Object tracking using direct methods in RGB-D cameras

En esta tesis se presenta un análisis en profundidad de cómo se deben utilizar dos tipos de métodos directos, Lucas-Kanade e Inverse Compositional, en imágenes RGB-D y se analiza la capacidad y precisión de los mismos en una serie de experimentos sintéticos. Estos simulan imágenes RGB, imágenes de profundidad (D) e imágenes RGB-D para comprobar cómo se comportan en cada una de las combinaciones. Además, se analizan estos métodos sin ninguna técnica adicional que modifique el algoritmo original ni que lo apoye en su tarea de optimización tal y como sucede en la mayoría de los artículos encontrados en la literatura. Esto se hace con el fin de poder entender cuándo y por qué los métodos convergen o divergen para que así en el futuro cualquier interesado pueda aplicar los conocimientos adquiridos en esta tesis de forma práctica. Esta tesis debería ayudar al futuro interesado a decidir qué algoritmo conviene más en una determinada situación y debería también ayudarle a entender qué problemas le pueden dar estos algoritmos para poder poner el remedio más apropiado. Las técnicas adicionales que sirven de remedio para estos problemas quedan fuera de los contenidos que abarca esta tesis, sin embargo, sí se hace una revisión sobre ellas.---ABSTRACT---This thesis presents an in-depth analysis about how direct methods such as Lucas- Kanade and Inverse Compositional can be applied in RGB-D images. The capability and accuracy of these methods is also analyzed employing a series of synthetic experiments. These simulate the efects produced by RGB images, depth images and RGB-D images so that diferent combinations can be evaluated. Moreover, these methods are analyzed without using any additional technique that modifies the original algorithm or that aids the algorithm in its search for a global optima unlike most of the articles found in the literature. Our goal is to understand when and why do these methods converge or diverge so that in the future, the knowledge extracted from the results presented here can efectively help a potential implementer. After reading this thesis, the implementer should be able to decide which algorithm fits best for a particular task and should also know which are the problems that have to be addressed in each algorithm so that an appropriate correction is implemented using additional techniques. These additional techniques are outside the scope of this thesis, however, they are reviewed from the literature.

Learning 3D structure from 2D images using LBP features

An automatic machine learning strategy for computing the 3D structure of monocular images from a single image query using Local Binary Patterns is presented. The 3D structure is inferred through a training set composed by a repository of color and depth images, assuming that images with similar structure present similar depth maps. Local Binary Patterns are used to characterize the structure of the color images. The depth maps of those color images with a similar structure to the query image are adaptively combined and filtered to estimate the final depth map. Using public databases, promising results have been obtained outperforming other state-of-the-art algorithms and with a computational cost similar to the most efficient 2D-to-3D algorithms.

Optimization methods for the operating room management under uncertainty: stochastic programming vs. decomposition approach

The operating theatres are the engine of the hospitals; proper management of the operating rooms and its staff represents a great challenge for managers and its results impact directly in the budget of the hospital. This work presents a MILP model for the efficient schedule of multiple surgeries in Operating Rooms (ORs) during a working day. This model considers multiple surgeons and ORs and different types of surgeries. Stochastic strategies are also implemented for taking into account the uncertain in surgery durations (pre-incision, incision, post-incision times). In addition, a heuristic-based methods and a MILP decomposition approach is proposed for solving large-scale ORs scheduling problems in computational efficient way. All these computer-aided strategies has been implemented in AIMMS, as an advanced modeling and optimization software, developing a user friendly solution tool for the operating room management under uncertainty.

