective differential geometry and Hamiltonians of hydrodynamic-type systems. It is shown that the projective structures defined by the Painlevé equations are not metrisable unless either the corresponding equations admit first integrals quadratic in first derivatives or they define projectively flat structures. The corresponding first integrals can be derived from Killing vectors associated to the metrics that solve the metrisability problem. Secondly, it is given a complete set of necessary and sufficient conditions for an arbitrary affine connection in 2D to admit, locally, 0, 1, 2 or 3 Killing forms. These conditions are tensorial and simpler than the ones in previous literature. By defining suitable affine connections, it is shown that the problem of existence of Killing forms is equivalent to the conditions of the existence of Hamiltonian structures for hydrodynamic-type systems of two components.
5
Marino, Nicholas John. "Vector Bundles and Projective Varieties." Case Western Reserve University School of Graduate Studies / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=case1544457943307018.
6
Beardsley, Paul Anthony. "Applications of projective geometry to robot vision." Thesis, University of Oxford, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.316854.
7
O'Keefe, Christine M. "Concerning t-spreads of PG ((s + 1) (t + 1)- 1, q)." Title page, contents and summary only, 1987. http://web4.library.adelaide.edu.au/theses/09PH/09pho41.pdf.
8
Niall, Keith. "Projective invariance and visual perception." Thesis, McGill University, 1987. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=75782.
Abstract:
Six experiments tested the assumption that, in visual perception, observers have reliable and direct access to the equivalence of shapes in projective geometry (I call this "the invariance hypothesis in the theory of shape constancy"). This assumption has been made in the study of vision since Helmholtz's time. Two experiments tested recognition of the projective equivalence of planar shapes. In another four experiments, subjects estimated the apparent shape of a solid object from different perspectives. Departure from projective equivalence was assessed in each study by measuring the cross ratio for the plane. This measure of projective invariance is new to perceptual research. Projective equivalence was not found to be perceived uniformly in any of the studies. A significant effect of change in perspective was found in each study. These results were construed as supporting the classical theory of depth cues against the invariance hypothesis.
9
Hønsen, Morten. "Compactifying locally Cohen-Macaulay projective curves." Doctoral thesis, Stockholm, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-470.
10
Ellis, Amanda. "Classification of conics in the tropical projective plane /." Diss., CLICK HERE for online access, 2005. http://contentdm.lib.byu.edu/ETD/image/etd1104.pdf.
11
McCallum, Rupert Gordon Mathematics & Statistics Faculty of Science UNSW. "Generalisations of the fundamental theorem of projective geometry." Publisher:University of New South Wales. Mathematics & Statistics, 2009. http://handle.unsw.edu.au/1959.4/43385.
Abstract:
The fundamental theorem of projective geometry states that a mapping from a projective space to itself whose range has a sufficient number of points in general position is a projective transformation possibly combined with a self-homomorphism of the underlying field. We obtain generalisations of this in many directions, dealing with the case where the mapping is only defined on an open subset of the underlying space, or a subset of positive measure, and dealing with many different spaces over many different rings.
12
Herman, Ivan. "The use of projective geometry in computer graphics /." Berlin ;Heidelberg ;New York ;London ;Paris ;Tokyo ;Hong Kong ;Barcelona ;Budapest : Springer, 1992. http://www.loc.gov/catdir/enhancements/fy0815/91043253-d.html.
13
Goetz, Peter D. "The noncommutative algebraic geometry of quantum projective spaces /." view abstract or download file of text, 2003. http://wwwlib.umi.com/cr/uoregon/fullcit?p3102165.
Abstract:
Thesis (Ph. D.)--University of Oregon, 2003.Typescript. Includes vita and abstract. Includes bibliographical references (leaves 106-108). Also available for download via the World Wide Web; free to University of Oregon users.
14
Fleming, Patrick Scott. "Finite projective planes and related topics." Laramie, Wyo. : University of Wyoming, 2006. http://proquest.umi.com/pqdweb?did=1225126281&sid=1&Fmt=2&clientId=18949&RQT=309&VName=PQD.
15
Cook, Gary Russell. "Arcs in a finite projective plane." Thesis, University of Sussex, 2011. http://sro.sussex.ac.uk/id/eprint/7510/.
