This thesis introduces geometric dynamic active contours in the context of visual tracking, augmenting geometric curve evolution with physically motivated dynamics. Adding additional state information to an evolving curve lifts the curve evolution problem to space dimensions larger than two and thus forbids the use of classical level set techniques. This thesis therefore develops and explores level set methods for problems of higher codimension, putting an emphasis on the vector distance function based approach. This formalism is very general, it is interesting in its own right and still a challenging topic. Two different implementations for geometric dynamic active contours are explored: the full level set approach as well as a simpler partial level set approach. The full level set approach results in full topological flexibility and can deal with curve intersections in the image plane. However, it is computationally expensive. On the other hand the partial level set approach gives up the topological flexibility (intersecting curves cannot be represented) for increased computational efficiency. Contours colliding with different dynamic information (e.g., objects crossing in the image plane) will be merged in the partial level set approach whereas they will correctly traverse each other in the full level set approach. Both implementations are illustrated on synthetic and real examples. Compared to the traditional static curve evolution case, fundamentally different evolution behaviors can be obtained by propagating additional information along with every point on a curve.

Submitted by Johnny Rodrigues (johnnyrodrigues@ufcg.edu.br) on 2018-08-09T18:04:07Z No. of bitstreams: 1 ANTONIO MARCOS DUARTE DE FRANÇA - DISSERTAÇÃO 2014..pdf: 1066992 bytes, checksum: 6e270db1611e61d65507f5f99e9bd161 (MD5) / Made available in DSpace on 2018-08-09T18:04:07Z (GMT). No. of bitstreams: 1 ANTONIO MARCOS DUARTE DE FRANÇA - DISSERTAÇÃO 2014..pdf: 1066992 bytes, checksum: 6e270db1611e61d65507f5f99e9bd161 (MD5) Previous issue date: 2014-10 / Capes / Para ler o resumo deste trabalho recomendamos o download do arquivo, uma vez que o mesmo possui fórmulas e caracteres matemáticos que não foram possíveis trascreve-los aqui. / To read the summary of this work we recommend downloading the file, since it has formulas and mathematical characters that were not possible to transcribe them here.

Submitted by Johnny Rodrigues (johnnyrodrigues@ufcg.edu.br) on 2018-07-27T15:29:31Z No. of bitstreams: 1 ANTONIO IGOR SILVA DE OLIVEIRA - DISSERTAÇÃO PPGMAT 2011..pdf: 599013 bytes, checksum: 2ae31549fdd89221db237ef278b5a688 (MD5) / Made available in DSpace on 2018-07-27T15:29:31Z (GMT). No. of bitstreams: 1 ANTONIO IGOR SILVA DE OLIVEIRA - DISSERTAÇÃO PPGMAT 2011..pdf: 599013 bytes, checksum: 2ae31549fdd89221db237ef278b5a688 (MD5) Previous issue date: 2011-09 / Capes / As ideias de codimensões e cocaracteres de uma PI-álgebra são de grande importância e são centrais nas aplicações das representações dos grupos simétricos à PIteoria (teoria das identidades polinomiais). Os conceitos de codimensão e cocaracter começaram a ser estudados em 1972 por Amitai Regev em seu importante trabalho sobre identidades polinomiais do produto tensorial de PI-álgebras. Ao longo das últimas décadas muitos resultados importantes surgiram com o uso das representações e dos métodos assintóticos na PI-teoria. Neste trabalho apresentaremos inicialmente ideias e resultados básicos da Teoria de Young sobre as representações dos grupos simétricos. De posse desses resultados, estudaremos as sequências limitadas de codimensões e as sequências de cocaracteres de álgebras que satisfazem alguma identidade de Capelli. Apresentaremos também os cálculos das codimensões e dos cocaracteres da álgebra de Grassmann. / The ideas of codimensions and cocharacters of a PI-algebra are of great and central importance in the applications of representations of symmetric groups to PI-theory (theory of the polynomial identities). The study of the concepts of codimensions and cocharacters started in 1972 by Amitai Regev in his important work about polynomial identities of the tensor product of PI-algebras. During the last decades many important results arose with the use of representations and asymptotic methods in PI-theory. In this work we will present firstly ideas and basic results in the Young’s theory about the representations of symmetric groups. With these results we shall study the limited sequences of codimensions and the cocharacter sequences of algebras that satisfy some of the Capelli identity. It will also be presented the calculation of the codimensions and cocharacters of the Grassmann Algebra.

Made available in DSpace on 2016-06-02T20:28:31Z (GMT). No. of bitstreams: 1 6450.pdf: 757192 bytes, checksum: 765b66ca6aed0686ecbcd10c145cefac (MD5) Previous issue date: 2014-11-28 / Financiadora de Estudos e Projetos / In this dissertation we ll present a discussion about the Representations of the Symmetric Group Sn and Alternating Group An. We ll study basics results of the Young s Theory about the representations of the Symmetric Group and discover the decomposition of the algebra FSn in simple subalgebras. After, we ll utilize this decomposition to find the decomposition of the algebra FAn in simple subalgebras. Finally, we ll use this decompositions, together with the PI Theory, for get the sequence of A-codimensions for the Grassmann Algebra (Exterior Algebra) infinitely generated. / Neste trabalho apresentamos uma discussão a respeito das Representações dos Grupos Simétrico Sn e do Grupo Alternante An. Estudaremos resultados básicos da Teoria de Young sobre as representações do grupo simétrico para encontrarmos a decomposição da álgebra de grupo FSn em subálgebras simples. Depois utilizaremos tal decomposição para encontrar a decomposição da álgebra de grupo FAn em subálgebras simples. Por fim empregaremos as informações a respeito das decomposições acima citadas, juntamente com a PI-Teoria, para obter a sequência de A-codimensões para a álgebra de Grassmann (álgebra exterior) infinitamente gerada.