Implementación de una Support Vector Machine en RVC – CAL para imágenes hiperespectrales

El análisis de imágenes hiperespectrales permite obtener información con una gran resolución espectral: cientos de bandas repartidas desde el espectro infrarrojo hasta el ultravioleta. El uso de dichas imágenes está teniendo un gran impacto en el campo de la medicina y, en concreto, destaca su utilización en la detección de distintos tipos de cáncer. Dentro de este campo, uno de los principales problemas que existen actualmente es el análisis de dichas imágenes en tiempo real ya que, debido al gran volumen de datos que componen estas imágenes, la capacidad de cómputo requerida es muy elevada. Una de las principales líneas de investigación acerca de la reducción de dicho tiempo de procesado se basa en la idea de repartir su análisis en diversos núcleos trabajando en paralelo. En relación a esta línea de investigación, en el presente trabajo se desarrolla una librería para el lenguaje RVC – CAL – lenguaje que está especialmente pensado para aplicaciones multimedia y que permite realizar la paralelización de una manera intuitiva – donde se recogen las funciones necesarias para implementar el clasificador conocido como Support Vector Machine – SVM. Cabe mencionar que este trabajo complementa el realizado en [1] y [2] donde se desarrollaron las funciones necesarias para implementar una cadena de procesado que utiliza el método unmixing para procesar la imagen hiperespectral. En concreto, este trabajo se encuentra dividido en varias partes. La primera de ellas expone razonadamente los motivos que han llevado a comenzar este Trabajo de Investigación y los objetivos que se pretenden conseguir con él. Tras esto, se hace un amplio estudio del estado del arte actual y, en él, se explican tanto las imágenes hiperespectrales como sus métodos de procesado y, en concreto, se detallará el método que utiliza el clasificador SVM. Una vez expuesta la base teórica, nos centraremos en la explicación del método seguido para convertir una versión en Matlab del clasificador SVM optimizado para analizar imágenes hiperespectrales; un punto importante en este apartado es que se desarrolla la versión secuencial del algoritmo y se asientan las bases para una futura paralelización del clasificador. Tras explicar el método utilizado, se exponen los resultados obtenidos primero comparando ambas versiones y, posteriormente, analizando por etapas la versión adaptada al lenguaje RVC – CAL. Por último, se aportan una serie de conclusiones obtenidas tras analizar las dos versiones del clasificador SVM en cuanto a bondad de resultados y tiempos de procesado y se proponen una serie de posibles líneas de actuación futuras relacionadas con dichos resultados. ABSTRACT. Hyperspectral imaging allows us to collect high resolution spectral information: hundred of bands covering from infrared to ultraviolet spectrum. These images have had strong repercussions in the medical field; in particular, we must highlight its use in cancer detection. In this field, the main problem we have to deal with is the real time analysis, because these images have a great data volume and they require a high computational power. One of the main research lines that deals with this problem is related with the analysis of these images using several cores working at the same time. According to this investigation line, this document describes the development of a RVC – CAL library – this language has been widely used for working with multimedia applications and allows an optimized system parallelization –, which joins all the functions needed to implement the Support Vector Machine – SVM - classifier. This research complements the research conducted in [1] and [2] where the necessary functions to implement the unmixing method to analyze hyperspectral images were developed. The document is divided in several chapters. The first of them introduces the motivation of the Master Thesis and the main objectives to achieve. After that, we study the state of the art of some technologies related with this work, like hyperspectral images, their processing methods and, concretely, the SVM classifier. Once we have exposed the theoretical bases, we will explain the followed methodology to translate a Matlab version of the SVM classifier optimized to process an hyperspectral image to RVC – CAL language; one of the most important issues in this chapter is that a sequential implementation is developed and the bases of a future parallelization of the SVM classifier are set. At this point, we will expose the results obtained in the comparative between versions and then, the results of the different steps that compose the SVM in its RVC – CAL version. Finally, we will extract some conclusions related with algorithm behavior and time processing. In the same way, we propose some future research lines according to the results obtained in this document.