Abstract:
The projective plane of order 11 is the dominant focus of this work. The motivation for working in the projective plane of order 11 is twofold. First, it is the smallest projective plane of prime power order such that the size of the largest (n, r)-arc is not known for all r ∈ {2,...,q + 1}. It is also the smallest projective plane of prime order such that the (n; 3)-arcs are not classified. Second, the number of (n, 3)-arcs is significantly higher in the projective plane of order 11 than it is in the projective plane of order 7, giving a large number of (n, 3)-arcs for study. The main application of (n, r)-arcs is to the study of linear codes. As a forerunner to the work in the projective plane of order eleven two algorithms are used to raise the lower bound on the size of the smallest complete n-arc in the projective plane of order thirty-one from 12 to 13. This work presents the classification up to projective equivalence of the complete (n, 3)- arcs in PG(2, 11) and the backtracking algorithm that is used in its construction. This algorithm is based on the algorithm used in [3]; it is adapted to work on (n, 3)-arcs as opposed to n-arcs. This algorithm yields one representative from every projectively inequivalent class of (n, 3)-arc. The equivalence classes of complete (n, 3)-arcs are then further classified according to their stabilizer group. The classification of all (n, 3)-arcs up to projective equivalence in PG(2, 11) is the foundation of an exhaustive search that takes one element from every equivalence class and determines if it can be extended to an (n′, 4)-arc. This search confirmed that in PG(2, 11) no (n, 3)-arc can be extended to a (33, 4)-arc and that subsequently m4(2, 11) = 32. This same algorithm is used to determine four projectively inequivalent complete (32, 4)-arcs, extended from complete (n, 3)-arcs. Various notions under the general title of symmetry are defined both for an (n, r)-arc and for sets of points and lines. The first of these makes the classification of incomplete (n; 3)- arcs in PG(2, 11) practical. The second establishes a symmetry based around the incidence structure of each of the four projectively inequivalent complete (32, 4)-arcs in PG(2, 11); this allows the discovery of their duals. Both notions of symmetry are used to analyze the incidence structure of n-arcs in PG(2, q), for q = 11, 13, 17, 19. The penultimate chapter demonstrates that it is possible to construct an (n, r)-arc with a stabilizer group that contains a subgroup of order p, where p is a prime, without reference to an (m < n, r)-arc, with stabilizer group isomorphic to ℤ1. This method is used to find q-arcs and (q + 1)-arcs in PG(2, q), for q = 23 and 29, supporting Conjecture 6.7. The work ends with an investigation into the effect of projectivities that are induced by a matrix of prime order p on the projective planes. This investigation looks at the points and subsets of points of order p that are closed under the right action of such matrices and their structure in the projective plane. An application of these structures is a restriction on the size of an (n, r)-arc in PG(2, q) that can be stabilized by a matrix of prime order p.
16
Oxenham, Martin Glen. "On n-covers of PG (3,q) and related structures /." Title page, contents and introduction only, 1991. http://web4.library.adelaide.edu.au/theses/09PH/09pho98.pdf.
17
Frost, George. "The projective parabolic geometry of Riemannian, Kähler and quaternion-Kähler metrics." Thesis, University of Bath, 2016. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.690742.
Abstract:
We present a uniform framework generalising and extending the classical theories of projective differential geometry, c-projective geometry, and almost quaternionic geometry. Such geometries, which we call \emph{projective parabolic geometries}, are abelian parabolic geometries whose flat model is an R-space $G\cdot\mathfrak{p}$ in the infinitesimal isotropy representation $\mathbb{W}$ of a larger self-dual symmetric R-space $H\cdot\mathfrak{q}$. We also give a classification of projective parabolic geometries with $H\cdot\mathfrak{q}$ irreducible which, in addition to the aforementioned classical geometries, includes a geometry modelled on the Cayley plane $\mathbb{OP}^2$ and conformal geometries of various signatures. The larger R-space $H\cdot\mathfrak{q}$ severely restricts the Lie-algebraic structure of a projective parabolic geometry. In particular, by exploiting a Jordan algebra structure on $\mathbb{W}$, we obtain a $\mathbb{Z}^2$-grading on the Lie algebra of $H$ in which we have tight control over Lie brackets between various summands. This allows us to generalise known results from the classical theories. For example, which riemannian metrics are compatible with the underlying geometry is controlled by the first BGG operator associated to $\mathbb{W}$. In the final chapter, we describe projective parabolic geometries admitting a $2$-dimensional family of compatible metrics. This is the usual setting for the classical projective structures; we find that many results which hold in these settings carry over with little to no changes in the general case.
18
Heuel, Stephan. "[Uncertain projective geometry] [statistical reasoning for polyhedral object reconstruction]." [Berlin Heidelberg] [Springer], 2002. http://dx.doi.org/10.1007/b97201.
19
Heuel, Stephan. "Uncertain projective geometry : statistical reasoning for polyhedral object reconstruction /." Berlin [u.a.] : Springer, 2004. http://www.loc.gov/catdir/enhancements/fy0813/2004104982-d.html.
