Dissertations / Theses on the topic 'Nonlinear projection'

In computer graphics a projection describes the mapping of scene geometry to the screen. While linear projections such as perspective and orthographic projection are common, increasing applications are being found for nonlinear projections, which do not necessarily map straight lines in the scene to straight lines on the screen. Nonlinear projections occur in reflections and refractions on curved surfaces, in art, and in visualisation. This thesis presents a new nonlinear projection technique called a trilinear projection that is based on the trilinear interpolation of surface normals used in Phong shading. Trilinear projections can be combined to represent more complicated nonlinear projections. Nonlinear projections have previously been implemented with ray tracing, where rays are generated by the nonlinear projections and traced into the scene. However for performance reasons, most current graphics software uses scanline rendering, where a scene point is imaged on a screen as a function of the projection parameters. The techniques developed in this thesis are of this nature. This thesis presents several algorithms used in trilinear projection: 1. An algorithm to analytically determine which screen locations image a given scene point. 2. An algorithm that correctly connects projected vertices. Each scene point may be imaged multiple times, which means a projected scene triangle may form from one to four different shapes of from two to nine vertices. Once connected, the projected shapes may be rendered with standard scanline algorithms. 3. An algorithm to more accurately render the curved edges between projected vertices. 4. A scene-space edge-clipping algorithm that handles continuity issues for projected shapes across composite projections. The trilinear projection technique is demonstrated in two different application areas: visualisation, and reflections and refractions. Specifically, various nonlinear projections that are congruent with pre-existing visualisation techniques are implemented with trilinear projections and a method for approximating the reflections and refractions on curved surfaces with trilinear projections is presented. Finally, the performance characteristics of the trilinear projection is explored over various parameter ranges and compared with a naive ray tracing approach.

Thesis (Ph. D.)--Mechanical Engineering, Georgia Institute of Technology, 2006.
Shapiro, Alexander, Committee Member ; Vidakovic, Brani, Committee Member ; Ume, Charles, Committee Member ; Sadegh, Nader, Committee Chair ; Liang, Steven, Committee Member. Vita.

This thesis derives an vision based feedback control strategy for a class of uncertain projector-camera systems that are used to animate two dimensional projected images on complex, three dimensional, articulated target objects. The target object of the robotic system is articulated using an open loop control strategy that generates a desired sequence of target poses that are designed using commercially available geometric modeling software. The ideal or desired image sequences are subsequently rendered in the geometric modeling software using an ideal camera/projector pose and ideal intrinsic parameter camera model. The rendered imagery from the ideal camera and projector pose are subsequently used to define tracking performance for the feedback control of the camera and projector. Uncertainty in actuator models of the camera and projector actuator subsystems in this paper includes contributions due to imprecision in camera pose and in intrinsic camera parameters. A feedback control strategy is derived that employs pixel coordinates of multiple tracked feature points in the target image sequence for pose estimation and tracking control problems. We establish sufficient conditions that guarantee the convergence and asymptotic stability of the pose estimation and tracking control problems for the class of uncertain, nonlinear systems studied in this thesis. Several numerical studies are summarized in the thesis that provide confidence in the derived theoretical results and further suggest robustness of the control strategy for the considered uncertainty class.
Master of Science

In this age, there are many applications of inverse problems to lots of areas ranging from astronomy, geoscience and so on. For example, image reconstruction and deblurring require the use of methods to solve inverse problems. Since the problems are subject to many factors and noise, we can't simply apply general inversion methods. Furthermore in the problems of interest, the number of unknown variables is huge, and some may depend nonlinearly on the data, such that we must solve nonlinear problems. It is quite different and significantly more challenging to solve nonlinear problems than linear inverse problems, and we need to use more sophisticated methods to solve these kinds of problems.
Master of Science
In various research areas, there are many required measurements which can't be observed due to physical and economical reasons. Instead, these unknown measurements can be recovered by known measurements. This phenomenon can be modeled and be solved by mathematics.

Abstract Training a visual inspection device is not straightforward but suffers from the high variation in material to be inspected. This variation causes major difficulties for a human, and this is directly reflected in classifier training. Many inspection devices utilize rule-based classifiers the building and training of which rely mainly on human expertise. While designing such a classifier, a human tries to find the questions that would provide proper categorization. In training, an operator tunes the classifier parameters, aiming to achieve as good classification accuracy as possible. Such classifiers require lot of time and expertise before they can be fully utilized. Supervised classifiers form another common category. These learn automatically from training material, but rely on labels that a human has set for it. However, these labels tend to be inconsistent and thus reduce the classification accuracy achieved. Furthermore, as class boundaries are learnt from training samples, they cannot in practise be later adjusted if needed. In this thesis, a visual based training method is presented. It avoids the problems related to traditional training methods by combining a classifier and a user interface. The method relies on unsupervised projection and provides an intuitive way to directly set and tune the class boundaries of high-dimensional data. As the method groups the data only by the similarities of its features, it is not affected by erroneous and inconsistent labelling made for training samples. Furthermore, it does not require knowledge of the internal structure of the classifier or iterative parameter tuning, where a combination of parameter values leading to the desired class boundaries are sought. On the contrary, the class boundaries can be set directly, changing the classification parameters. The time need to take such a classifier into use is small and tuning the class boundaries can happen even on-line, if needed. The proposed method is tested with various experiments in this thesis. Different projection methods are evaluated from the point of view of visual based training. The method is further evaluated using a self-organizing map (SOM) as the projection method and wood as the test material. Parameters such as accuracy, map size, and speed are measured and discussed, and overall the method is found to be an advantageous training and classification scheme.

