Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This thesis we will make a study of the quadrics, which can be de ned as quadratic equations solutions with three variables, with the main objective recognition of same through a simpli cation of the quadratic form associated, whose procedure involves the diagonalization of symmetric matrices. Throughout we this work, will address the requirements for the reader with little familiarity on the subject, can understand each stage of its development, as Euclidean spaces and matrix diagonalization. / Nesta disserta ção faremos um estudo das qu ádricas, as quais podem ser de finidas como solu ções de equa ções do segundo grau com três vari áveis, tendo como objetivo principal o reconhecimento das mesmas por meio de uma simpli fica ção da forma quadr ática associada, cujo procedimento envolve a diagonaliza ção de matrizes sim étricas. Ao longo deste trabalho, serão abordados os prée-requisitos necess ários para que o leitor, com pouca familiaridade no assunto, possa compreender cada etapa de seu desenvolvimento, como espa ços euclidianos e diagonaliza ção de matrizes.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-05-29T14:33:20Z No. of bitstreams: 1 williamfredericovasconcellossilva.pdf: 451866 bytes, checksum: bfeb4aa8aa637b66cf493889e77ebca1 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-05-29T19:47:08Z (GMT) No. of bitstreams: 1 williamfredericovasconcellossilva.pdf: 451866 bytes, checksum: bfeb4aa8aa637b66cf493889e77ebca1 (MD5) / Made available in DSpace on 2017-05-29T19:47:08Z (GMT). No. of bitstreams: 1 williamfredericovasconcellossilva.pdf: 451866 bytes, checksum: bfeb4aa8aa637b66cf493889e77ebca1 (MD5) Previous issue date: 2012-07-12 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / O principal objetivo do trabalho é estudar a relação entre o espaço de Moduli de feixes de quádricas em Pn e o espaço de Moduli de formas binárias de grau (n + 1). Este estudo foi baseado no artigo (AVRITZER; LANGE, 2000). Em linhas gerais, um espaço de Moduli é uma variedade algébrica que parametriza uma coleção de objetos C, módulo uma relação de equivalência. No nosso caso, C é o conjunto de feixes de quádricas em Pn ou o conjunto de formas binárias de grau (n + 1), e a relação de equivalência é pertencer à mesma órbita pela ação de um grupo G. Para estabelecermos a relação entre esses espaços foi importante considerar o símbolo de Segre que é um invariante dos feixes de quádricas. Além disso, estudamos a forma normal, uma maneira de reescrever o feixe de quádricas, na qual conhecemos facilmente o símbolo de Segre. Estudamos ação de grupos, para podermos classificar um feixe de quádrica e uma forma binária como estável, semi-estável ou instável, e quociente categórico, já que os espaços de Moduli são obtidos através do quociente. / The main objective is to study the relationship between space Moduli of pencil of quadrics, and Moduli space of binary forms. This study was based on article (AVRITZER; LANGE, 2000). In general, a Moduli space is an algebraic variety that parametrizes a collection of objects C, modulo an equivalence relation. In our case, C is the set of pencil of quadrics or set of binary forms of degree (n + 1), and the equivalence relation is to belong to the same orbit by the action of a group G. To establish the relationship between these spaces is important to consider the Segre symbol of which is an invariant of pencils of quadrics. Furthermore, we studied the normal form, a way to rewrite the pencil of quadrics, which easily met the Segre symbol, action of groups, in order to classify a pencil of quadric and a binary form as stable or semistable unstable, and quotient categorical, since the spaces's moduli are obtained by quotient.

