Learning Low-Dimensional Signal Models

Sampling, coding, and streaming even the most essential data, e.g., in medical imaging and weather-monitoring applications, produce a data deluge that severely stresses the avail able analog-to-digital converter, communication bandwidth, and digital-storage resources. Surprisingly, while the ambient data dimension is large in many problems, the relevant information in the data can reside in a much lower dimensional space. This observation has led to several important theoretical and algorithmic developments under different low-dimensional modeling frameworks, such as compressive sensing (CS), matrix completion, and general factor-model representations. These approaches have enabled new measurement systems, tools, and methods for information extraction from dimensionality-reduced or incomplete data. A key aspect of maximizing the potential of such techniques is to develop appropriate data models. In this article, we investigate this challenge from the perspective of nonparametric Bayesian analysis

Human Pose Estimation from Monocular Images : a Comprehensive Survey

Human pose estimation refers to the estimation of the location of body parts and how they are connected in an image. Human pose estimation from monocular images has wide applications (e.g., image indexing). Several surveys on human pose estimation can be found in the literature, but they focus on a certain category; for example, model-based approaches or human motion analysis, etc. As far as we know, an overall review of this problem domain has yet to be provided. Furthermore, recent advancements based on deep learning have brought novel algorithms for this problem. In this paper, a comprehensive survey of human pose estimation from monocular images is carried out including milestone works and recent advancements. Based on one standard pipeline for the solution of computer vision problems, this survey splits the problema into several modules: feature extraction and description, human body models, and modelin methods. Problem modeling methods are approached based on two means of categorization in this survey. One way to categorize includes top-down and bottom-up methods, and another way includes generative and discriminative methods. Considering the fact that one direct application of human pose estimation is to provide initialization for automatic video surveillance, there are additional sections for motion-related methods in all modules: motion features, motion models, and motion-based methods. Finally, the paper also collects 26 publicly available data sets for validation and provides error measurement methods that are frequently used