20
Eskeland, II John T. "Searching for Constructed Form: A Station for Projective Geometry." Thesis, Virginia Tech, 2015. http://hdl.handle.net/10919/78192.
Abstract:
The project is dreamed as a monumental edifice standing beside the rail corridor of South-Western Virginia. Two pairs of towers rise from the earth transitioning from squares to ellipses. The towers are cut mid-ascent to shape an eastern face, orienting the project and the rail traffic beneath.Master of Architecture
21
Ruffoni, Lorenzo <1989>. "The Geometry of Branched Complex Projective Structures on Surfaces." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amsdottorato.unibo.it/7860/1/ruffoni_lorenzo_tesi.pdf.
Abstract:
We study the geometry of deformations of structures locally modelled on the Riemann sphere, up to branched covers, focusing on structures with quasi-Fuchsian holonomy and on structures which admit holomorphically trivial deformations. Applications to Riemann-Hilbert problems are discussed.
22
Castro, Renata Brandão de [UNESP]. "Tópicos da geometria projetiva." Universidade Estadual Paulista (UNESP), 2012. http://hdl.handle.net/11449/94354.
Abstract:
Made available in DSpace on 2014-06-11T19:27:09Z (GMT). No. of bitstreams: 0
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castro_rb_me_rcla.pdf: 774630 bytes, checksum: b9499068a589a33827880e026c206fd9 (MD5)Neste projeto tratamos da Geometria Projetiva advinda da generalização da Geometria Afim do Plano Euclidiano. Estabelecemos um Sistema Axiomático para a Geometria Projetiva e provamos resultados de sustentabilidade para esta geometria, sobretudo resultados sobre Perspectivas e Projeções. Também exploramos Cônicas dentro deste contexto. O principal livro usado como referência deste trabalho foi [1] de Judith Cederberg e como textos auxiliares consultaremos [2] e [3]
This project dealt with the Projective Geometry arising from the generalization of the Affine Geometry of the Euclidean Plane. Established an Axiomatic System for Projective Geometry and prove sustainability outcomes for this geometry, particularly on results Prospects and Projections. We also explored conics within this context
23
Castro, Renata Brandão de. "Tópicos da geometria projetiva /." Rio Claro : [s.n.], 2012. http://hdl.handle.net/11449/94354.
Abstract:
Orientador: Elíris Cristina RizziolliBanca: Grazielle Feliciani Barbosa
Banca: Carina Alves
Resumo: Neste projeto tratamos da Geometria Projetiva advinda da generalização da Geometria Afim do Plano Euclidiano. Estabelecemos um Sistema Axiomático para a Geometria Projetiva e provamos resultados de sustentabilidade para esta geometria, sobretudo resultados sobre Perspectivas e Projeções. Também exploramos Cônicas dentro deste contexto. O principal livro usado como referência deste trabalho foi [1] de Judith Cederberg e como textos auxiliares consultaremos [2] e [3]
Abstract: This project dealt with the Projective Geometry arising from the generalization of the Affine Geometry of the Euclidean Plane. Established an Axiomatic System for Projective Geometry and prove sustainability outcomes for this geometry, particularly on results Prospects and Projections. We also explored conics within this context
Mestre
24
Neretin, Yurii A., and Andreas Cap@esi ac at. "Geometry of GL$_n$(C) on Infinity: Hinges, Projective Compactifications." ESI preprints, 2000. ftp://ftp.esi.ac.at/pub/Preprints/esi971.ps.
25
Shabbir, Ghulam. "Curvature and projective symmetries in space-times." Thesis, University of Aberdeen, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.364690.
Abstract:
In this thesis a number of problems concerning proper curvature collineations, proper Weyl collineations and projective vector fields will be considered. The work on the above areas can be summarised as: (i) A study of proper curvature collineations in plane symmetric static, spherically symmetric static and Bianchi type I spacetimes will be presented by considering the rank of their 6 x 6 Riemann tensors and using a theorem which eliminates those space-times where proper curvature collineations can not exist; (ii) A study of proper Weyl collineations is given by using the algebraic classification and associated rank of the Weyl tensor and using a theorem similar to that used in (i); (iii) A technique is developed to study projective vector fields in the Friedmann Robertson-Walker models and plane symmetric static spacetimes; (iv) The situations when conformally flat spacetimes admit proper curvature collineations are fully explored.
26
Pichanick, E. V. D. "Bounds for complete arcs in finite projective planes." Thesis, University of Sussex, 2016. http://sro.sussex.ac.uk/id/eprint/63459/.
