Dans cette thèse, nous développons une approche supervisée de reconnaissance d’objets basée sur l’utilisation de nouveaux descripteurs d’images globaux inspirés du modèle du cortex visuel humain primaire V1 en tant que groupe de roto-translations semi-discrètes SE (2,N)=R² x ZN produit semi-direct entre R² et ZN. La méthode proposée est basée sur des descripteurs de Fourier généralisés et rotationnels définis sur le groupe SE (2,N), qui sont invariants aux transformations géométriques (translations, et rotations). De plus, nous montrons que ces descripteur de Fourier sont faiblement complets, dans le sens qu’ils permettent de discriminer sur un ensemble ouvert et dense L² (SE(2,N)) de fonctions à support compact, donc distinguer entre des images réelles. Ces descripteurs sont ensuite utilisés pour alimenter un classifieur de type SVM dans le cadre de la reconnaissance d’objets. Nous avons mené une séries d’expérimentations dans le but d’évaluer notre méthode sur les bases de visages RL, CVL et ORL et sur la base d’images d’objets variés COIL-100, et de comparer ses performances à celles des méthodes basées sur des descripteurs globaux et locaux. Les résultats obtenus ont montré que notre approche est en mesure de concurrencer de nombreuses techniques de reconnaissance d’objets existantes et de surpasser de nombreuse autres. Ces résultats ont également montré que notre méthode est robuste aux bruits. Enfin, nous avons employé la technique proposée pour reconnaître des navires dans un contexte de surveillance maritime. / In this thesis, we develop a supervised object recognition method using new global image descriptors inspired by the model of the human primary visual cortex V1. Mathematically speaking, the latter is modeled as the semi-discrete roto-translation group SE (2,N)=R² x ZN semi-direct product between R² and ZN. Therefore, our technique is based on generalized and rotational Fourier descriptors defined in SE (2,N) , and which are invariant to natural geometric transformations (translations, and rotations). Furthermore, we show that such Fourier descriptors are weakly complete, in the sense that they allow to distinguish over an open and dense set of compactly supported functions in L² (SE(2,N)) , hence between real-world images. These descriptors are later used in order to feed a Support Vector Machine (SVM) classifier for object recognition purposes. We have conducted a series of experiments aiming both at evaluating and comparing the performances of our method against existing both local - and global - descriptor based state of the art techniques, using the RL, the CVL, and the ORL face databases, and the COIL-100 image database (containing various types of objects). The obtained results have demonstrated that our approach was able to compete with many existing state of the art object recognition techniques, and to outperform many others. These results have also shown that our method is robust to noise. Finally, we have applied the proposed method on vessels recognition in the framework of maritime surveillance.

Orientador: Prof. Dr. Márcio Fabiano da Silva / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Mestrado Profissional em Matemática em Rede Nacional, 2015. / Este trabalho tem por objetivo estudar o processo de inversão geométrica na elipse que nada mais é do que uma transformação geométrica sofrida em uma superfície não plana. Mais do que isso, é uma forma de propor um trabalho diferenciado ao professor do Ensino Médio baseado nas aplicações da Elipse e de suas propriedades e que a partir de um trabalho de pesquisa pode ser estendido para as demais cônicas. Diferente da inversão geométrica clássica na circunferência, utilizamos a elipse como agente inversor. Primeiramente trazemos um apanhado da história da elipse. Apresentamos seus elementos, seus conceitos e propriedades básicas.Recordamos a homotetia, que é uma transformação geométrica do plano e que faz parte do estudo dos resultados das inversões estudadas. Em seguida, passamos a estudar as inversões na elipse. Então, para finalizar, são sugeridas atividades envolvendo as elipses e outras as inversões que nela ocorrem. Tais atividades podem ser aplicadas em sala de aula desde as primeiras séries do ensino fundamental II, desmistificando a famosa pergunta: Onde e/ou para que vou usar "isso", professor? São atividades de pesquisa, atividades interativas e de trabalho com o software de geometria dinâmica Geogebrar. / This work aims to study the geometric inversion process on the ellipse which is nothing more than a geometric transformation suffered in a non-planar surface. More than that, it¿s a way of proposing a differentiated work to high school teacher based on practical applications of Ellipse and its properties and that from a research paper can be extended to other conical. Unlike the classic geometric inversion in the circle, we use the ellipse as inverter agent. First we bring an overview of the history of the ellipse. We present its elements, its concepts and basic properties. We recall about dilation, which is a geometric transformation on plane very important to study the results of studied inversions. Then, we began to study the inversions on Ellipse. Finally, we suggest activities involving the ellipses and other inversions that occur in it. Such activities can be applied in the classroom from the early grades of elementary school, demystifying the famous question: Where and / or I will use " it ", Professor? Are research activities, interactive activities and work with dynamic geometry software Geogebrar.

Submitted by Maria Suzana Diniz (msuzanad@hotmail.com) on 2015-11-27T11:58:14Z No. of bitstreams: 1 arquivototal.pdf: 8972192 bytes, checksum: e0a82ad433e62b83d048d78778d60dd2 (MD5) / Approved for entry into archive by Viviane Lima da Cunha (viviane@biblioteca.ufpb.br) on 2015-11-30T10:51:37Z (GMT) No. of bitstreams: 1 arquivototal.pdf: 8972192 bytes, checksum: e0a82ad433e62b83d048d78778d60dd2 (MD5) / Made available in DSpace on 2015-11-30T10:51:37Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 8972192 bytes, checksum: e0a82ad433e62b83d048d78778d60dd2 (MD5) Previous issue date: 2013-04-12 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Here we present a research about fractals, its history, mathematical concepts and applications. Some constructions were developed using some basic concepts of the Theory of Numbers, Trigonometry and Linear Algebra that can be applied in High School. We presented some activities that can be applied in High School’s classes in order to develop mathematical concepts such as geometric transformations, Geometry, Trigonometry, Logarithm, notions of limit among other topics. Keywords: Fractal Geometry, Geometric Transformation, Logarithm, Pascal Triangle, Arrays, Linear Algebra, High School. / Este trabalho apresenta uma pesquisa sobre os fractais, sua história, conceitos matemáticos utilizados e aplicações. Foram desenvolvidas algumas construções de fractais utilizando-se alguns conceitos básicos de Teoria dos Números, Trigonometria e Álgebra Linear que podem ser explorados no Ensino Médio. Foram apresentadas algumas atividades que podem ser aplicadas em sala de aula do Ensino Médio no desenvolvimento de conceitos matemáticos como Progressão Geométrica, Geometria, Trigonometria, Logaritmo e noções de limite entre outros temas.

The goal of the thesis is to find general nonlinear geometric transformation, which compensates irregular deformation of images, so that they could be registered. In the introductory part, necessary mathematical tools are stated, especially convolution, correlation and Fourier transform. In the next part, method of phase correlation is stated, followed by algorithms used for finding the geometric transformation. Those algorithms are implemented in computer program, that is included.

The aim of this master’s thesis is evaluation of images by computer vision methods. The elaborated scene is billiard game scanned by camera. Using pre-processing, image segmentation and object classification we will try to understand the gameplay situation and uvaluate it in accordance with applicable rules.

No description available.

This work is focused on the description of the dynamic contrast-enhanced CT examination and its contribution in the pneumooncology. It includes a program for creating a two-dimensional model of the scan from the thorax and for the perfuse examination simulation using the time-density curve. Real CT data are simulated more authentic using rigid geometric transformations and noise. The model will be used for the validation of registration algorithms that is used to suppress the spatial deformation generated by patient motions during the long time examination.