Adaptation strategies for high order discontinuous Galerkin methods based on Tau-estimation

In this paper three p-adaptation strategies based on the minimization of the truncation error are presented for high order discontinuous Galerkin methods. The truncation error is approximated by means of a ? -estimation procedure and enables the identification of mesh regions that require adaptation. Three adaptation strategies are developed and termed a posteriori, quasi-a priori and quasi-a priori corrected. All strategies require fine solutions, which are obtained by enriching the polynomial order, but while the former needs time converged solutions, the last two rely on non-converged solutions, which lead to faster computations. In addition, the high order method permits the spatial decoupling for the estimated errors and enables anisotropic p-adaptation. These strategies are verified and compared in terms of accuracy and computational cost for the Euler and the compressible Navier?Stokes equations. It is shown that the two quasi- a priori methods achieve a significant reduction in computational cost when compared to a uniform polynomial enrichment. Namely, for a viscous boundary layer flow, we obtain a speedup of 6.6 and 7.6 for the quasi-a priori and quasi-a priori corrected approaches, respectively.

Estimación eficiente de atributos demográficos del rostro humano en imágenes

Sin duda, el rostro humano ofrece mucha más información de la que pensamos. La cara transmite sin nuestro consentimiento señales no verbales, a partir de las interacciones faciales, que dejan al descubierto nuestro estado afectivo, actividad cognitiva, personalidad y enfermedades. Estudios recientes [OFT14, TODMS15] demuestran que muchas de nuestras decisiones sociales e interpersonales derivan de un previo análisis facial de la cara que nos permite establecer si esa persona es confiable, trabajadora, inteligente, etc. Esta interpretación, propensa a errores, deriva de la capacidad innata de los seres humanas de encontrar estas señales e interpretarlas. Esta capacidad es motivo de estudio, con un especial interés en desarrollar métodos que tengan la habilidad de calcular de manera automática estas señales o atributos asociados a la cara. Así, el interés por la estimación de atributos faciales ha crecido rápidamente en los últimos años por las diversas aplicaciones en que estos métodos pueden ser utilizados: marketing dirigido, sistemas de seguridad, interacción hombre-máquina, etc. Sin embargo, éstos están lejos de ser perfectos y robustos en cualquier dominio de problemas. La principal dificultad encontrada es causada por la alta variabilidad intra-clase debida a los cambios en la condición de la imagen: cambios de iluminación, oclusiones, expresiones faciales, edad, género, etnia, etc.; encontradas frecuentemente en imágenes adquiridas en entornos no controlados. Este de trabajo de investigación estudia técnicas de análisis de imágenes para estimar atributos faciales como el género, la edad y la postura, empleando métodos lineales y explotando las dependencias estadísticas entre estos atributos. Adicionalmente, nuestra propuesta se centrará en la construcción de estimadores que tengan una fuerte relación entre rendimiento y coste computacional. Con respecto a éste último punto, estudiamos un conjunto de estrategias para la clasificación de género y las comparamos con una propuesta basada en un clasificador Bayesiano y una adecuada extracción de características. Analizamos en profundidad el motivo de porqué las técnicas lineales no han logrado resultados competitivos hasta la fecha y mostramos cómo obtener rendimientos similares a las mejores técnicas no-lineales. Se propone un segundo algoritmo para la estimación de edad, basado en un regresor K-NN y una adecuada selección de características tal como se propuso para la clasificación de género. A partir de los experimentos desarrollados, observamos que el rendimiento de los clasificadores se reduce significativamente si los ´estos han sido entrenados y probados sobre diferentes bases de datos. Hemos encontrado que una de las causas es la existencia de dependencias entre atributos faciales que no han sido consideradas en la construcción de los clasificadores. Nuestro resultados demuestran que la variabilidad intra-clase puede ser reducida cuando se consideran las dependencias estadísticas entre los atributos faciales de el género, la edad y la pose; mejorando el rendimiento de nuestros clasificadores de atributos faciales con un coste computacional pequeño. Abstract Surely the human face provides much more information than we think. The face provides without our consent nonverbal cues from facial interactions that reveal our emotional state, cognitive activity, personality and disease. Recent studies [OFT14, TODMS15] show that many of our social and interpersonal decisions derive from a previous facial analysis that allows us to establish whether that person is trustworthy, hardworking, intelligent, etc. This error-prone interpretation derives from the innate ability of human beings to find and interpret these signals. This capability is being studied, with a special interest in developing methods that have the ability to automatically calculate these signs or attributes associated with the face. Thus, the interest in the estimation of facial attributes has grown rapidly in recent years by the various applications in which these methods can be used: targeted marketing, security systems, human-computer interaction, etc. However, these are far from being perfect and robust in any domain of problems. The main difficulty encountered is caused by the high intra-class variability due to changes in the condition of the image: lighting changes, occlusions, facial expressions, age, gender, ethnicity, etc.; often found in images acquired in uncontrolled environments. This research work studies image analysis techniques to estimate facial attributes such as gender, age and pose, using linear methods, and exploiting the statistical dependencies between these attributes. In addition, our proposal will focus on the construction of classifiers that have a good balance between performance and computational cost. We studied a set of strategies for gender classification and we compare them with a proposal based on a Bayesian classifier and a suitable feature extraction based on Linear Discriminant Analysis. We study in depth why linear techniques have failed to provide competitive results to date and show how to obtain similar performances to the best non-linear techniques. A second algorithm is proposed for estimating age, which is based on a K-NN regressor and proper selection of features such as those proposed for the classification of gender. From our experiments we note that performance estimates are significantly reduced if they have been trained and tested on different databases. We have found that one of the causes is the existence of dependencies between facial features that have not been considered in the construction of classifiers. Our results demonstrate that intra-class variability can be reduced when considering the statistical dependencies between facial attributes gender, age and pose, thus improving the performance of our classifiers with a reduced computational cost.