Abstract:
This thesis uses algebraic and combinatorial methods to study subsets of the Desarguesian plane IIq = PG(2, q). Emphasis, in particular, is given to complete (k, n)-arcs and plane projective curves. Known Diophantine equations for subsets of PG(2, q), no more than n of which are collinear, have been applied to k-arcs of arbitrary degree. This yields a new lower bound for complete (k, n)-arcs in PG(2, q) and is a generalization of a classical result of Barlotti. The bound is one of few known results for complete arcs of arbitrary degree and establishes new restrictions upon the parameters of associated projective codes. New results governing the relationship between (k, 3)-arcs and blocking sets are also provided. Here, a sufficient condition ensuring that a blocking set is induced by a complete (k, 3)-arc in the dual plane q is established and shown to complement existing knowledge of relationships between k-arcs and blocking sets. Combinatorial techniques analyzing (k, 3)-arcs in suitable planes are then introduced. Utilizing the numeric properties of non-singular cubic curves, plane (k, 3)-arcs satisfying prescribed incidence conditions are shown not to attain existing upper bounds. The relative sizes of (k, 3)-arcs and non-singular cubic curves are also considered. It is conjectured that m3(2, q), the size of the largest complete (k, 3)-arc in PG(2, q), exceeds the number of rational points on an elliptic curve. Here, a sufficient condition for its positive resolution is given using combinatorial analysis. Exploiting its structure as a (k, 3)-arc, the elliptic curve is then considered as a method of constructing cubic arcs and results governing completeness are established. Finally, classical theorems relating the order of the plane q to the existence of an elliptic curve with a specified number of rational points are used to extend theoretical results providing upper bounds to t3(2, q), the size of the smallest possible complete (k, 3)-arc in PG(2, q).
27
Hamed, Zainab Shehab. "Arcs of degree four in a finite projective plane." Thesis, University of Sussex, 2018. http://sro.sussex.ac.uk/id/eprint/77816/.
Abstract:
The projective plane, PG(2;q), over a Galois field Fq is an incidence structure of points and lines. A (k;n)-arc K in PG(2;q) is a set of k points such that no n+1 of them are collinear but some n are collinear. A (k;n)-arc K in PG(2;q) is called complete if it is not contained in any (k+1;n)-arc. The existence of arcs for particular values of k and n pose interesting problems in finite geometry. It connects with coding theory and graph theory, with important applications in computer science. The main problem, known as the packing problem, is to determine the largest size mn(2;q) of K in PG(2;q). This problem has received much attention. Here, the work establishes complete arcs with a large number of points. In contrast, the problem to determine the smallest size tn(2;q) of a complete (k;n)-arc is mostly based on the lower bound arising from theoretical investigations. This thesis has several goals. The first goal is to classify certain (k;4)-arcs for k = 6,...,38 in PG(2;13). This classification is established through an approach in Chapter 2. This approach uses a new geometrical method; it is a combination of projective inequivalence of (k;4)-arcs up to k = 6 and certain sdinequivalent (k;4)-arcs that have sd-inequivalent classes of secant distributions for k = 7,...,38. The part related to projectively inequivalent (k;4)-arcs up to k=6 starts by fixing the frame points f1;2;3;88g and then classify the projectively inequivalent (5;4)-arcs. Among these (5;4)-arcs and (6;4)-arcs, the lexicographically least set are found. Now, the part regarding sd-inequivalent (k;4)-arcs in this method starts by choosing five sd-inequivalent (7;4)-arcs. This classification method may not produce all sd-inequivalent classes of (k;4)-arcs. However, it was necessary to employ this method due to the increasing number of (k;4)-arcs in PG(2;13) and the extreme computational difficulty of the problem. It reduces the constructed number of (k;4)-arcs in each process for large k. Consequently, it reduces the executed time for the computation which could last for years. Also, this method decreases the memory usage needed for the classification. The largest size of (k;4)-arc established through this method is k = 38. The classification of certain (k;4)-arcs up to projective equivalence, for k = 34,35,36,37,38, is also established. This classification starts from the 77 incomplete (34;4)-arcs that are constructed from the sd-inequivalent (33;4)-arcs given in Section 2.29, Table 2.35. Here, the largest size of (k;4)-arc is still k = 38. In addition, the previous process is re-iterated with a different choice of five sd-inequivalent (7;4)-arcs. The purpose of this choice is to find a new size of complete (k;4)-arc for k > 38. This particular computation of (k;4)-arcs found no complete (k;4)-arc for k > 38. In contrast, a new size of complete (k;4)-arc in PG(2;13) is discovered. This size is k = 36 which is the largest complete (k;4)-arc in this computation. This result raises the second largest size of complete (k;4)-arc found in the first classification from k = 35 to k = 36. The second goal is to discuss the incidence structure of