Autonomous mobile robots - both aerial and terrestrial vehicles - have gained immense importance due to the broad spectrum of their potential military and civilian applications. One of the indispensable requirements for the autonomy of a mobile vehicle is the vehicle's capability of planning and executing its motion, that is, finding appropriate control inputs for the vehicle such that the resulting vehicle motion satisfies the requirements of the vehicular task. The motion planning and control problem is inherently complex because it involves two disparate sub-problems: (1) satisfaction of the vehicular task requirements, which requires tools from combinatorics and/or formal methods, and (2) design of the vehicle control laws, which requires tools from dynamical systems and control theory. Accordingly, this problem is usually decomposed and solved over two levels of hierarchy. The higher level, called the geometric path planning level, finds a geometric path that satisfies the vehicular task requirements, e.g., obstacle avoidance. The lower level, called the trajectory planning level, involves sufficient smoothening of this geometric path followed by a suitable time parametrization to obtain a reference trajectory for the vehicle. Although simple and efficient, such hierarchical separation suffers a serious drawback: the geometric path planner has no information of the kinematic and dynamic constraints of the vehicle. Consequently, the geometric planner may produce paths that the trajectory planner cannot transform into a feasible reference trajectory. Two main ideas appear in the literature to remedy this problem: (a) randomized sampling-based planning, which eliminates altogether the geometric planner by planning in the vehicle state space, and (b) geometric planning supported by feedback control laws. The former class of methods suffer from a lack of optimality of the resultant trajectory, while the latter class of methods makes a restrictive assumption concerning the vehicle kinematic model. In this thesis, we propose a hierarchical motion planning framework based on a novel mode of interaction between these two levels of planning. This interaction rests on the solution of a special shortest-path problem on graphs, namely, one using costs defined on multiple edge transitions in the path instead of the usual single edge transition costs. These costs are provided by a local trajectory generation algorithm, which we implement using model predictive control and the concept of effective target sets for simplifying the non-convex constraints involved in the problem. The proposed motion planner ensures "consistency" between the two levels of planning, i.e., a guarantee that the higher level geometric path is always associated with a kinematically and dynamically feasible trajectory. We show that the proposed motion planning approach offers distinct advantages in comparison with the competing approaches of discretization of the state space, of randomized sampling-based motion planning, and of local feedback-based, decoupled hierarchical motion planning. Finally, we propose a multi-resolution implementation of the proposed motion planner, which requires accurate descriptions of the environment and the vehicle only for short-term, local motion planning in the immediate vicinity of the vehicle.

O problema de corte consiste no corte de objetos maiores para produção de peças menores, de modo que uma certa função objetivo seja otimizada, por exemplo, a perda seja minimizada. O problema de empacotamento pode também ser visto como um problema de corte, onde as peças menores são arranjadas dentro dos objetos. Uma abordagem em grafo E/OU para a resolução de problemas de corte e empacotamento foi proposta inicialmente por Morabito (1989) para problemas de corte bidimensionais e, mais tarde, estendida para problemas tridimensionais (Morabito, 1992). Nesta abordagem foi utilizada uma técnica de busca híbrida, onde se combinou a busca em profundidade primeiro com limite de profundidade e a busca hill-climbing, utilizando-se heurísticas baseadas nos limitantes superiores e inferiores. Experiências computacionais mostraram a viabilidade de uso na prática desta abordagem. Mais tarde, Arenales (1993) generalizou esta a abordagem em grafo E/OU mostrando como diferentes problemas de corte poderiam ser resolvidos, independentemente da dimensão, formas dos objetos e itens, baseado em simples hipóteses, sem realizar, entretanto, estudos computacionais. O presente trabalho tem por objetivo estender a abordagem em grafo E/OU para tratar outros casos não analisados pelos trabalhos anteriores, tais como situações envolvendo diferentes processos de corte, bem como a implementação computacional de métodos baseados na abordagem em grafo E/OU, mostrando, assim, a versatilidade da abordagem para tratar diversas situações práticas de problemas de corte e sua viabilidade computacional. / The cutting problem consists of cutting larger objects in order to produce smaller pieces, in such a way as to optimizing a given objective function, for example, minimizing the waste. The packing problem can also be seen as a cutting problem, where the position that each smaller piece is arranged inside of the objects can be seen as the place it was cut from. An AND/OR-graph approach to solve cutting and packing problems was initially proposed by Morabito (1989) for two-dimensional cutting problem and, later, extended to threedimensional problems (Morabito, 1992). That approach uses a hybrid search, which combines depth-first search under depth bound and hill-climbing strategy. Heuristics were devised based on upper and lower bounds. Computational experiences demonstrated its practical feasibility. The AND/OR-graph approach was later generalized by Arenales (1993) based on simple hypothesis. He showed that different cutting problems Gould be solved using the AND/ORgraph approach, independently of the dimension and shapes. The main objective of this thesis is the practical extension of the AND/OR-graph approach to handle other cases not considered by previous works. It was considered different cutting processes, as well as the analysis of computational implementation, showing how can it be adapted to many classes of practical cutting and packing problems.