Model order reduction is necessary even in a time where the parallel processing is usual in almost any personal computer. The recent Model Reduction Methods are useful tools nowadays on reducing the problem processing. This work intends to describe a combination between POD (Proper Orthogonal Decomposition) and Ritz vectors that achieve an efficient Galerkin projection that changes during the processing, comparing the development of the error and the convergence rate between the full space and the projection space, in addition to check the stability of the projection space, leading to an adaptive model order reduction for nonlinear dynamical problems more efficient. This model reduction is supported by a secant formulation, which is updated by BFGS (Broyden - Fletcher - Goldfarb - Shanno) method to accelerate convergence of the model, and a tangent formulation to correct the projection space. Furthermore, this research shows that this method permits a correction of the reduced model at low cost, especially when the classical POD is no more efficient to represent accurately the solution.
A Redução de ordem de modelo é necessária, mesmo em uma época onde o processamento paralelo é usado em praticamente qualquer computador pessoal. Os recentes métodos de redução de modelo são ferramentas úteis nos dias de hoje para a redução de processamento de um problema. Este trabalho pretende descrever uma combinação entre POD (Proper Orthogonal Decomposition) e vetores de Ritz para uma projecção de Galerkin eficiente que sofre alterações durante o processamento, comparando o desenvolvimento do erro e a taxa de convergência entre o espaço total e o espaço de projeção, além da verificação de estabilidade do espaço de projeção, levando a uma redução de ordem do modelo adaptativo mais eficiente para problemas dinâmicos não-lineares. Esta redução de modelo é assistida por uma formulação secante, que é atualizado pela formula de BFGS (Broyden - Fletcher- Goldfarb - Shanno) com o intuito de acelerar a convergência do modelo, e uma formulação tangente para a correção do espaço de projeção. Além disso, esta pesquisa mostra que este método permite a correção do modelo reduzido com baixo custo, especialmente quando o clássico POD não é mais eficiente para representar com precisão a solução.

MOR (Model Order Reduction) est devenu un domaine très répondu dans la recherche grâce à l'intérêt qu'il peut apporter dans la réduction des systèmes, ce qui permet d'économiser du temps, de la mémoire et le coût de CPU pour les outils de CAO. Ce domaine contient principalement deux branches: linéaires et non linéaires. MOR linéaire est un domaine mature avec des techniques numériques bien établie et bien connus dans la domaine de la recherche, par contre le domaine non linéaire reste vague, et jusqu'à présent il n'a pas montré des bons résultats dans la simulation des circuits électriques. La recherche est toujours en cours dans ce domaine, en raison de l’intérêt qu'il peut fournir aux simulateurs contemporains, surtout avec la croissance des puces électroniques en termes de taille et de complexité, et les exigences industrielles vers l'intégration des systèmes sur la même puce.Une contribution significative, pour résoudre le problème de Harmonic Balance (Equilibrage Harmonique) en utilisant la technique MOR, a été proposé en 2002 par E. Gad et M. Nakhla. La technique a montré une réduction substantielle de la dimension du système, tout en préservant, en sortie, la précision de l'analyse en régime permanent. Cette méthode de MOR utilise la technique de projection par l'intermédiaire de Krylov, et il préserve la passivité du système. Cependant, il souffre de quelques limitations importantes dans la construction de la matrice “pre-conditioner“ qui permettrait de réduire le système. La limitation principale est la nécessité d'une factorisation explicite comme une suite numérique de l'équation des dispositifs non linéaires . cette limitation rend la technique difficile à appliquer dans les conditions générales d'un simulateur. Cette thèse examinera les aspects non linéaires du modèle de réduction pour les équations de bilan harmoniques, et il étudiera les solutions pour surmonter les limitations mentionnées ci-dessus, en particulier en utilisant des approches de dérivateur numériques
MOR recently became a well-known research field, due to the interest that it shows in reducing the system, which saves time, memory, and CPU cost for CAD tools. This field contains two branches, linear and nonlinear MOR, the linear MOR is a mature domain with well-established theory and numerical techniques. Meanwhile, nonlinear MOR domain is still stammering, and so far it didn’t show good and successful results in electrical circuit simulation. Some improvements however started to pop-up recently, and research is still going on this field because of the help that it can give to the contemporary simulators, especially with the growth of the electronic chips in terms of size and complexity due to industrial demands towards integrating systems on the same chip. A significant contribution in the MOR technique of HB solution has been proposed a decade ago by E. Gad and M. Nakhla. The technique has shown to provide a substantial system dimension reduction while preserving the precision of the output in steady state analysis. This MOR method uses the technique of projection via Krylov, and it preserves the passivity of the system. However, it suffers a number of important limitations in the construction of the pre-conditioner matrix which is ought to reduce the system. The main limitation is the necessity for explicit factorization as a power series of the equation of the nonlinear devices. This makes the technique difficult to apply in general purpose simulator conditions. This thesis will review the aspects of the nonlinear model order reduction technique for harmonic balance equations, and it will study solutions to overcome the above mentioned limitations, in particular using numerical differentiation approaches