Title from PDF of title page. / Document formatted into pages; contains 76 pages. / Thesis (M.S.E.E.)--University of South Florida, 2003. / Includes bibliographical references. / Text (Electronic thesis) in PDF format. / ABSTRACT: The use of digitized information is rapidly gaining acceptance in bio-medical applications. Video compression plays an important role in the archiving and transmission of different digital diagnostic modalities. The present scheme of video compression for low bit-rate networks is not suitable for medical video sequences. The instability is the result of block artifacts resulting from the block based DCT coefficient quantization. The possibility of applying deformable motion estimation techniques to make the video compression standard (H.263) more adaptable for bio-medial applications was studied in detail. The study on the network characteristics and the behavior of various congestion control mechanisms was used to analyze the complete characteristics of existing low bit rate video compression algorithms. The study was conducted in three phases. The first phase involved the implementation and study of the present H.263 compression standard and its limitations. / ABSTRACT: The second phase dealt with the analysis of an external force for active contours which was used to obtain estimates for deformable objects. The external force, which is termed Gradient Vector Flow (GVF), was computed as a diffusion of the gradient vectors associated with a gray-level or binary edge map derived from the image. The mathematical aspect of a multi-scale framework based on a medial representation for the segmentation and shape characterization of anatomical objects in medical imagery was derived in detail. The medial representations were based on a hierarchical representation of linked figural models such as protrusions, indentations, neighboring figures and included figures--which represented solid regions and their boundaries. The third phase dealt with the vital parameters for effective video streaming over the internet in the bottleneck bandwidth, which gives the upper limit for the speed of data delivery from one end point to the other in a network. / ABSTRACT: If a codec attempts to send data beyond this limit, all packets above the limit will be lost. On the other hand, sending under this limit will clearly result in suboptimal video quality. During this phase the packet-drop-rate (PDR) performance of TCP(1/2) was investigated in conjunction with a few representative TCP-friendly congestion control protocols (CCP). The CCPs were TCP(1/256), SQRT(1/256) and TFRC (256), with and without self clocking. The CCPs were studied when subjected to an abrupt reduction in the available bandwidth. Additionally, the investigation studied the effect on the drop rates of TCP-Compatible algorithms by changing the queuing scheme from Random Early Detection (RED) to DropTail. / System requirements: World Wide Web browser and PDF reader. / Mode of access: World Wide Web.

Les plantes sont des éléments essentiels du monde qui nous entoure. Ainsi, si l’on veut créer des environnements virtuels qui soient à la fois agréables et réalistes, un effort doit être fait pour modéliser les plantes. Malgré les immenses progrès en vision par ordinateur pour reconstruire des objets de plus en plus compliqués, les plantes restent difficiles à reconstruire à cause de la complexité de leur topologie. Cette thèse se divise en deux grandes parties. La première partie s’intéresse à la modélisation de plantes, biologiquement réalistes, à partir d’une seule image. Nous générons un modèle de plante respectant les contraintes biologiques de son espèce et tel que sa projection soit la plus fidèle possible à l’image. La première étape consiste à extraire de l’image le squelette de la plante. Dans la plupart de nos images, aucune branche n’est visible et les images peuvent être de qualité moyenne. Notre première contribution consiste en une méthode de squelettisation basée sur les champs de vecteurs. Le squelette est extrait suite à un partitionnement non déterministe du feuillage de l’image assurant son réalisme. Dans un deuxième temps, la plante est modélisée en 3D. Notre deuxième contribution est la création de modèles pour différents types de plantes, basée sur les L-systèmes. Puis, un processus d’analyse-par-synthèse permet de choisir le modèle 3D final : plusieurs propositions de squelette sont générées et un processus bayésien permet d’extraire le modèle maximisant le critère a posteriori. Le terme d’attache aux données (vraisemblance) mesure la similarité entre l’image et la reprojection du modèle, la probabilité a priori mesure le réalisme du modèle. Après avoir généré des modèles de plantes, des modèles de fruits doivent être créés. Ayant travaillé principalement sur les pieds de vigne, nous avons développé une méthode pour reconstruire une grappe de raisin à partir d’au moins deux vues. Chaque baie est assimilée à un ellipsoïde de révolution. La méthode obtenue peut être plus généralement adaptée à tout type de fruits assimilables à une quadrique de révolution. La seconde partie de cette thèse s’intéresse à la reconstruction de quadriques de révolution à partir d’une ou plusieurs vues. La reconstruction de quadriques et, en général, la reconstruction de surfaces 3D est un problème très