the orbits of the groups of the projectively inequivalent (6;4)-arcs and also the incidence structures of the orbits of the groups other than the identity group of the sd-inequivalent (k;4)-arcs. In Chapter 3, these incidence structures are given for k = 6,7,8,9,10,11,12,13,14,38. Also, the pictures of the geometric configurations of the lines and the points of the orbits are described. The third goal is to find the sizes of certain sd-inequivalent complete (k;4)-arcs in PG(2;13). These sizes of complete (k;4)-arcs are given in Chapter 4 where the smallest size of complete (k;4)-arc is at most k = 24 and the largest size is at least k = 38. The fourth goal is to give an example of an associated non-singular quartic curve C for each complete (k;4)-arc and to discuss the algebraic properties of each curve in terms of the number I of inflexion points, the number jC \K j of rational points on the corresponding arc, and the number N1 of rational points of C . These curves are given in Chapter 5. Also, the algebraic properties of complete arcs of the most interesting sizes investigated in this thesis are studied. In addition, there are two examples of quartic curves C (g0 1) and C (g0 2) attaining the Hasse-Weil- Serre upper bound for the number N1 of rational points on a curve over the finite field of order thirteen. This number is 32. The fifth goal is to classify the (k;4)-arcs in PG(2;13) up to projective inequivalence for k < 10. This classification is established in Chapter 6. It starts by fixing a triad, U1, on the projective line, PG(1;13). Here, the number of projectively inequivalent (k;4)-arcs are tested by using the tool given in Chapter 2. Then, among the number of the projectively inequivalent (10;4)-arcs found, the classification of sd-inequivalent (k;4)-arcs for k = 10 is made. The number of these sd-inequivalent arcs is 36. Then, the 36 sd-inequivalent arcs are extended. The aim here is to investigate if there is a new size of sd-inequivalent (k;4)-arc for k > 38 that can be obtained from these arcs. The largest size of sd-inequivalent (k;4)-arc in this process is the same as the largest size of the sd-inequivalent (k;4)-arc established in Chapter 2, that is, k = 38. In addition, the classification of (k;n)-arcs in PG(2;13) is extended from n = 4 to n = 6. This extension is given in Chapter 7 where some results of the classification of certain (k;6)-arcs for k = 9; : : : ;25 are obtained using the same method as in Chapter 2 for k = 7,...,38. This process starts by fixing a certain (8;6)-arc containing six collinear points in PG(2;13).
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Leite, Douglas Gonçalves. "Método de perspectiva e Brouillon project : dois estudos de Desargues sobre perspectiva e geometria de projeções /." Rio Claro, 2018. http://hdl.handle.net/11449/154504.
Abstract:
Orientador: Marcos Vieira TeixeiraResumo: O presente trabalho discorre a respeito de dois textos do arquiteto e matemático francês Girard Desargues. As obras que aqui chamamos de Método de Perspectiva (1636) e Brouillon Project (1639), foram desenvolvidas em um período com ampla produção teórica relacionada a técnicas de representação. No trabalho de 1636 Desargues descreveu o processo necessário para representar uma gaiola em perspectiva. No trabalho, Brouillon Project, ele trata de propriedades geométricas envolvendo feixe de retas aproximando-se dos conceitos existentes no campo das projeções de figuras, contudo parte das referências utilizadas, como Chasles, Poudra, Taton, entre outros, consideraram que o Brouillon Project foi um trabalho relacionado as seções cônicas. Nosso objetivo é apresentar uma análise envolvendo os conteúdos geométricos explorados nas duas obras citadas com o intuito de relacioná-las com o campo da perspectiva e projeção de figuras. Para isso, desenvolvemos uma pesquisa em história da matemática envolvendo história perspectiva, história da geometria, forma de produção do conhecimento daquele período, em conjunto com teorias que estavam sendo produzidas até o séc. XVII
Abstract: The present work deals with two texts of the French architect and mathematician Girard Desargues. The works that we call the Method of Perspective (1636) and Brouillon Project (1639) were developed in a period with a large theoretical production related to representations of figures in perspective. In the work of 1636 Desargues described the process necessary to represent a cage in perspective. At work, Brouillon Project, he dealt with geometric properties involving beam of straight lines approaching the existing concepts in the field of projections of figures. However, some of the references used, such as Chasles, Poudra, Taton, and others, consider that the Brouillon Project was a work related to the conic sections. Our objective is to present a study involving the geometric contents explored in the two works mentioned, seeking to relate them to the field of perspective and projection of figures. For this, we developed a research in history of mathematics involving history, perspective, history of geometry, form of knowledge production of that period, together with theories that were being produced until the century. XVII
Mestre
29
Flórez, Rigoberto. "Four studies in geometry of biased graphs." Online access via UMI:, 2005.