Adaptation Strategies for Discontinuous Galerkin Spectral Element Methods by means of Truncation Error Estimations

In this work a p-adaptation (modification of the polynomial order) strategy based on the minimization of the truncation error is developed for high order discontinuous Galerkin methods. The truncation error is approximated by means of a truncation error estimation procedure and enables the identification of mesh regions that require adaptation. Three truncation error estimation approaches are developed and termed a posteriori, quasi-a priori and quasi-a priori corrected. Fine solutions, which are obtained by enriching the polynomial order, are required to solve the numerical problem with adequate accuracy. For the three truncation error estimation methods the former needs time converged solutions, while the last two rely on non-converged solutions, which lead to faster computations. Based on these truncation error estimation methods, algorithms for mesh adaptation were designed and tested. Firstly, an isotropic adaptation approach is presented, which leads to equally distributed polynomial orders in different coordinate directions. This first implementation is improved by incorporating a method to extrapolate the truncation error. This results in a significant reduction of computational cost. Secondly, the employed high order method permits the spatial decoupling of the estimated errors and enables anisotropic p-adaptation. The incorporation of anisotropic features leads to meshes with different polynomial orders in the different coordinate directions such that flow-features related to the geometry are resolved in a better manner. These adaptations result in a significant reduction of degrees of freedom and computational cost, while the amount of improvement depends on the test-case. Finally, this anisotropic approach is extended by using error extrapolation which leads to an even higher reduction in computational cost. These strategies are verified and compared in terms of accuracy and computational cost for the Euler and the compressible Navier-Stokes equations. The main result is that the two quasi-a priori methods achieve a significant reduction in computational cost when compared to a uniform polynomial enrichment. Namely, for a viscous boundary layer flow, we obtain a speedup of a factor of 6.6 and 7.6 for the quasi-a priori and quasi-a priori corrected approaches, respectively. RESUMEN En este trabajo se ha desarrollado una estrategia de adaptación-p (modificación del orden polinómico) para métodos Galerkin discontinuo de alto orden basada en la minimización del error de truncación. El error de truncación se estima utilizando el método tau-estimation. El estimador permite la identificación de zonas de la malla que requieren adaptación. Se distinguen tres técnicas de estimación: a posteriori, quasi a priori y quasi a priori con correción. Todas las estrategias requieren una solución obtenida en una malla fina, la cual es obtenida aumentando de manera uniforme el orden polinómico. Sin embargo, mientras que el primero requiere que esta solución esté convergida temporalmente, el resto utiliza soluciones no convergidas, lo que se traduce en un menor coste computacional. En este trabajo se han diseñado y probado algoritmos de adaptación de malla basados en métodos tau-estimation. En primer lugar, se presenta un algoritmo de adaptacin isótropo, que conduce a discretizaciones con el mismo orden polinómico en todas las direcciones espaciales. Esta primera implementación se mejora incluyendo un método para extrapolar el error de truncación. Esto resulta en una reducción significativa del coste computacional. En segundo lugar, el método de alto orden permite el desacoplamiento espacial de los errores estimados, permitiendo la adaptación anisotropica. Las mallas obtenidas mediante esta técnica tienen distintos órdenes polinómicos en cada una de las direcciones espaciales. La malla final tiene una distribución óptima de órdenes polinómicos, los cuales guardan relación con las características del flujo que, a su vez, depenen de la geometría. Estas técnicas de adaptación reducen de manera significativa los grados de libertad y el coste computacional. Por último, esta aproximación anisotropica se extiende usando extrapolación del error de truncación, lo que conlleva un coste computational aún menor. Las estrategias se verifican y se comparan en téminors de precisión y coste computacional utilizando las ecuaciones de Euler y Navier Stokes. Los dos métodos quasi a priori consiguen una reducción significativa del coste computacional en comparación con aumento uniforme del orden polinómico. En concreto, para una capa límite viscosa, obtenemos una mejora en tiempo de computación de 6.6 y 7.6 respectivamente, para las aproximaciones quasi-a priori y quasi-a priori con corrección.

