This dissertation is concerned with surface representations which record surface properties as a function of surface orientation. The Extended Gaussian Image (EGI) of an object records the variation of surface area with surface orientation. When the object is polyhedral, the EGI takes the form of a set of vectors, one for each face, parallel to the outer surface normal of the face. The length of a vector is the area of the corresponding face. The EGI uniquely represents convex objects and is easily derived from conventional models of an object. An iterative algorithm is described which converts an EGI into an object model in terms of coordinates of vertices, edges, and faces. The algorithm converges to a solution by constrained optimization. There are two aspects to describing shape for polyhedral objects: first, the way in which faces intersect each other, termed the adjacency structure, and, second, the location of the faces in space. The latter may change without altering the former, but not vice versa. The algorithm for shape recovery determines both elements of shape. The continuous support function is described in terms of the area function for curves, permitting a qualitative comparison of the smoothness of the two functions. The next Section describes a method of curve segmentation based on extrema of the support function. Because the support function varies with translation, its behaviour under translation is studied, leading to proposals for several candidate centres of support. The study of these ideas suggests some interesting problems in computational geometry. The EGI has been applied to determine object attitude, the rotation in 3-space bringing a sample object into correspondence with a prototype. The methods developed for the inversion problem can be applied to attitude determination. Experiments show attitude determination using the new method to be more robust than area matching methods. The method given here can be applied at lower resolution of orientation, so that it is possible to sample the space of attitudes more densely, leading to increased accuracy in attitude determination. The discussion finally is broadened to include non-convex objects, where surface orientation is not unique. The generalizations of the EGI do not support shape reconstruction for arbitrary non-convex objects. However, surfaces of revolution do allow a natural generalization of the EGI. The topological structure of regions of constant sign of curvature is invariant under Euclidean motion, and may be useful for recognition tasks. / Science, Faculty of / Computer Science, Department of / Graduate

Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 31-32).

Thesis (Doctoral)--Rheinische Friedrich-Wilhelms-Universtät Bonn, 1990. / Includes bibliographical references.

Thesis (Ph.D.)--University of Delaware, 2008. / Principal faculty advisor: Qing Xiang, Dept. of Mathematical Sciences. Includes bibliographical references.

Orientador: Paulo Roberto Brumatti / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-06T01:03:00Z (GMT). No. of bitstreams: 1 Lopes_RodrigoFrancisco_M.pdf: 640692 bytes, checksum: 75ad1ee35d8a529904fe79cc7c944a7b (MD5) Previous issue date: 2006 / Mestrado / Algebra / Mestre em Matemática

Orientador: Clésio Luis Tozzi / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação / Made available in DSpace on 2018-08-16T06:32:57Z (GMT). No. of bitstreams: 1 Freitas_GreiceMartinsde_M.pdf: 16453422 bytes, checksum: fa0ae64561fd346237c57310fb0d0073 (MD5) Previous issue date: 2010 / Resumo: A crescente utilização de câmeras de vídeo para o monitoramento de ambientes, auxiliando no controle de entrada, saída e trânsito de indivíduos ou veículos tem aumentado a busca por sistemas visando a automatização do processo de monitoramento por vídeos. Como requisitos para estes sistemas identificam-se o tratamento da entrada e saída de objetos na cena, variações na forma e movimentação dos alvos seguidos, interações entre os alvos como encontros e separações, variações na iluminação da cena e o tratamento de ruídos presentes no vídeo. O presente trabalho analisa e avalia as principais etapas de um sistema de rastreamento de múltiplos objetos através de uma câmera de vídeo fixa e propõe um sistema de rastreamento baseado em sistemas encontrados na literatura. O sistema proposto é composto de três fases: identificação do foreground através de técnicas de subtração de fundo; associação de objetos quadro a quadro através de métricas de cor, área e posição do centróide - com o auxílio da aplicação do filtro de Kalman - e, finalmente, classificação dos objetos a cada quadro segundo um sistema de gerenciamento de objetos. Com o objetivo de verificar a eficiência do sistema de rastreamento proposto, testes foram realizados utilizando vídeos das bases de dados PETS e CAVIAR. A etapa de subtração de fundo foi avaliada através da comparação do modelo Eigenbackground, utilizado no presente sistema, com o modelo Mistura de Gaussianas, modelo de subtração de fundo mais utilizado em sistemas de rastreamento. O sistema de gerenciamento de objeto foi avaliado por meio da classificação e contagem manual dos objetos a cada quadro do vídeo. Estes resultados foram comparados à saída do sistema de gerenciamento de objetos. Os resultados obtidos mostraram que o sistema de rastreamento proposto foi capaz de reconhecer e rastrear objetos em movimento em sequências de vídeos, lidando com oclusões e separações, mostrando adequabilidade para aplicação em sistemas de segurança em tempo real / Abstract: There are immediate needs for the use of video cameras in environment monitoring, which can be verified by the task of assisting the entrance, exit and transit registering of people or vehicles in a area. In this context, automated surveillance systems based on video images are increasingly gaining interest. As requisites for these systems, it can be identified the treatment of entrances and exits of objects on a scene, shape variation and movement of followed targets, interactions between targets (such as meetings and splits), lighting variations and video noises. This work analyses and evaluates the main steps of a multiple target tracking system through a fixed video camera and proposes a tracking system based on approaches found in the literature. The proposed system is composed of three steps: foreground identification through background subtraction techniques; object association through color, area and centroid position matching, by using the Kalman filter to estimate the object's position in the next frame, and, lastly, object classification according an object management system. In order to assess the efficiency of the proposed tracking system, tests were performed by using videos from PETS and CAVIAR datasets. The background subtraction step was evaluated by means of a comparison between the Eigenbackground model, used in the proposed tracking system, and the Mixture of Gaussians model, one of the most used background subtraction models. The object management system was evaluated through manual classification and counting of objects on each video frame. These results were compared with the output of the object management system. The obtained results showed that the proposed tracking system was able to recognize and track objects in movement on videos, as well as dealing with occlusions and separations, and, at the same time, encouraging future studies in order for its application on real time security systems / Mestrado / Engenharia de Computação / Mestre em Engenharia Elétrica