Orientador: Ernesto Kemp / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-08-25T18:38:19Z (GMT). No. of bitstreams: 1 Silva_MarceloZimbres_D.pdf: 8568193 bytes, checksum: 2348942e48cd0c1c610715988bd1d2f6 (MD5) Previous issue date: 2014 / Resumo: Devido à ação do campo magnético cósmico, trajetórias de raios cósmicos provenientes de uma mesma fonte podem ser defletidas e dar origem a estruturas filamentares cujos eventos são ordenados de acordo com suas energias, os multipletos. Nesse trabalho, propomos um novo método para identificação de multipletos, baseado no uso de uma classe de funções definidas sobre a esfera, chamadas de wavelets esféricos. Para testar o método aplicamos a análise em dados simulados. Primeiramente usamos um fundo isotrópico, onde um multipleto pode ocorrer apenas ao acaso. Posteriormente fazemos a análise colocando um multipleto em uma posição aleatória no mesmo fundo isotrópico. Com isso calculamos erros de tipo I e II. O método também é aplicado em dados obtidos pelo Observatório Pierre Auger para eventos com energia E > 15 x10^{18}eV / Abstract: Due to the action of the intervening cosmic magnetic fields, the trajectories of ultra-high energy cosmic rays (UHECRs) can be deflected in such a way as to create clustered energy-ordered filamentary structures in the arrival directions of these particles, the so-called multiplets. In this work we propose a new method based on the spherical wavelet transform to identify multiplets in sky maps containing arrival directions of UHECRs. The method is illustrated in simulations with a multiplet embedded in isotropic backgrounds with different numbers of events, and on data from the Pierre Auger Observatory. The efficiency of the algorithm is assessed through the calculation of Type I and II erros / Doutorado / Física / Doutor em Ciências

In this thesis, we propose and evaluate two novel scale-based decomposable representations of shape for the segmentation and morphometric analysis of anatomical structures in medical imaging. We propose two representations that are adapted to a particular class of anatomical structures and allow for a richer shape description and a more fine-grained control over the deformation of models based on these representations, when compared to previous techniques. In the first part of this thesis, we introduce the concept of a scale-space shape filter for implicit shape representations that measures the deviation from a tubular shape in a local neighborhood of points, given a particular scale of analysis. We use these filters for the segmentation of blood vessels, and introduce the notion of segmentation with a soft shape prior, where the segmented model is not globally constrained to a predefined shape space, but is penalized locally if it deviates strongly from a tubular structure. Using this filter, we derive a region-based active contour segmentation algorithm for tubular structures that penalizes leakages. We present results on synthetic and real 2D and 3D datasets. In the second part of this thesis, we present a novel multi-scale parametric shape representation using spherical wavelets. Our proposed shape representation encodes shape variations in a population at various scales to be used as prior in a probabilistic segmentation framework. We derive a probabilistic active surface segmentation algorithm using the multi-scale prior coefficients as parameters for our optimization procedure. One nice benefit of this algorithm is that the optimization method can be applied in a coarse-to-fine manner. We present results on 3D sub-cortical brain structures. We also present a novel method of statistical surface-based morphometry based on the use of non-parametric permutation tests and the spherical wavelet shape representation. As an application, we analyze two sub-cortical brain structures, the caudate nucleus and hippocampus.