When excitable cardiac tissue is electrically paced at a sufficiently high rate, the duration of excitation can alternate from beat to beat despite a constant stimulation period. This rhythm, known as alternans, has been identified as an early stage in a sequence of increasingly complex instabilities leading to the lethal arrhythmia ventricular fibrillation (VF). This connection served as as a motivation for research into the control of alternans as a strategy to prevent VF. Control methods that do not use a model of the dynamics have been used for the suppression of alternans. However, these methods possess limitations. In this thesis we study theoretically model-based control techniques with the goal of developing protocols that would overcome the shortcomings of non model-based approaches. We consider one dimensional tissue in two different geometrical configurations: a ring and a fiber with free ends (open fiber). We apply standard control methods for linear time invariant systems to a stroboscopic map of the linearized dynamics around the normal rhythm. We found that, in the ring geometry, model-based control is able to suppress alternans faster and with lower current, thereby reducing the risk of tissue damage, compared with non-model-based control. In the open fiber, model-based control is able to suppress alternans for longer fibers and higher pacing frequencies in comparison with non-model-based control. The methodology presented here can be extended to two- and three-dimensional tissue, and could eventually lead to the suppression of alternans on the entire ventricles.

Bundle adjustment is the process of simultaneously optimizing camera poses and 3D structure given image point tracks. In structure-from-motion, it is typically used as the final refinement step due to the nonlinearity of the problem, meaning that it requires sufficiently good initialization. Contrary to this belief, recent literature showed that useful solutions can be obtained even from arbitrary initialization for fixed-rank matrix factorization problems, including bundle adjustment with affine cameras. This property of wide convergence basin of high quality optima is desirable for any nonlinear optimization algorithm since obtaining good initial values can often be non-trivial. The aim of this thesis is to find the key factor behind the success of these recent matrix factorization algorithms and explore the potential applicability of the findings to bundle adjustment, which is closely related to matrix factorization. The thesis begins by unifying a handful of matrix factorization algorithms and comparing similarities and differences between them. The theoretical analysis shows that the set of successful algorithms actually stems from the same root of the optimization method called variable projection (VarPro). The investigation then extends to address why VarPro outperforms the joint optimization technique, which is widely used in computer vision. This algorithmic comparison of these methods yields a larger unification, leading to a conclusion that VarPro benefits from an unequal trust region assumption between two matrix factors. The thesis then explores ways to incorporate VarPro to bundle adjustment problems using projective and perspective cameras. Unfortunately, the added nonlinearity causes a substantial decrease in the convergence basin of VarPro, and therefore a bootstrapping strategy is proposed to bypass this issue. Experimental results show that it is possible to yield feasible metric reconstructions and pose estimations from arbitrary initialization given relatively clean point tracks, taking one step towards initialization-free structure-from-motion.

L'objectif de cette thèse consiste à étudier la méthode de pénalité-projection vectorielle notée VPP (Vector Penalty-Projection method), qui est une méthode à pas fractionnaire pour la résolution des équations de Navier-Stokes incompressible avec conditions aux limites ouvertes. Nous présentons une revue bibliographique des méthodes de projection traitant le couplage de vitesse et de pression. Nous nous intéressons dans un premier temps aux conditions de Dirichlet sur toute la frontière. Les tests numériques montrent une convergence d'ordre deux en temps pour la vitesse et la pression et prouvent que la méthode est rapide et peu coûteuse en terme de nombre d'itérations par pas de temps. En outre, nous établissons des estimations d'erreurs de la vitesse et de la pression et les essais numériques révèlent une parfaite concordance avec les résultats théoriques. En revanche, la contrainte d'incompressibilité n'est pas exactement nulle et converge avec un ordre de O(varepsilondelta t) où varepsilon est un paramètre de pénalité choisi assez petit et delta t le pas temps. Dans un second temps, la thèse traite les conditions aux limites ouvertes naturelles. Trois types de conditions de sortie sont étudiés et testés numériquement pour l'étape de projection. Nous effectuons des comparaisons quantitatives des résultats avec d'autres méthodes de projection. Les essais numériques sont en concordance avec les estimations théoriques également établies. Le dernier chapitre est consacré à l'étude numérique du schéma VPP en présence d'une condition aux limites ouvertes non-linéaire sur une frontière artificielle modélisant une charge singulière pour le problème de Navier-Stokes
Motivated by solving the incompressible Navier-Stokes equations with open boundary conditions, this thesis studies the Vector Penalty-Projection method denoted VPP, which is a splitting method in time. We first present a literature review of the projection methods addressing the issue of the velocity-pressure coupling in the incompressible Navier-Stokes system. First, we focus on the case of Dirichlet conditions on the entire boundary. The numerical tests show a second-order convergence in time for both the velocity and the pressure. They also show that the VPP method is fast and cheap in terms of number of iterations at each time step. In addition, we established for the Stokes problem optimal error estimates for the velocity and pressure and the numerical experiments are in perfect agreement with the theoretical results. However, the incompressibility constraint is not exactly equal to zero and it scales as O(varepsilondelta t) where $varepsilon$ is a penalty parameter chosen small enough and delta t is the time step. Moreover, we deal with the natural outflow boundary condition. Three types of outflow boundary conditions are presented and numerically tested for the projection step. We perform quantitative comparisons of the results with those obtained by other methods in the literature. Besides, a theoretical study of the VPP method with outflow boundary conditions is stated and the numerical tests prove to be in good agreement with the theoretical results. In the last chapter, we focus on the numerical study of the VPP scheme with a nonlinear open artificial boundary condition modelling a singular load for the unsteady incompressible Navier-Stokes problem