Development of a hand-gesture recognition system for human-computer interaction

The aim of this Master Thesis is the analysis, design and development of a robust and reliable Human-Computer Interaction interface, based on visual hand-gesture recognition. The implementation of the required functions is oriented to the simulation of a classical hardware interaction device: the mouse, by recognizing a specific hand-gesture vocabulary in color video sequences. For this purpose, a prototype of a hand-gesture recognition system has been designed and implemented, which is composed of three stages: detection, tracking and recognition. This system is based on machine learning methods and pattern recognition techniques, which have been integrated together with other image processing approaches to get a high recognition accuracy and a low computational cost. Regarding pattern recongition techniques, several algorithms and strategies have been designed and implemented, which are applicable to color images and video sequences. The design of these algorithms has the purpose of extracting spatial and spatio-temporal features from static and dynamic hand gestures, in order to identify them in a robust and reliable way. Finally, a visual database containing the necessary vocabulary of gestures for interacting with the computer has been created.

Measuring the thickness of the human cerebral cortex from magnetic resonance images

Accurate and automated methods for measuring the thickness of human cerebral cortex could provide powerful tools for diagnosing and studying a variety of neurodegenerative and psychiatric disorders. Manual methods for estimating cortical thickness from neuroimaging data are labor intensive, requiring several days of effort by a trained anatomist. Furthermore, the highly folded nature of the cortex is problematic for manual techniques, frequently resulting in measurement errors in regions in which the cortical surface is not perpendicular to any of the cardinal axes. As a consequence, it has been impractical to obtain accurate thickness estimates for the entire cortex in individual subjects, or group statistics for patient or control populations. Here, we present an automated method for accurately measuring the thickness of the cerebral cortex across the entire brain and for generating cross-subject statistics in a coordinate system based on cortical anatomy. The intersubject standard deviation of the thickness measures is shown to be less than 0.5 mm, implying the ability to detect focal atrophy in small populations or even individual subjects. The reliability and accuracy of this new method are assessed by within-subject test–retest studies, as well as by comparison of cross-subject regional thickness measures with published values.