Advanced physics-based and data-driven strategies

Simulation Based Engineering Science (SBES) has brought major improvements in optimization, control and inverse analysis, all leading to a deeper understanding in many processes occuring in the real world. These noticeable breakthroughts are present in a vast variety of sectors such as aeronautic or automotive industries, mobile telecommunications or healthcare among many other fields. Nevertheless, SBES is currently confronting several difficulties to provide accurate results in complex industrial problems. Apart from the high computational costs associated with industrial applications, the errors introduced by constitutive modeling become more and more important when dealing with new materials. Concurrently, an unceasingly growing interest in concepts such as Big-Data, Machine Learning or Data-Analytics has been experienced. Indeed, this interest is intrinsically motivated by an exhaustive development in both data-acquisition and data-storage systems. For instance, an aircraft may produce over 500 GB of data during a single flight. This panorama brings a perfect opportunity to the so-called Dynamic Data Driven Application Systems (DDDAS), whose main objective is to merge classical simulation algorithms with data coming from experimental measures in a dynamic way. Within this scenario, data and simulations would no longer be uncoupled but rather a symbiosis that is to be exploited would achieve milestones which were inconceivable until these days. Indeed, data will no longer be understood as a static calibration of a given constitutive model but rather the model will be corrected dynamicly as soon as experimental data and simulations tend to diverge. Several numerical algorithms will be presented throughout this manuscript whose main objective is to strengthen the link between data and computational mechanics. The first part of the thesis is mainly focused on parameter identification, data-driven and data completion techniques. The second part is focused on Model Order Reduction (MOR) techniques, since they constitute a fundamental ally to achieve real time constraints arising from DDDAS framework.La Ciencia de la Ingeniería Basada en la Simulación (SBES) ha aportado importantes mejoras en la optimización, el control y el análisis inverso, todo lo cual ha llevado a una comprensión más profunda de muchos de los procesos que ocurren en el mundo real. Estos notables avances están presentes en una gran variedad de sectores como la industria aeronáutica o automotriz, las telecomunicaciones móviles o la salud, entre muchos otros campos. Sin embargo, SBES se enfrenta actualmente a varias dificultades para proporcionar resultados precisos en problemas industriales complejos. Aparte de los altos costes computacionales asociados a las aplicaciones industriales, los errores introducidos por el modelado constitutivo son cada vez más importantes a la hora de tratar con nuevos materiales. Al mismo tiempo, se ha experimentado un interés cada vez mayor en conceptos como Big-Data, Machine Learning o Data-Analytics. Ciertamente, este interés está intrínsecamente motivado por un desarrollo exhaustivo de los sistemas de adquisición y almacenamiento de datos. Por ejemplo, una aeronave puede producir más de 500 GB de datos durante un solo vuelo. Este panorama brinda una oportunidad perfecta a los denominados Sistemas de Aplicación Dinámicos Impulsados por Datos (DDDAS), cuyo objetivo principal es fusionar de forma dinámica los algoritmos clásicos de simulación con los datos procedentes de medidas experimentales. En este escenario, los datos y las simulaciones ya no se desacoplarían, sino que aprovechando una simbiosis se alcanzaría hitos que hasta ahora eran inconcebibles. Mas en detalle, los datos ya no se entenderán como una calibración estática de un modelo constitutivo dado, sino que el modelo se corregirá dinámicamente tan pronto como los datos experimentales y las simulaciones tiendan a diverger. A lo largo de este manuscrito se presentarán varios algoritmos numéricos cuyo objetivo principal es fortalecer el vínculo entre los datos y la mecánica computacional. La primera parte de la tesis se centra principalmente en técnicas de identificación de parámetros, basadas en datos y de compleción de datos. La segunda parte se centra en las técnicas de Reducción de Modelo (MOR), ya que constituyen un aliado fundamental para conseguir las restricciones de tiempo real derivadas del marco DDDAS.Les sciences de l'ingénieur basées sur la simulation (Simulation Based Engineering Science, SBES) ont apporté des améliorations majeures dans l'optimisation, le contrôle et l'analyse inverse, menant toutes à une meilleure compréhension de nombreux processus se produisant dans le monde réel. Ces percées notables sont présentes dans une grande variété de secteurs tels que l'aéronautique ou l'automobile, les télécommunications mobiles ou la santé, entre autres. Néanmoins, les SBES sont actuellement confrontées à plusieurs dificultés pour fournir des résultats précis dans des problèmes industriels complexes. Outre les coûts de calcul élevés associés aux applications industrielles, les erreurs introduites par la modélisation constitutive deviennent de plus en plus importantes lorsqu'il s'agit de nouveaux matériaux. Parallèlement, un intérêt sans cesse croissant pour des concepts tels que les données massives (big data), l'apprentissage machine ou l'analyse de données a été constaté. En effet, cet intérêt est intrinsèquement motivé par un développement exhaustif des systèmes d'acquisition et de stockage de données. Par exemple, un avion peut produire plus de 500 Go de données au cours d'un seul vol. Ce panorama apporte une opportunité parfaite aux systèmes d'application dynamiques pilotés par les données (Dynamic Data Driven Application Systems, DDDAS), dont l'objectif principal est de fusionner de manière dynamique des algorithmes de simulation classiques avec des données provenant de mesures expérimentales. Dans ce scénario, les données et les simulations ne seraient plus découplées, mais une symbiose à exploiter permettrait d'envisager des situations jusqu'alors inconcevables. En effet, les données ne seront plus comprises comme un étalonnage statique d'un modèle constitutif donné mais plutôt comme une correction dynamique du modèle dès que les données expérimentales et les simulations auront tendance à diverger. Plusieurs algorithmes numériques seront présentés tout au long de ce manuscrit dont l'objectif principal est de renforcer le lien entre les données et la mécanique computationnelle. La première partie de la thèse est principalement axée sur l'identification des paramètres, les techniques d'analyse des données et les techniques de complétion de données. La deuxième partie est axée sur les techniques de réduction de modèle (MOR), car elles constituent un allié fondamental pour satisfaire les contraintes temps réel découlant du cadre DDDAS

Doctor of Philosophy

dissertationVolumetric parameterization is an emerging field in computer graphics, where volumetric representations that have a semi-regular tensor-product structure are desired in applications such as three-dimensional (3D) texture mapping and physically-based simulation. At the same time, volumetric parameterization is also needed in the Isogeometric Analysis (IA) paradigm, which uses the same parametric space for representing geometry, simulation attributes and solutions. One of the main advantages of the IA framework is that the user gets feedback directly as attributes of the NURBS model representation, which can represent geometry exactly, avoiding both the need to generate a finite element mesh and the need to reverse engineer the simulation results from the finite element mesh back into the model. Research in this area has largely been concerned with issues of the quality of the analysis and simulation results assuming the existence of a high quality volumetric NURBS model that is appropriate for simulation. However, there are currently no generally applicable approaches to generating such a model or visualizing the higher order smooth isosurfaces of the simulation attributes, either as a part of current Computer Aided Design or Reverse Engineering systems and methodologies. Furthermore, even though the mesh generation pipeline is circumvented in the concept of IA, the quality of the model still significantly influences the analysis result. This work presents a pipeline to create, analyze and visualize NURBS geometries. Based on the concept of analysis-aware modeling, this work focusses in particular on methodologies to decompose a volumetric domain into simpler pieces based on appropriate midstructures by respecting other relevant interior material attributes. The domain is decomposed such that a tensor-product style parameterization can be established on the subvolumes, where the parameterization matches along subvolume boundaries. The volumetric parameterization is optimized using gradient-based nonlinear optimization algorithms and datafitting methods are introduced to fit trivariate B-splines to the parameterized subvolumes with guaranteed order of accuracy. Then, a visualization method is proposed allowing to directly inspect isosurfaces of attributes, such as the results of analysis, embedded in the NURBS geometry. Finally, the various methodologies proposed in this work are demonstrated on complex representations arising in practice and research