It is well established that many physical and chemical phenomena such as those in chemical reaction kinetics, laser cavities, rotating fluids, and in plasmas and in solid state physics are governed by nonlinear differential equations whose solutions are of variable character and even may lack regularities. Such systems are usually first studied qualitatively by examining their temporal behavior near singular points of their phase portrait. In this work we will be concerned with systems governed by the time evolution equations [see PDF for mathematical formulas] The xi may generally be considered to be concentrations of species in a chemical reaction, in which case the k's are rate constants. In some cases the xi may be considered to be position and momentum variables in a mechanical system. We will divide the equations into two classes: those in which the evolution can be carried out by the action of one of Lie's transformation groups of the plane, and those for which this is not possible. Members of the first class can be integrated by quadrature either directly or by use of an integrating factor; those in the second class cannot. Of those in the first class the most interesting evolve by transformations of the projective group, and these, as well as the equations that cannot be integrated by quadrature, we study in some detail. We seek a qualitative analysis of systems which have no linear terms in their evolution equations when the origin from which the xi are measured is a critical point. The standard, linear, phase plane analysis is of course not adequate for our purposes.

This thesis considers the problem of tracking an object in world coordinates using measurements obtained from multiple uncalibrated cameras. A general approach to track the location of a target involves different phases including calibrating the camera, detecting the object's feature points over frames, tracking the object over frames and analyzing object's motion and behavior. The approach contains two stages. First, the problem of camera calibration using a calibration object is studied. This approach retrieves the camera parameters from the known locations of ground data in 3D and their corresponding image coordinates. The next important part of this work is to develop an automated system to estimate the trajectory of the object in 3D from image sequences. This is achieved by combining, adapting and integrating several state-of-the-art algorithms. Synthetic data based on a nearly constant velocity object motion model is used to evaluate the performance of camera calibration and state estimation algorithms.

The goal of this thesis is two-fold. On the one hand, it pursues to provide a contribution to the conjugate duality by proposing a new duality concept, which can be understood as an umbrella for different meaningful perturbation methods. On the other hand, this thesis aims to investigate minimax location problems by means of the duality concept introduced in the first part of this work, followed by a numerical approach using epigraphical splitting methods. After summarizing some elements of the convex analysis as well as introducing important results needed later, we consider an optimization problem with geometric and cone constraints, whose objective function is a composition of n+1 functions. For this problem we propose a conjugate dual problem, where the functions involved in the objective function of the primal problem are decomposed. Furthermore, we formulate generalized interior point regularity conditions for strong duality and give necessary and sufficient optimality conditions. As applications of this approach we determine the formulae of the conjugate as well as the biconjugate of the objective function of the primal problem and analyze an optimization problem having as objective function the sum of reciprocals of concave functions. In the second part of this thesis we discuss in the sense of the introduced duality concept three classes of minimax location problems. The first one consists of nonlinear and linear single minimax location problems with geometric constraints, where the maximum of nonlinear or linear functions composed with gauges between pairs of a new and existing points will be minimized. The version of the nonlinear location problem is additionally considered with set-up costs. The second class of minimax location problems deals with multifacility location problems as suggested by Drezner (1991), where for each given point the sum of weighted distances to all facilities plus set-up costs is determined and the maximal value of these sums is to be minimized. As the last and third class the classical multifacility location problem with geometrical constraints is considered in a generalized form where the maximum of gauges between pairs of new facilities and the maximum of gauges between pairs of new and existing facilities will be minimized. To each of these location problems associated dual problems will be formulated as well as corresponding duality statements and necessary and sufficient optimality conditions. To illustrate the results of the duality approach and to give a more detailed characterization of the relations between the location problems and their corresponding duals, we consider examples in the Euclidean space. This thesis ends with a numerical approach for solving minimax location problems by epigraphical splitting methods. In this framework, we give formulae for the projections onto the epigraphs of several sums of powers of weighted norms as well as formulae for the projection onto the epigraphs of gauges. Numerical experiments document the usefulness of our approach for the discussed location problems.