ancien en vision par ordinateur qui a donné lieu à de nombreux travaux. Nous rappelons les notions nécessaires de géométrie projective des quadriques, et de vision par ordinateur puis, nous présentons un état de l’art sur les méthodes existantes sur la reconstruction de surfaces quadratiques. Nous détaillons un premier algorithme permettant de retrouver les images des foyers principaux d’une quadrique de révolution à partir d’une vue « calibrée », c’est-à-dire pour laquelle les paramètres intrinsèques de la caméra sont connus. Puis, nous détaillons comment utiliser ce résultat pour reconstruire, à partir d’un schéma de triangulation linéaire, tout type de quadriques de révolution à partir d’au moins deux vues. Enfin, nous montrons comment il est possible de retrouver la pose 3D d’une quadrique de révolution dont on connaît les paramètres à partir d’un seul contour occultant. Nous évaluons les performances de nos méthodes et montrons quelques applications possibles. / Plants are essential elements of our world. Thus, 3D plant models are necessary to create realistic virtual environments. Mature computer vision techniques allow the reconstruction of 3D objects from images. However, due to the complexity of the topology of plants, dedicated methods for generating 3D plant models must be devised. This thesis is divided into two parts. The first part focuses on the modeling of biologically realistic plants from a single image. We propose to generate a 3D model of a plant, using an analysis-by-synthesis method considering both a priori information of the plant species and a single image. First, a dedicated 2D skeletonisation algorithm generates possible branching structures from the foliage segmentation. Then, we built a 3D generative model based on a parametric model of branching systems taking into account botanical knowledge. The resulting skeleton follows the hierarchical organisation of natural branching structures. Varying parameter values of the generative model (main branching structure of the plant and foliage), we produce a series of candidate models. A Bayesian model optimizes a posterior criterion which is composed of a likelihood function which measures the similarity between the image and the reprojected 3D model and a prior probability measuring the realism of the model. After modeling plant models branching systems and foliage, we propose to model the fruits. As we mainly worked on vines, we propose a method for reconstructing a vine grape from at least two views. Each bay is considered to be an ellipsoid of revolution. The resulting method can be adapted to any type of fruits with a shape similar to a quadric of revolution. The second part of this thesis focuses on the reconstruction of quadrics of revolution from one or several views. Reconstruction of quadrics, and in general, 3D surface reconstruction is a very classical problem in computer vision. First, we recall the necessary background in projective geometry quadrics and computer vision and present existing methods for the reconstruction of quadrics or more generally quadratic surfaces. A first algorithm identifies the images of the principal foci of a quadric of revolution from a "calibrated" view (that is, the intrinsic parameters of the camera are given). Then we show how to use this result to reconstruct, from a linear triangulation scheme, any type of quadrics of revolution from at least two views. Finally, we show that we can derive the 3D pose of a given quadric of revolution from a single occluding contour. We evaluate the performance of our methods and show some possible applications.

Submitted by ANA KARLA PEREIRA RODRIGUES (anakarla_@hotmail.com) on 2017-08-17T12:22:57Z No. of bitstreams: 1 arquivototal.pdf: 697305 bytes, checksum: 0b28f8f8c4f8b4509047eb441817be7c (MD5) / Made available in DSpace on 2017-08-17T12:22:57Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 697305 bytes, checksum: 0b28f8f8c4f8b4509047eb441817be7c (MD5) Previous issue date: 2016-03-09 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work, we present an explicit geometric characterization for the space of quadratcs form vanishing precisely on a twisted cubic. We show that the set of degenerate quadrics lying on a net of quadrics containing a twisted cubic is described by a curve whose equation is given by the square of an irreducible conic. Conversely, if is a net of quadrics whosw intersection with the set of degenerate quadrics is a curve given by the square of an irreducible conic, we furnish conditions under which the cammon zero locus of turns out to be a twisted cubic. It is enough to require that does not contain a pair of planes. / Neste trabalho, apresentamos uma caracteriza c~ao geom etrica expl cita para o espa co das formas quadr aticas que se anulam precisamente sobre uma c ubica reversa. Mostramos que o conjunto das qu adricas degeneradas pertencentes a uma rede de qu adricas que cont em a c ubica reversa e descrita por uma curva cuja equa c~ao e dada pelo quadrado de uma c^onica irredut vel. Rec procamente, se e uma rede de qu adricas cuja interse c~ao com o conjunto das qu adricas n~ao degeneradas e uma curva dada pelo quadrado de uma c^onica irredut vel, fornecemos condi c~oes sob as quais o lugar dos zeros comuns de seja uma c ubica reversa. E su ciente que n~ao contenha um par de plano.