30
Heuel, Stephan [Verfasser]. "[Uncertain projective geometry] : [statistical reasoning for polyhedral object reconstruction] / [Stephan Heuel]." [Berlin, 2004. http://d-nb.info/972277110/34.
31
Ellis, Amanda. "Classifcation of Conics in the Tropical Projective Plane." BYU ScholarsArchive, 2005. https://scholarsarchive.byu.edu/etd/697.
Abstract:
This paper defines tropical projective space, TP^n, and the tropical general linear group TPGL(n). After discussing some simple examples of tropical polynomials and their hypersurfaces, a strategy is given for finding all conics in the tropical projective plane. The classification of conics and an analysis of the coefficient space corresponding to such conics is given.
32
McKinnon, David N. R. "The multiple view geometry of implicit curves and surfaces /." [St. Lucia, Qld.], 2006. http://www.library.uq.edu.au/pdfserve.php?image=thesisabs/absthe19677.pdf.
33
Yoon, Young-jin. "Characterizations of Some Combinatorial Geometries." Thesis, University of North Texas, 1992. https://digital.library.unt.edu/ark:/67531/metadc277894/.
Abstract:
We give several characterizations of partition lattices and projective geometries. Most of these characterizations use characteristic polynomials. A geometry is non—splitting if it cannot be expressed as the union of two of its proper flats. A geometry G is upper homogeneous if for all k, k = 1, 2, ... , r(G), and for every pair x, y of flats of rank k, the contraction G/x is isomorphic to the contraction G/y. Given a signed graph, we define a corresponding signed—graphic geometry. We give a characterization of supersolvable signed graphs. Finally, we give the following characterization of non—splitting supersolvable signed-graphic geometries : If a non-splitting supersolvable ternary geometry does not contain the Reid geometry as a subgeometry, then it is signed—graphic.
34
Packer, S. "On sets of odd type and caps in Galois geometries of order four." Thesis, University of Sussex, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.262299.
35
Giuzzi, Luca. "Hermitian varieties over finite fields." Thesis, University of Sussex, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.326913.
36
Tate, Dominic. "On the Fock-Goncharov Moduli Space for Real Projective Structures on Surfaces: Cell Decomposition, Buildings and Compactification." Thesis, The University of Sydney, 2020. https://hdl.handle.net/2123/22342.
Abstract:
Let S be a non-compact surface with empty boundary and negative Euler characteristic. Fock and Goncharov [2006, 2007] devise coordinate systems for the space of properly convex projective structures on S and for the space of doubly-decorated finite-area projective structures on S. These are known as the spaces of X-coordinates and A-coordinates respectively. We use the former to provide straightforward proofs of known results regarding the moduli space of convex projective structures on surfaces of finite area, due to Marquis [2010], and closed surfaces, due to Goldman [1990]. The latter coordinate space is then shown to have a natural cell decomposition induced by the canonical cell decomposition of a real projective surface due to Cooper and Long [2015]. In the final chapter we recall Parreau's [2012] generalisation of Thurston's [1988] compactification of Teichmüller space via length spectra. Subsequently, Parreau [2015] provides a method of assigning an action of the fundamental group of S on a Euclidean building to points on the boundary of this compactified space as well as a fundamental group-invariant subset of the building for some such points. Parreau's construction depends upon a choice of ideal triangulation so a natural question to ask is whether or not for each point on the ideal boundary of the moduli space there exists an ideal triangulation with respect to which Parreau's construction provides a fundamental group-invariant subset of the building. We answer this question in the negative. We modify Parreau's construction to provide a fundamental group-invariant subset to a dense subset of the boundary points. Moreover this is done in a way that is independent of the choice of ideal triangulation used to define the X-coordinates.
37
Huang, Jen-Fa. "On finding generator polynomials and parity-check sums of binary projective geometry codes." Thesis, University of Ottawa (Canada), 1985. http://hdl.handle.net/10393/4800.
38
White, Clinton T. Wilson R. M. "Two cyclic arrangement problems in finite projective geometry : parallelisms and two-intersection sets /." Diss., Pasadena, Calif. : California Institute of Technology, 2002. http://resolver.caltech.edu/CaltechETD:etd-06052006-143933.
39
Oliveira, Júnior José William de. "Três pontos de vista sobre cônicas." Mestrado Profissional em Matemática, 2018. http://ri.ufs.br/jspui/handle/riufs/9321.