This thesis presents the development of a surveillance testbed using wireless sensors and video cameras for vehicle detection and tracking. The experimental study includes testbed design and discusses some of the implementation issues in using wireless sensors and video cameras for a practical application. A group of sensor devices equipped with light sensors are used to detect and localize the position of moving vehicle. Background subtraction method is used to detect the moving vehicle from the video sequences. Vehicle centroid is calculated in each frame. A non-linear minimization method is used to estimate the perspective transformation which project 3D points to 2D image points. Vehicle location estimates from three cameras are fused to form a single trajectory representing the vehicle motion. Experimental results using both sensors and cameras are presented. Average error between vehicle location estimates from the cameras and the wireless sensors is around 0.5ft.

U disertaciji su posmatrani projektivni postupci tipa konjugovanih gradijenata za rešavanje nelinearnih monotonih sistema velikih dimenzija. Ovi postupci kombinuju projektivnu metodu sa pravcima pretraživanja tipa konjugovanih gradijenata. Zbog osobine monotonosti sistema, projektivna metoda omogućava jednostavnu globalizaciju, a pravci pretraživanja tipa konjugovanih gradijenata zahtevaju maloračunarske memorije pa su pogodni za rešavanje sistema velikih dimenzija. Projektivni postupci tipa konjugovanih gradijenata ne koriste izvode niti funkciju cilja i zasnovani su samo na izračunavanju vrednosti funkcije sistema, pa su pogodni i za rešavanje neglatkih monotonih sistema. Pošto se globalna konvergencija dokazuje bez pretpostavki o regularnosti, ovi postupci se mogu koristiti i za rešavanje sistema sa singularnim rešenjima. U disertaciji su definisana tri nova tročlana pravca pretraživanjatipa Flečer-Rivs i dva nova hibridna pravca tipa Hu-Stori. Formulisani su projektivni postupci sa novim pravcima pretraživanja i dokazana je njihova globalna konvergencija. Numeričke performanse postupaka testirane su na relevantnim primerima i poređene sa poznatim postupcima iz literature. Numerički rezultati potvrđuju da su novi postupci robusni, efikasni i uporedivi sa postojećim postupcima.
Projection based CG methods for solving large-scale nonlinear monotone systems are considered in this thesis. These methods combine hyperplane projection technique with conjugate gradient (CG) search directions. Hyperplane projection method is suitable for monotone systems, because it enables simply globalization, while CG directions are efficient for large-scale nonlinear systems, due to low memory. Projection based CG methods are funcion-value based, they don’t use merit function and derivatives, and because of that they are also suitable for solving nonsmooth monotone systems. The global convergence of these methods are ensured without additional regularity assumptions, so they can be used for solving singular systems.Three new three-term search directions of Fletcher-Reeves type and two new hybrid search directions of Hu-Storey type are defined. PCG algorithm with five new CG type directions is proposed and its global convergence is established. Numerical performances of methods are tested on relevant examples from literature. These results point out that new projection based CG methods have good computational performances. They are efficient, robust and competitive with other methods.

Continuing advances in laser and photonic technology has seen the development of lasers with increasing power and increasingly short pulsewidths, which have become available over an increasing range of wavelengths. As the availability of laser sources grow, so do their applications. To make better use of this improving technology, understanding and controlling laser propagation in free space is critical, as is understanding the interaction between laser light and matter. The need to better control the light obtained from increasingly advanced laser sources leads to the emergence of beam engineering, the systematic understanding and control of light through refractive media and free space. Beam engineering enables control over the beam shape, energy and spectral composition during propagation, which can be achieved through a variety of means. In this dissertation, several methods of beam engineering are investigated. These methods enable improved control over the shape and propagation of laser light. Laser-matter interaction is also investigated, as it provides both a means to control the propagation of pulsed laser light through the atmosphere, and provides a means to generation remote sources of radiation.
Ph.D.
Doctorate
Physics
Sciences
Physics

