Many production systems have split and merge operations to increase production capac- ity and variety, improve product quality, and implement product control and scheduling policies. This thesis presents analytical methods to model and analyze split and merge production systems with Bernoulli and exponential reliability machines under circulate, priority and percentage policies. The recursive procedures for performance analysis are de- rived, and the convergence of the procedures and uniqueness of the solutions, along with the structural properties, are proved analytically, and the accuracy of the estimation is justi¯ed numerically with high precision. In addition, comparisons among the e®ects of di®erent policies in system performance are carried out.

Dans ce travail nous nous intéressons à la segmentation d’image 3D. Le but est de définir un cadre permettant, étant donnée une problématique de segmentation, de développer rapidement un algorithme apportant une solution à cette problématique. Afin de ne pas être restreint à un sous ensemble des types de problématique de segmentation, ce cadre doit permettre de mettre en oeuvre efficacement les différentes méthodes et les différents critères de segmentation existants, dans le but de les combiner pour définir les nouveaux algorithmes. Ce cadre doit reposer sur un modèle de structuration d’image qui représente la topologie et la géométrie d’une partition et permet d’en extraire efficacement les informations requises. Dans ce document, les différentes méthodes de segmentation existantes sont présentées afin de définir un ensemble d’opération nécessaire à leur implémentation. Une présentation des modèles existants est faite pour en déterminer avantages et inconvénients, puis le nouveau modèle est ensuite défini. Sa mise en oeuvre complète est détaillée ainsi qu’une analyse de sa complexité en temps et en mémoire pour l’ensemble des opérations précédemment définies. Des exemples d’utilisation du modèle sur des cas concrets sont ensuite décrits, ainsi que les possibilités d’extension du modèle et d’implémentation sur architecture parallèle. / In this work we focus on 3D image segmentation. The aim consists in defining a framework which, given a segmentation problem, allows to design efficiently an algorithm solving this problem. Since this framework has to be unspecific according to the kind of segmentation problem, it has to allow an efficient implementation of most segmentation techniques and criteria, in order to combine them to define new algorithms. This framework has to rely on a structuring model both representing the topology and the geometry of the partition of an image, in order to efficiently extract required information. In this document, different segmentation techniques are presented in order to define a set of primitives required for their implementation. Existing models are presented with their advantages and drawbacks, then the new structuring model is defined. Its whole implementation including details of its memory consumption and time complexity for each primitives of the previously defined set of requirements is given. Some examples of use with real image analysis problems are described, with also possible extensions of the model and its implementation on parallel architecture.

Made available in DSpace on 2016-06-02T20:04:53Z (GMT). No. of bitstreams: 1 6510.pdf: 2213423 bytes, checksum: 0c9b206a1b5f88772031ed160e9691b3 (MD5) Previous issue date: 2014-12-19 / Financiadora de Estudos e Projetos / We proposed a new split-merge MCMC algorithm for image segmentation. We describe how an image can be subdivided into multiple disjoint regions, with each region having an associated latent indicator variable. The latent indicator variables are modeled with a prior Gibbs distribution governed by a spatial regularization parameter. Regions with same label define a component. Pixels within a component are distributed according to a Gaussian distribution. We treat the spatial regularization parameter and the number of components K as unknown. To estimate K, the spatial regularization parameter and the component parameters we propose the Metropolised split-merge (MSM) algorithm. The MSM comprises two type of moves. The first one, is a data-driven split-merge move. These movements change the number of components K in the neighborhood K _ 1 and are accepted according to Metropolis-Hastings acceptance probability. After a split-merge step, the component parameters, the spatial regularization parameter and latent allocation variables are updated conditional on K by using the Gibbs sampling, the Metropolis- Hastings and Swendsen-Wang algorithm, respectively. The main advantage of the proposed algorithm is that it is easy to implement and the acceptance probability for split-merge movements depends only of the observed data. The performance of the proposed algorithm is verified using artificial datasets as well as real datasets. / Nesta tese, modelamos uma imagem através de uma grade regular retangular e assumimos que esta grade é dividida em múltiplas regiões disjuntas de pixels. Quando duas ou mais regiões apresentam a mesma característica, a união dessas regiões forma um conjunto chamado de componente. Associamos a cada pixel da imagem uma variável indicadora não observável que indica a componente a que o pixel pertence. Estas variáveis indicadoras não observáveis são modeladas através da distribuição de probabilidade de Gibbs com parâmetro de regularização espacial _. Assumimos que _ e o número de componentes K são desconhecidos. Para estimação conjunta dos parâmetros de interesse, propomos um algoritmo MCMC denominado de ejeção-absorção metropolizado (EAM). Algumas vantagens do algoritmo proposto são: (i) O algoritmo não necessita da especificação de uma função de transição para realização dos movimentos ejeção e absorção. Ao contrário do algoritmo reversible jump (RJ) que requer a especificação de boas funções de transição para ser computacionalmente eficiente; (ii) Os movimentos ejeção e absorção são desenvolvidos com base nos dados observados e podem ser rapidamente propostos e testados; (iii) Novas componentes são criadas com base em informações provenientes de regiões de observações e os parâmetros das novas componentes são gerados das distribuições a posteriori. Ilustramos o desempenho do algoritmo EAM utilizando conjuntos de dados simulados e reais.