An approach to three-dimensional structures of biomolecules by using single-molecule diffraction images

We describe an approach to the high-resolution three-dimensional structural determination of macromolecules that utilizes ultrashort, intense x-ray pulses to record diffraction data in combination with direct phase retrieval by the oversampling technique. It is shown that a simulated molecular diffraction pattern at 2.5-Å resolution accumulated from multiple copies of single rubisco biomolecules, each generated by a femtosecond-level x-ray free electron laser pulse, can be successfully phased and transformed into an accurate electron density map comparable to that obtained by more conventional methods. The phase problem is solved by using an iterative algorithm with a random phase set as an initial input. The convergence speed of the algorithm is reasonably fast, typically around a few hundred iterations. This approach and phasing method do not require any ab initio information about the molecule, do not require an extended ordered lattice array, and can tolerate high noise and some missing intensity data at the center of the diffraction pattern. With the prospects of the x-ray free electron lasers, this approach could provide a major new opportunity for the high-resolution three-dimensional structure determination of single biomolecules.

Incorporação do espalhamento Compton no modelo de TBC modificado

No último século, houve grande avanço no entendimento das interações das radiações com a matéria. Essa compreensão se faz necessária para diversas aplicações, entre elas o uso de raios X no diagnóstico por imagens. Neste caso, imagens são formadas pelo contraste resultante da diferença na atenuação dos raios X pelos diferentes tecidos do corpo. Entretanto, algumas das interações dos raios X com a matéria podem levar à redução da qualidade destas imagens, como é o caso dos fenômenos de espalhamento. Muitas abordagens foram propostas para estimar a distribuição espectral de fótons espalhados por uma barreira, ou seja, como no caso de um feixe de campo largo, ao atingir um plano detector, tais como modelos que utilizam métodos de Monte Carlo e modelos que utilizam aproximações analíticas. Supondo-se um espectro de um feixe primário que não interage com nenhum objeto após sua emissão pelo tubo de raios X, este espectro é, essencialmente representado pelos modelos propostos anteriormente. Contudo, considerando-se um feixe largo de radiação X, interagindo com um objeto, a radiação a ser detectada por um espectrômetro, passa a ser composta pelo feixe primário, atenuado pelo material adicionado, e uma fração de radiação espalhada. A soma destas duas contribuições passa a compor o feixe resultante. Esta soma do feixe primário atenuado, com o feixe de radiação espalhada, é o que se mede em um detector real na condição de feixe largo. O modelo proposto neste trabalho visa calcular o espectro de um tubo de raios X, em situação de feixe largo, o mais fidedigno possível ao que se medem em condições reais. Neste trabalho se propõe a discretização do volume de interação em pequenos elementos de volume, nos quais se calcula o espalhamento Compton, fazendo uso de um espectro de fótons gerado pelo Modelo de TBC, a equação de Klein-Nishina e considerações geométricas. Por fim, o espectro de fótons espalhados em cada elemento de volume é somado ao espalhamento dos demais elementos de volume, resultando no espectro total espalhado. O modelo proposto foi implementado em ambiente computacional MATLAB® e comparado com medições experimentais para sua validação. O modelo proposto foi capaz de produzir espectros espalhados em diferentes condições, apresentando boa conformidade com os valores medidos, tanto em termos quantitativos, nas quais a diferença entre kerma no ar calculado e kerma no ar medido é menor que 10%, quanto qualitativos, com fatores de mérito superiores a 90%.

Elastografia em imagens de ultrassom utilizando elementos de contorno.