O objetivo deste trabalho é investigar se os multiplicadores de gastos do governo diferem de acordo com o estado do ciclo de negócios para o período 1999: I- 2016: II. Para tanto é utilizado o Método de Projeção Local de Jordà para estimar as funções resposta ao impulso e os multiplicadores fiscais sob dois regimes diferentes: recessão e expansão. Para definir os diferentes regimes foram utilizadas as variáveis comumente usadas na literatura (o hiato do produto, o nível de utilização da capacidade instalada, a taxa de crescimento do PIB, a taxa de desemprego), além da datação oficial de ciclos do CODACE. A estimação do modelo não linear resulta em multiplicadores de gastos do governo, após um e dois anos, maiores nos períodos de recessão do que nos períodos de expansão, independentemente da variável escolhida para diferenciar os regimes. Porém, os multiplicadores obtidos não parecem ser diferentes estatisticamente entre os regimes. Infelizmente, como observado por Ramey e Zubairy (2017) a existência de séries históricas é fundamental para a estimação dos multiplicadores fiscais e sua ausência para a economia brasileira limita muito o que é possível dizer sobre o assunto
This paper aims to investigate whether government spending multipliers are different according to the state of the business cycle for the Brazilian economy during the period 1999:I-2016:II. In order to do so we use Jordà\'s Local Projection Method to estimate impulse response functions and fiscal multipliers under two different regimes: recession and expansion. To define the different regimes we use several variables commonly used in the literature: the output gap, the capacity utilization level, the GDP growth rate, the unemployment rate and CODACE. The nonlinear model estimations result in larger multipliers, after one and two years, in periods of economic recession than in periods of economic expansion, regardless of the variable chosen to differentiate regimes. However, the multipliers do not seem to be statistically different between regimes. Unfortunately, as observed by Ramey and Zubairy (2017), long historical series are fundamental for the adequate estimation of fiscal multipliers and their absence for the Brazilian economy does not allow anyone to say much about the subject.

De nos jours, l'utilisation des drones miniatures à voilure tournante pour des missions d'observation dans des environnements hostiles est en pleine expansion. Ces appareils, grâce à leurs capacités à combiner le vol de translation avec le vol stationnaire, sont en eff et bien adaptés aux besoins de ces missions. L'étude présentée dans cette thèse concerne un nouveau concept de drone appelé GLMAV (pour Gun Launched Micro Aerial Vehicle), qui consiste à rendre très rapidement opérationnel un véhicule hybride projectile - drone. La di fficulté dans le pilotage de ce type de véhicules est d'assurer de bonnes performances de suivi de trajectoires tout en garantissant une résistance aux perturbations aérodynamiques. Après une étape de modélisation, le cœur de la thèse présente plusieurs stratégies de commande, aussi bien linéaires que non linéaires, permettant la navigation autonome du drone. Plusieurs approches permettant l'estimation et la prise en compte dans la commande des eff orts parasites liés aux phénomènes aérodynamiques sont également détaillées. L'e fficacité de tous les algorithmes de commande est ensuite illustrée par de nombreuses simulations numériques. Du point de vue pratique, une simple loi de commande ne suffi t pas. En eff et, des techniques de filtrage particulières ou des aménagements spécifi ques doivent être utilisés pour reconstruire l'état du drone. Les performances de l'ensemble de la boucle de commande sont d'abord testées en simulation avant l'implantation sur le prototype du GLMAV développé par l'Institut franco-allemand de recherches de Saint-Louis.

L’objectif de cette thèse est l’étude d’un schéma numérique pour l’approximation des solutions d’équations différentielles doublement stochastiques rétrogrades (EDDSR). Durant les deux dernières décennies, plusieurs méthodes ont été proposées afin de permettre la résolution numérique des équations différentielles stochastiques rétrogrades standards. Dans cette thèse, on propose une extension de l’une de ces méthodes au cas doublement stochastique. Notre méthode numérique nous permet d’attaquer une large gamme d’équations aux dérivées partielles stochastiques (EDPS) nonlinéaires. Ceci est possible par le biais de leur représentation probabiliste en termes d’EDDSRs. Dans la dernière partie, nous étudions une nouvelle méthode des particules dans le cadre des études de protection en neutroniques
The purpose of this thesis is to study a numerical method for backward doubly stochastic differential equations (BDSDEs in short). In the last two decades, several methods were proposed to approximate solutions of standard backward stochastic differential equations. In this thesis, we propose an extension of one of these methods to the doubly stochastic framework. Our numerical method allows us to tackle a large class of nonlinear stochastic partial differential equations (SPDEs in short), thanks to their probabilistic interpretation. In the last part, we study a new particle method in the context of shielding studies