Optical coherence tomography (OCT) is a safe and non-invasive imaging technique providing high axial resolution. A spectral-domain OCT scanner capable of acquiring volumetric data of the retina is becoming an increasingly important modality in ophthalmology for the diagnosis and management of a variety of retinal diseases such as glaucoma, diabetic retinopathy and age related macular degeneration (AMD) which are major causes of a loss of vision. To analyze and track these ocular diseases, developments of the automated methods for detecting intraretinal layers, optic discs and retinal blood vessels from spectral-domain OCT scans are highly required recently. The major contributions of this thesis include: 1) developing a fast method that can automatically segment ten intraretinal layers in the spectral-domain macular OCT scan for the layer thickness analysis, 2) developing a method that can automatically segment the optic disc cup and neuroretinal rim in the spectral-domain OCT scan centered at the optic nerve head (ONH) to measure the cup-to-disc ratio, an important structural indicator for the progression of glaucoma, and 3) developing a method that can automatically segment the 3-D retinal blood vessels in the spectral-domain ONH-centered OCT scan to extract 3-D features of the vessels for the diagnosis of retinal vascular diseases.

A segmentação de imagens consiste em dividir uma imagem em regiões ou objetos que a compõem, como, por exemplo, para isolar os pixels de um objeto alvo de uma dada aplicação. Em segmentação de imagens médicas, o objeto de interesse comumente apresenta transições em suas bordas predominantemente do tipo claro para escuro ou escuro para claro. Métodos tradicionais por região, como a conexidade fuzzy relativa (RFC - Relative Fuzzy Connectedness), não distinguem bem entre essas bordas similares com orientações opostas. A especificação da polaridade de contorno pode ajudar a amenizar esse problema, o que requer uma formulação matemática em grafos dirigidos. Uma discussão sobre como incorporar essa propriedade no arcabouço do RFC é apresentada neste trabalho. Uma prova teórica da otimalidade do novo algoritmo, chamado conexidade fuzzy relativa com orientação (ORFC - Oriented Relative Fuzzy Connectedness), em termos de uma função de energia em grafos dirigidos sujeita as restrições de sementes é apresentada, bem como a sua apli- cação em poderosos métodos híbridos de segmentação. O método híbrido proposto ORFC &Graph Cut preserva a robustez do ORFC em relação à escolha de sementes, evitando o problema do viés de encolhimento do método de Corte em Grafo (GC - Graph Cut), e mantém o forte controle do GC no delineamento de contornos de bordas irregulares da imagem. Os métodos propostos são avaliados usando imagens médicas de ressonáncia magnética (RM) e tomografia computadorizada (TC) do cérebro humano e de estudos torácicos. / Image segmentation consists of dividing an image into its composing regions or objects, for example, to isolate the pixels of a target object of a given application. In segmentation of medical images, the object of interest commonly presents transitions at its border predominantly from bright to dark or dark to bright. Traditional region-based methods of image segmentation, such as Relative Fuzzy Connectedness (RFC), do not distinguish well between similar boundaries with opposite orientations. The specification of the boundary polarity can help to alleviate this problem but this requires a mathematical formulation on directed graphs. A discussion on how to incorporate this property in the RFC framework is presented in this work. A theoretical proof of the optimality of the new algorithm, called Oriented Relative Fuzzy Connectedness (ORFC), in terms of an energy function on directed graphs subject to seed constraints is presented, and its application in powerful hybrid segmentation methods. The hybrid method proposed ORFC&Graph Cut preserves the robustness of ORFC respect to the seed choice, avoiding the shrinking problem of Graph Cut (GC), and keeps the strong control of the GC in the contour delination of irregular image boundaries. The proposed methods are evaluated using magnetic resonance medical imaging (MR) and computed tomography (CT) of the human brain and thoracic studies.