Soient $X$ et $Y$ des variétés au dessus d’un corps $F$. Dans de nombreuses situations, il s’avère important de savoir si un cycle algébrique modulo équivalence rationnelle y sur Y, défini au dessus du corps des fonctions $F(X)$ de $X$, est en fait déjà défini au niveau du corps de base $F$. Dans cet essai, on traite de cette question, en faisant varier la variété $X$ parmi des variétés telles que des quadriques, des variétés projectives homogènes ou des espaces principaux homogènes. Dans chaque situation, on utilise des outils appropriés tels que les opérations de Steenrod, des résultats de décomposition motivique, ou certains invariants cohomologiques de groupes algébriques. / Let $X$ and $Y$ be some varieties over a field $F$. In many situations, it is important to know if an algebraic cycle modulo rational equivalence $y$ on $Y$ defined over the function field $F(X)$ of $X$ is actually defined over the base field $F$. In this dissertation, we study that matter, making the variety $X$ vary among varieties such as quadrics, projective homogeneous varieties or principal homogeneous spaces. In each situation, we use appropriate tools, such as Steenrod operations, motivic decomposition results or cohomological invariants of algebraic groups.

[pt] O contato com modelos geométricos tais como planos, esferas ou quádricas é uma importante ferramenta para entender a geometria diferencial de uma superfície. Nesta tese, estudamos o contato de superfícies com quádricas, e mais particularmente, com as quádricas de Moutard. Estendemos os resultados conhecidos para o caso de pontos parabólicos e curvas flecnodais em superfícies genéricas. Consideramos também o contato de hipersuperfícies com hiperquádricas de Moutard. / [en] The contact with generic models like planes, spheres or quadrics is an important tool to understand the differential geometry of a surface. In this thesis, we study the contact of surfaces with quadrics, more specifically, with Moutard quadrics. We extend the known results for the case of parabolic points and flecnodal curves in generic surfaces. We consider also the contact of hypersurfaces with Moutard hyperquadrics.

Submitted by Alisson de Carvalho Reinol null (alissoncarv@gmail.com) on 2017-07-18T15:03:51Z No. of bitstreams: 1 tese_alisson_final.pdf: 6086108 bytes, checksum: 610534618b19a1d27cfff678d44f1a4a (MD5) / Approved for entry into archive by LUIZA DE MENEZES ROMANETTO (luizamenezes@reitoria.unesp.br) on 2017-07-19T14:22:46Z (GMT) No. of bitstreams: 1 reinol_ac_dr_sjrp.pdf: 6086108 bytes, checksum: 610534618b19a1d27cfff678d44f1a4a (MD5) / Made available in DSpace on 2017-07-19T14:22:46Z (GMT). No. of bitstreams: 1 reinol_ac_dr_sjrp.pdf: 6086108 bytes, checksum: 610534618b19a1d27cfff678d44f1a4a (MD5) Previous issue date: 2017-07-05 / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Neste trabalho, consideramos aspectos algébricos e dinâmicos de alguns problemas envolvendo superfícies algébricas invariantes em sistemas diferenciais polinomiais definidos em R³. Determinamos o número máximo de planos invariantes que um sistema diferencial quadrático pode ter e estudamos a realização e integrabilidade de tais sistemas. Fornecemos a forma normal para sistemas diferenciais com quádricas invariantes e estudamos de forma mais detalhada a dinâmica e integrabilidade de sistemas diferenciais quadráticos com um paraboloide elíptico como superfície algébrica invariante. Por fim, estudamos as consequências dinâmicas ao se perturbar um sistema diferencial, cujo espaço de fase é folheado por superfícies algébricas invariantes. Para tal, consideramos o sistema diferencial quadrático conhecido como sistema Sprott A, que depende de um parâmetro real a e apresenta comportamento caótico mesmo sem ter pontos de equilíbrio, tendo, assim, um hidden attractor para valores adequados do parâmetro a. Provamos que, para a=0, o espaço de fase desse sistema é folheado por esferas concêntricas invariantes. Utilizando a Teoria do Averaging e o Teorema KAM (Kolmogorov-Arnold-Moser), provamos que, para a>0 suficientemente pequeno, uma órbita periódica orbitalmente estável emerge de um equilíbrio do tipo zero-Hopf não isolado localizado na origem e que formam-se toros invariantes em torno desta órbita periódica. Concluímos que a ocorrência de tais fatos tem um papel importante na formação do hidden attractor. / In this work, we consider algebraic and dynamical aspects of some problems involving invariant algebraic surfaces in polynomial differential systems defined in R³. We determine the