Abstract:
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESIn the present work, we tried to investigate the conics in the synthetic, analytical and projective contexts, as well as to know some applications and properties of these curves. In the synthetic approach, it was emphasized a lithe of the historical aspects, the works made by Apollonius and Dandelin, a characterization for tangent and normal lines and re ecting properties. In the analytical approach, the Cartesian, polar and parametric equations were described, as well as the applications in the Kepler Laws. In the projective approach, the concepts of projective plane, projective point, projective line and projective applications were used to give meaning to the conic in the projective universe, in addition the Theorews of Pascal and Brianchon were demonstrated.
No presente trabalho, procurou-se investigar as cônicas nos contextos sintético, analítico e projetivo, bem como conhecer algumas aplicações e propriedades dessas curvas. Na abordagem sintética, foram enfatizados um pouco do aspecto histórico, os trabalhos feitos por Apolônio e Dandelin, uma caracterização para retas tangentes e normais e as propriedades refletoras. Na abordagem analítica, foram descritas as equações cartesianas, polares e paramétricas, como também as aplicações nas Leis de Kepler. Na abordagem projetiva, foram trabalhados os conceitos de plano projetivo, ponto projetivo, reta projetiva e aplicações projetivas para dar significado as cônicas no universo projetivo, além disso foram demonstrados os teoremas de Pascal e Brianchon.
São Cristóvão, SE
40
Culbert, Craig W. "Spreads of three-dimensional and five-dimensional finite projective geometries." Access to citation, abstract and download form provided by ProQuest Information and Learning Company; downloadable PDF file, 101 p, 2009. http://proquest.umi.com/pqdweb?did=1891555371&sid=3&Fmt=2&clientId=8331&RQT=309&VName=PQD.
41
Abuaf, Roland. "Dualité homologique projective et résolutions catégoriques des singularités." Thesis, Grenoble, 2013. http://www.theses.fr/2013GRENM057/document.
Abstract:
Soit $X$ une variété algébrique de Gorenstein à singularités rationnelles. Une résolution des singularités crépante de $X$ est souvent considérée comme une résolution des singularités minimales de $X$. Malheureusement, les résolutions crépantes sont très rares. Ainsi, les variétés déterminantielles de matrices anti-symétriques n'admettent jamais de résolution crépante des singularités. Dans cette thèse, on discutera de diverses notions de résolutions catégoriques crépantes développées par Alexander Kuznetsov. Conjecturalement, ces résolutions doivent être minimale du point de vue catégorique. On introduit dans ce manuscrit la notion de résolution magnifiques des singularités et on montre que tout variété munie d'une telle résolution admet une résolution catégorique faiblement crépante. On en déduit que toutes les variétés déterminantielles (carrées, symétriques et anti-symétriques) admettent des résolutions catégoriques faiblement crépantes. Finalement, on s'intéressera à des hypersurfaces quartiques issues du carré magique de Tits-Freudenthal. On ne peut pas construire de résolution magnifique des singularités pour de telles hypersurfaces, mais on montrera qu'elles admettent tout de même des résolutions catégorique faiblement crépantes des singularités. Ce résultat devrait s'avérer intéressant pour la construction de duales projectives homologiques de certaines Grassmaniennes symplectiques sur les algèbres de compositionLet $X$ be an algebraic variety with Gorenstein rational singularities. A crepant resolution of $X$ is often considered to be a minimal resolution of singularities for $X$. Unfortunately, crepant resolution of singularities are very rare. For instance, determinantal varieties of skew-symmetric matrices never admit crepant resolution of singularities. In this thesis, we discuss various notions of categorical crepant resolution of singularities as defined by Alexander Kuznetsov. Conjecturally, these resolutions are minimal from the categorical point of view. We introduce the notion of wonderful resolution of singularities and we prove that a variety endowed with such a resolution admits a weakly crepant resolution of singularities. As a corollary, we prove that all determinantal varieties (square, as well as symmetric and skew-symmetric) admit weakly crepant resolution of singularities. Finally, we study some quartics hypersurfaces which come from the Tits-Freudenthal magic square. Though they do no admit any wonderful resolution of singularities, we are still able to prove that they have a weakly crepant resolution of singularities. This last result should be of interest in order to construct homological projective duals for some symplectic Grassmannians over the composition algebras
42
Vereecke, Sam K. J. "Some properties of arcs, caps and quadrics in projective spaces in finite order." Thesis, University of Sussex, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.263915.
43
Velebová, Jana. "Fotogrammetrická analýza obrazů." Master's thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2011. http://www.nusl.cz/ntk/nusl-412846.
Abstract:
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.
44
Andrade, Andréa Ferreira Faccioni de [UNESP]. "Um estudo da geometria projetiva elíptica." Universidade Estadual Paulista (UNESP), 2015. http://hdl.handle.net/11449/134030.