Cette thèse traite de la conception de méthodes automatisées ou semi-automatisées pour détecter et identifier des algorithmes cryptographiques dans des programmes compilés en langage machine. La première méthode proposée a pour but l'identification de primitives symétriques. L'implémentation en langage machine d'une primitive symétrique, assimilée à une suite d'instructions, est représentée par un graphe. Sous cette forme, le code est modifié à l'aide de règles de réécriture tout en préservant une certaine notion de sémantique lors d'une phase dite de normalisation. L'objectif est de faire émerger des expressions communes à différentes implémentations d'une même primitive. Ces expressions servent alors de base à la création de signatures efficaces. La recherche de ces signatures s'effectue à l'aide d'un algorithme énumérant les isomorphismes de sous-graphe. La seconde méthode, conçue en complément de la première, produit une représentation synthétique facilitant l'identification des modes opératoires. Cette représentation se définit comme le plus petit sous-graphe préservant les distances entre des sous-ensembles de nœuds précédemment identifiés comme étant les paramètres d'entrée et de sortie des primitives impliquées. / This thesis is about the design of automatic or semi-automatic methods to detect and identify cryptographic algorithms inside programs compiled into machine code. Two methods are presented. The objective of the first method is to identify cryptographic primitives. A machine code implementation of a cryptographic primitive, regarded as a sequence of instructions, is represented by a graph structure. During a normalization phase, a set of rewrite rules is used to modify this graph representation while preserving a specific notion of semantics. The goal is to converge towards expressions which are shared across several implementations of the same primitive. We use these expressions as a basis to create efficient signatures. A subgraph isomorphism enumeration algorithm is used to search for signatures. The second method is built on top of the first one. It produces a synthetic representation designed to help in the identification of modes of operation. This synthetic representation is defined as the smallest subgraph which preserve distances between sets of vertices previously identified as the input and output parameters of the primitives involved within the mode of operation.

A segmentação de imagens consiste em dividir uma imagem em regiões ou objetos que a compõem, como, por exemplo, para isolar os pixels de um objeto alvo de uma dada aplicação. Em segmentação de imagens médicas, o objeto de interesse comumente apresenta transições em suas bordas predominantemente do tipo claro para escuro ou escuro para claro. Métodos tradicionais por região, como a conexidade fuzzy relativa (RFC - Relative Fuzzy Connectedness), não distinguem bem entre essas bordas similares com orientações opostas. A especificação da polaridade de contorno pode ajudar a amenizar esse problema, o que requer uma formulação matemática em grafos dirigidos. Uma discussão sobre como incorporar essa propriedade no arcabouço do RFC é apresentada neste trabalho. Uma prova teórica da otimalidade do novo algoritmo, chamado conexidade fuzzy relativa com orientação (ORFC - Oriented Relative Fuzzy Connectedness), em termos de uma função de energia em grafos dirigidos sujeita as restrições de sementes é apresentada, bem como a sua apli- cação em poderosos métodos híbridos de segmentação. O método híbrido proposto ORFC &Graph Cut preserva a robustez do ORFC em relação à escolha de sementes, evitando o problema do viés de encolhimento do método de Corte em Grafo (GC - Graph Cut), e mantém o forte controle do GC no delineamento de contornos de bordas irregulares da imagem. Os métodos propostos são avaliados usando imagens médicas de ressonáncia magnética (RM) e tomografia computadorizada (TC) do cérebro humano e de estudos torácicos. / Image segmentation consists of dividing an image into its composing regions or objects, for example, to isolate the pixels of a target object of a given application. In segmentation of medical images, the object of interest commonly presents transitions at its border predominantly from bright to dark or dark to bright. Traditional region-based methods of image segmentation, such as Relative Fuzzy Connectedness (RFC), do not distinguish well between similar boundaries with opposite orientations. The specification of the boundary polarity can help to alleviate this problem but this requires a mathematical formulation on directed graphs. A discussion on how to incorporate this property in the RFC framework is presented in this work. A theoretical proof of the optimality of the new algorithm, called Oriented Relative Fuzzy Connectedness (ORFC), in terms of an energy function on directed graphs subject to seed constraints is presented, and its application in powerful hybrid segmentation methods. The hybrid method proposed ORFC&Graph Cut preserves the robustness of ORFC respect to the seed choice, avoiding the shrinking problem of Graph Cut (GC), and keeps the strong control of the GC in the contour delination of irregular image boundaries. The proposed methods are evaluated using magnetic resonance medical imaging (MR) and computed tomography (CT) of the human brain and thoracic studies.

Integrated quantum photonics show monolithic waveguide chips to be a promising platform for realizing the next generation of quantum optical circuits. This work proposes the implementation of quantum page Rank algorithm on a photonic waveguide lattice. Our contributions are as follows: Continuous-time quantum stochastic walk(QSW)-an alternate paradigm of quantum computing, is a hybrid quantum walk that incorporates both unitary and non-unitary effects. We propose the use of QSW which necessitates the hopping of the quantum crawler on a directed graph, for the quantum page Rank problem. We propose the implementation of quantum page Rank on a photonic waveguide lattice, where we allow the density matrix to evolve according to the Lindblad-Kossakowski master equation, the diagonal of which gives the quantum page Rank. We have also shown the use of the metric of positional Kolmogorov Complexity as an efficient tool for determining whether or not the quantum channel has been compromised. We appositionally encode multi-photon decoy pulses within the stream of single photon pulses. This positional encoding is chosen in such a way as to have low Kolmogorov complexity. The PNS attack on the multi-photon decoy pulses causes a dip in the ratio of the transmittance of the decoy pulses to the signal pulses in the conventional analysis.