Este trabalho apresenta uma nova metodologia para elastografia virtual em imagens simuladas de ultrassom utilizando métodos numéricos e métodos de visão computacional. O objetivo é estimar o módulo de elasticidade de diferentes tecidos tendo como entrada duas imagens da mesma seção transversal obtidas em instantes de tempo e pressões aplicadas diferentes. Esta metodologia consiste em calcular um campo de deslocamento das imagens com um método de fluxo óptico e aplicar um método iterativo para estimar os módulos de elasticidade (análise inversa) utilizando métodos numéricos. Para o cálculo dos deslocamentos, duas formulações são utilizadas para fluxo óptico: Lucas-Kanade e Brox. A análise inversa é realizada utilizando duas técnicas numéricas distintas: o Método dos Elementos Finitos (MEF) e o Método dos Elementos de Contorno (MEC), sendo ambos implementados em Unidades de Processamento Gráfico de uso geral, GpGPUs ( \"General Purpose Graphics Units\" ). Considerando uma quantidade qualquer de materiais a serem determinados, para a implementação do Método dos Elementos de Contorno é empregada a técnica de sub-regiões para acoplar as matrizes de diferentes estruturas identificadas na imagem. O processo de otimização utilizado para determinar as constantes elásticas é realizado de forma semi-analítica utilizando cálculo por variáveis complexas. A metodologia é testada em três etapas distintas, com simulações sem ruído, simulações com adição de ruído branco gaussiano e phantoms matemáticos utilizando rastreamento de ruído speckle. Os resultados das simulações apontam o uso do MEF como mais preciso, porém computacionalmente mais caro, enquanto o MEC apresenta erros toleráveis e maior velocidade no tempo de processamento.

Estimação de imagens acústicas com arranjos de microfones.

Nas últimas décadas, a poluição sonora tornou-se um grande problema para a sociedade. É por esta razão que a indústria tem aumentado seus esforços para reduzir a emissão de ruído. Para fazer isso, é importante localizar quais partes das fontes sonoras são as que emitem maior energia acústica. Conhecer os pontos de emissão é necessário para ter o controle das mesmas e assim poder reduzir o impacto acústico-ambiental. Técnicas como \"beamforming\" e \"Near-Field Acoustic Holography\" (NAH) permitem a obtenção de imagens acústicas. Essas imagens são obtidas usando um arranjo de microfones localizado a uma distância relativa de uma fonte emissora de ruído. Uma vez adquiridos os dados experimentais pode-se obter a localização e magnitude dos principais pontos de emissão de ruído. Do mesmo modo, ajudam a localizar fontes aeroacústicas e vibro acústicas porque são ferramentas de propósito geral. Usualmente, estes tipos de fontes trabalham em diferentes faixas de frequência de emissão. Recentemente, foi desenvolvida a transformada de Kronecker para arranjos de microfones, a qual fornece uma redução significativa do custo computacional quando aplicada a diversos métodos de reconstrução de imagens, desde que os microfones estejam distribuídos em um arranjo separável. Este trabalho de mestrado propõe realizar medições com sinais reais, usando diversos algoritmos desenvolvidos anteriormente em uma tese de doutorado, quanto à qualidade do resultado obtido e à complexidade computacional, e o desenvolvimento de alternativas para tratamento de dados quando alguns microfones do arranjo apresentarem defeito. Para reduzir o impacto de falhas em microfones e manter a condição de que o arranjo seja separável, foi desenvolvida uma alternativa para utilizar os algoritmos rápidos, eliminando-se apenas os microfones com defeito, de maneira que os resultados finais serão obtidos levando-se em conta todos os microfones do arranjo.

A system to communicate hidden information using color images

The objective of this paper is to present a system to communicate hidden information among different users by means of images. The tasks that the system is able to carry on can be divided in two different groups of utilities, implemented in java. The first group of utilities are related with the possibility to hide information in color images, using a steganographic function based on the least significant bit (LSB) methods. The second group of utilities allows us to communicate with other users with the aim to send or receive images, where some information have been previously embedded. Thus, this is the most significant characteristic of the implementation, we have built an environment where we join the email capabilities to send and receive text and images as attached files, with the main objective of hiding information.

Local convergence of quasi-Newton methods under metric regularity

We consider quasi-Newton methods for generalized equations in Banach spaces under metric regularity and give a sufficient condition for q-linear convergence. Then we show that the well-known Broyden update satisfies this sufficient condition in Hilbert spaces. We also establish various modes of q-superlinear convergence of the Broyden update under strong metric subregularity, metric regularity and strong metric regularity. In particular, we show that the Broyden update applied to a generalized equation in Hilbert spaces satisfies the Dennis–Moré condition for q-superlinear convergence. Simple numerical examples illustrate the results.