Abstract:
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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
45
Andrade, Andréa Ferreira Faccioni de. "Um estudo da geometria projetiva elíptica /." Rio Claro, 2015. http://hdl.handle.net/11449/134030.
Abstract:
Orientador: Alice Kimie Miwa LibardiBanca: 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
46
Zeng, Rui. "Homography estimation: From geometry to deep learning." Thesis, Queensland University of Technology, 2019. https://eprints.qut.edu.au/134132/1/Rui_Zeng_Thesis.pdf.
Abstract:
Homography is an important area of computer vision for scene understanding and plays a key role in extracting relationships across different viewpoints of a scene. This thesis focuses on studying homography transformations between images from both geometric and deep learning perspectives. We have developed an accurate and effective homography estimation system for sports scenes analysis an efficient and novel 3D perspective feature to improve 3D object recognition especially for the vehicle recognition.
47
Lai, Po-Lun. "Shape Recovery by Exploiting Planar Topology in 3D Projective Space." The Ohio State University, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=osu1268187247.
48
Chu, Lei. "Colouring Cayley Graphs." Thesis, University of Waterloo, 2005. http://hdl.handle.net/10012/1125.
Abstract:
We will discuss three ways to bound the chromatic number on a Cayley graph.
1. If the connection set contains information about a smaller graph, then these two graphs are related. Using this information, we will show that Cayley graphs cannot have chromatic number three.
2. We will prove a general statement that all vertex-transitive maximal triangle-free graphs on n vertices with valency greater than n/3 are 3-colourable. Since Cayley graphs are vertex-transitive, the bound of general graphs also applies to Cayley graphs.
3. Since Cayley graphs for abelian groups arise from vector spaces, we can view the connection set as a set of points in a projective geometry. We will give a characterization of all large complete caps, from which we derive that all maximal triangle-free cubelike graphs on 2n vertices and valency greater than 2n/4 are either bipartite or 4-colourable.
49
Chowdhury, Ameerah. "Colouring Subspaces." Thesis, University of Waterloo, 2005. http://hdl.handle.net/10012/1026.
Abstract:
This thesis was originally motivated by considering vector space analogues of problems in extremal set theory, but our main results concern colouring a graph that is intimately related to these vector space analogues. The vertices of the q-Kneser graph are the k-dimensional subspaces of a vector space of dimension v over Fq, and two k-subspaces are adjacent if they have trivial intersection. The new results in this thesis involve colouring the q-Kneser graph when k=2. There are two cases. When k=2 and v=4, the chromatic number is q2+q. If k=2 and v>4, the chromatic number is (q(v-1)-1)/(q-1). In both cases, we characterise the minimal colourings. We develop some theory for colouring the q-Kneser graph in general.
50
Huang, Haifei. "The common self-polar triangle of conics and its applications to computer vision." HKBU Institutional Repository, 2017. https://repository.hkbu.edu.hk/etd_oa/407.
Abstract:
In projective geometry, the common self-polar triangle has often been used to discuss the location relationship of two planar conics. However, there are few researches on the properties of the common self-polar triangle, especially when the two planar conics are special conics. In this thesis, the properties of the common self-polar triangle of special conics are studied and their applications to computer vision are presented. Specifically, the applications focus on the two topics of the computer vision: camera calibration and homography estimation. This thesis first studies the common self-polar triangle of two sphere images and also that the common self-polar triangle of two concentric circles, and exploits its properties to solve the problem of camera calibration. For the sphere images, by recovering the constraints on the imaged absolute conic from the vertices of the common self-polar triangles, a novel method for estimating the intrinsic parameters of a camera from an image of three spheres has been developed. For the other case of concentric circles, it is shown in this thesis that the imaged circle center and the vanishing line of the support plane can be recovered simultaneously. Furthermore, many orthogonal vanishing points can be obtained from the common self-polar triangles. Consequently, two novel calibration methods have been developed. Based on our method, one of the state-of-the-art calibration methods has been well interpreted. This thesis then studies the common self-polar triangle of two separate ellipses, and applies it to planar homography estimation. For two images of the separate ellipses, by inducing four corresponding lines from the common self-polar triangle, a homography estimation method has been developed without ambiguity. Based on these results, a special case of planar rectification with two identical circles is also studied. It is shown that given one image of the two identical circles, the vanishing line of the support plane can be recovered from the common self-polar triangle and the imaged circle points can be obtained by intersecting the vanishing line with the image of the circle. Accordingly, a novel method for estimating the rectification homography has been developed and experimental results show the feasibility of our method.