Im Mittelpunkt dieser Arbeit stehen virtuelle 3D-Stadtmodelle, die Objekte, Phänomene und Prozesse in urbanen Räumen in digitaler Form repräsentieren. Sie haben sich zu einem Kernthema von Geoinformationssystemen entwickelt und bilden einen zentralen Bestandteil geovirtueller 3D-Welten. Virtuelle 3D-Stadtmodelle finden nicht nur Verwendung als Mittel für Experten in Bereichen wie Stadtplanung, Funknetzplanung, oder Lärmanalyse, sondern auch für allgemeine Nutzer, die realitätsnah dargestellte virtuelle Städte in Bereichen wie Bürgerbeteiligung, Tourismus oder Unterhaltung nutzen und z. B. in Anwendungen wie GoogleEarth eine räumliche Umgebung intuitiv erkunden und durch eigene 3D-Modelle oder zusätzliche Informationen erweitern. Die Erzeugung und Darstellung virtueller 3D-Stadtmodelle besteht aus einer Vielzahl von Prozessschritten, von denen in der vorliegenden Arbeit zwei näher betrachtet werden: Texturierung und Visualisierung. Im Bereich der Texturierung werden Konzepte und Verfahren zur automatischen Ableitung von Fototexturen aus georeferenzierten Schrägluftbildern sowie zur Speicherung oberflächengebundener Daten in virtuellen 3D-Stadtmodellen entwickelt. Im Bereich der Visualisierung werden Konzepte und Verfahren für die multiperspektivische Darstellung sowie für die hochqualitative Darstellung nichtlinearer Projektionen virtueller 3D-Stadtmodelle in interaktiven Systemen vorgestellt. Die automatische Ableitung von Fototexturen aus georeferenzierten Schrägluftbildern ermöglicht die Veredelung vorliegender virtueller 3D-Stadtmodelle. Schrägluftbilder bieten sich zur Texturierung an, da sie einen Großteil der Oberflächen einer Stadt, insbesondere Gebäudefassaden, mit hoher Redundanz erfassen. Das Verfahren extrahiert aus dem verfügbaren Bildmaterial alle Ansichten einer Oberfläche und fügt diese pixelpräzise zu einer Textur zusammen. Durch Anwendung auf alle Oberflächen wird das virtuelle 3D-Stadtmodell flächendeckend texturiert. Der beschriebene Ansatz wurde am Beispiel des offiziellen Berliner 3D-Stadtmodells sowie der in GoogleEarth integrierten Innenstadt von München erprobt. Die Speicherung oberflächengebundener Daten, zu denen auch Texturen zählen, wurde im Kontext von CityGML, einem international standardisierten Datenmodell und Austauschformat für virtuelle 3D-Stadtmodelle, untersucht. Es wird ein Datenmodell auf Basis computergrafischer Konzepte entworfen und in den CityGML-Standard integriert. Dieses Datenmodell richtet sich dabei an praktischen Anwendungsfällen aus und lässt sich domänenübergreifend verwenden. Die interaktive multiperspektivische Darstellung virtueller 3D-Stadtmodelle ergänzt die gewohnte perspektivische Darstellung nahtlos um eine zweite Perspektive mit dem Ziel, den Informationsgehalt der Darstellung zu erhöhen. Diese Art der Darstellung ist durch die Panoramakarten von H. C. Berann inspiriert; Hauptproblem ist die Übertragung des multiperspektivischen Prinzips auf ein interaktives System. Die Arbeit stellt eine technische Umsetzung dieser Darstellung für 3D-Grafikhardware vor und demonstriert die Erweiterung von Vogel- und Fußgängerperspektive. Die hochqualitative Darstellung nichtlinearer Projektionen beschreibt deren Umsetzung auf 3D-Grafikhardware, wobei neben der Bildwiederholrate die Bildqualität das wesentliche Entwicklungskriterium ist. Insbesondere erlauben die beiden vorgestellten Verfahren, dynamische Geometrieverfeinerung und stückweise perspektivische Projektionen, die uneingeschränkte Nutzung aller hardwareseitig verfügbaren, qualitätssteigernden Funktionen wie z.~B. Bildraumgradienten oder anisotroper Texturfilterung. Beide Verfahren sind generisch und unterstützen verschiedene Projektionstypen. Sie ermöglichen die anpassungsfreie Verwendung gängiger computergrafischer Effekte wie Stilisierungsverfahren oder prozeduraler Texturen für nichtlineare Projektionen bei optimaler Bildqualität. Die vorliegende Arbeit beschreibt wesentliche Technologien für die Verarbeitung virtueller 3D-Stadtmodelle: Zum einen lassen sich mit den Ergebnissen der Arbeit Texturen für virtuelle 3D-Stadtmodelle automatisiert herstellen und als eigenständige Attribute in das virtuelle 3D-Stadtmodell einfügen. Somit trägt diese Arbeit dazu bei, die Herstellung und Fortführung texturierter virtueller 3D-Stadtmodelle zu verbessern. Zum anderen zeigt die Arbeit Varianten und technische Lösungen für neuartige Projektionstypen für virtueller 3D-Stadtmodelle in interaktiven Visualisierungen. Solche nichtlinearen Projektionen stellen Schlüsselbausteine dar, um neuartige Benutzungsschnittstellen für und Interaktionsformen mit virtuellen 3D-Stadtmodellen zu ermöglichen, insbesondere für mobile Geräte und immersive Umgebungen.
This thesis concentrates on virtual 3D city models that digitally encode objects, phenomena, and processes in urban environments. Such models have become core elements of geographic information systems and constitute a major component of geovirtual 3D worlds. Expert users make use of virtual 3D city models in various application domains, such as urban planning, radio-network planning, and noise immision simulation. Regular users utilize virtual 3D city models in domains, such as tourism, and entertainment. They intuitively explore photorealistic virtual 3D city models through mainstream applications such as GoogleEarth, which additionally enable users to extend virtual 3D city models by custom 3D models and supplemental information. Creation and rendering of virtual 3D city models comprise a large number of processes, from which texturing and visualization are in the focus of this thesis. In the area of texturing, this thesis presents concepts and techniques for automatic derivation of photo textures from georeferenced oblique aerial imagery and a concept for the integration of surface-bound data into virtual 3D city model datasets. In the area of visualization, this thesis presents concepts and techniques for multiperspective views and for high-quality rendering of nonlinearly projected virtual 3D city models in interactive systems. The automatic derivation of photo textures from georeferenced oblique aerial imagery is a refinement process for a given virtual 3D city model. Our approach uses oblique aerial imagery, since it provides a citywide highly redundant coverage of surfaces, particularly building facades. From this imagery, our approach extracts all views of a given surface and creates a photo texture by selecting the best view on a pixel level. By processing all surfaces, the virtual 3D city model becomes completely textured. This approach has been tested for the official 3D city model of Berlin and the model of the inner city of Munich accessible in GoogleEarth. The integration of surface-bound data, which include textures, into virtual 3D city model datasets has been performed in the context of CityGML, an international standard for the exchange and storage of virtual 3D city models. We derive a data model from a set of use cases and integrate it into the CityGML standard. The data model uses well-known concepts from computer graphics for data representation. Interactive multiperspective views of virtual 3D city models seamlessly supplement a regular perspective view with a second perspective. Such a construction is inspired by panorama maps by H. C. Berann and aims at increasing the amount of information in the image. Key aspect is the construction's use in an interactive system. This thesis presents an approach to create multiperspective views on 3D graphics hardware and exemplifies the extension of bird's eye and pedestrian views. High-quality rendering of nonlinearly projected virtual 3D city models focuses on the implementation of nonlinear projections on 3D graphics hardware. The developed concepts and techniques focus on high image quality. This thesis presents two such concepts, namely dynamic mesh refinement and piecewise perspective projections, which both enable the use of all graphics hardware features, such as screen space gradients and anisotropic texture filtering under nonlinear projections. Both concepts are generic and customizable towards specific projections. They enable the use of common computer graphics effects, such as stylization effects or procedural textures, for nonlinear projections at optimal image quality and interactive frame rates. This thesis comprises essential techniques for virtual 3D city model processing. First, the results of this thesis enable automated creation of textures for and their integration as individual attributes into virtual 3D city models. Hence, this thesis contributes to an improved creation and continuation of textured virtual 3D city models. Furthermore, the results provide novel approaches to and technical solutions for projecting virtual 3D city models in interactive visualizations. Such nonlinear projections are key components of novel user interfaces and interaction techniques for virtual 3D city models, particularly on mobile devices and in immersive environments.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1993.
Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 139-149).