maximum number of invariant planes that a quadratic differential system can have and we study the realization and integrability of such systems. We provide the normal form for differential systems having an invariant quadric and we study in more detail the dynamics and integrability of quadratic differential systems having an elliptic paraboloid as invariant algebraic surface. Finally, we study the dynamic consequences of perturbing differential system whose phase space is foliated by invariant algebraic surfaces. For this we consider the quadratic differential system known as Sprott A system, which depends on one real parameter a and presents chaotic behavior even without having any equilibrium point, thus having a hidden attractor for suitable values of parameter a. We prove that, for a=0, the phase space of this system is foliated by invariant concentric spheres. By using the Averaging Theory and the KAM (Kolmogorov-Arnold-Moser) Theorem, we prove that, for a>0 sufficiently small, an orbitally stable periodic orbit emerges from a zero-Hopf nonisolated equilibrium point located at the origin and that invariant tori are formed around this periodic orbit. We conclude that the occurrence of these facts has an important role in the formation of the hidden attractor. / FAPESP: 2013/26602-7

[pt] A Geometria Diferencial Discreta tem por objetivo desenvolver uma teoria discreta que respeite os aspectos fundamentais da teoria suave. Com isto em mente, são apresentados incialmente resultados da teoria suave da Geometria Afim que terão suas versões discretas tratadas a posteriori. O primeiro objetivo deste trabalho é construir uma estrutura afim discreta para as redes assintóticas definidas no espaço tridimensional, com métrica de Blaschke indefinida e parâmetros assintóticos. Com este intuito, são definidos um campo conormal, que satisfaz as equações de Lelieuvre e está associado a um parâmetro real, e um normal afim que define a forma cúbica da rede e torna a estrutura bem definida. Esta estrutura permite, por exemplo, o estudo das superfícies regradas, com ênfase nas esferas afins impróprias. Além disso, propõe-se uma definição para as singularidades no caso das esferas afins impróprias discretas a partir da construção centrocorda. Outro objetivo deste trabalho é propor uma definição para as superfícies afins discretas com curvatura afim média constante (CAMC), de forma que englobe as superfícies afins mínimas e as esferas afins. As superfícies afins mínimas discretas recebem uma caracterização geométrica bastante interessane e ligada diretamente às quádricas de Lie discretas. O trabalho se completa com o principal resultado, referente à versão discreta das superfícies de Cayley, esferas afins impróprias regradas caracterizadas a partir da conexão afim induzida: uma rede assintótica com CAMC é congruente equiafim à uma superfície de Cayley se, e somente se, a forma cúbica é não nula e a conexão afim induzida é paralela. / [en] Discrete Differential Geometry aims to develop a discrete theory which respects fundamental aspects of smooth theory. With this in mind, some results of smooth theory of Affine Geometry are firstly introduced since their discrete counterparts shall be treated a posteriori. The first goal of this work is construct a discrete affine structure for nets in a three-dimensional space with indefinite Blaschke metric and asymptotic parameters. For this purpose, one defines a conormal vector field, which satisfies Lelieuvre s equations and it is associated to a real parameter; and an affine normal vector field, which defines the cubic form of the net and makes the structure well defined. This structure allows to study, e.g., ruled surfaces with emphasis on improper affine spheres. Moreover, a definition for singularities is proposed in the case of discrete improper affine spheres from the center-chord construction. Another goal here is to propose a definition for an asymptotic net with constant affine mean curvature (CAMC), in a way that encompasses discrete affine minimal surfaces and discrete affine spheres. Discrete affine minimal surfaces receive a beautiful geometrical characterization directly linked to discrete Lie quadrics. This work is completed with the main result about a discrete version of Cayley surfaces, which are ruled improper affine spheres that can be characterized by the induced connection as: an asymptotic net with CAMC is equiaffinely congruent to a Cayley surface if and only if the cubic form does not vanish and the affine induced connection is parallel.