碩士
國立臺北科技大學
機電整合研究所
101
In this study, the virtual scene projected through the projector to the windshield of a car has been corrected by automatic image vision processing to create a surround effect so that the driver will be immersed in a vivid virtual reality. Curved screen projection technology is widely used in the entertainment system, surround movies, virtual reality and then industry. Projection on a curved screen always to produce nonlinear distortion correction which requires tremendous human resources to correct and do not have much flexibility of operation. Therefore, this study analyzed the relationship between screen virtual scenes and real cameras to identify the projected image space corresponding calibration marks, and use the digital image processing technology, such as Canny edge detection and Hough transform, identify each feature marks that needed to corrected to automatically. By using computer instead of a human operator, the present study can save resources as well as to improve the correction efficiency and accuracy.

Most modern industrial and architectural designs need to satisfy the requirements of their targeted performance and respect the limitations of available fabrication technologies. At the same time, they should reflect the artistic considerations and personal taste of the designers, which cannot be simply formulated as optimization goals with single best solutions. This thesis aims at a general, flexible yet e cient computational framework for interactive creation, exploration and discovery of serviceable, constructible, and stylish designs. By formulating nonlinear engineering considerations as linear or quadratic expressions by introducing auxiliary variables, the constrained space could be e ciently accessed by the proposed algorithm Guided Projection, with the guidance of aesthetic formulations. The approach is introduced through applications in different scenarios, its effectiveness is demonstrated by examples that were difficult or even impossible to be computationally designed before. The first application is the design of meshes under both geometric and static constraints, including self-supporting polyhedral meshes that are not height fields. Then, with a formulation bridging mesh based and spline based representations, the application is extended to developable surfaces including origami with curved creases. Finally, general approaches to extend hard constraints and soft energies are discussed, followed by a concluding remark outlooking possible future studies.

In this paper we present an approach to the nonlinear model reduction based on representing the nonlinear system with a piecewise-linear system and then reducing each of the pieces with a Krylov projection. However, rather than approximating the individual components to make a system with exponentially many different linear regions, we instead generate a small set of linearizations about the state trajectory which is the response to a 'training input'. Computational results and performance data are presented for a nonlinear circuit and a micromachined fixed-fixed beam example. These examples demonstrate that the macromodels obtained with the proposed reduction algorithm are significantly more accurate than models obtained with linear or the recently developed quadratic reduction techniques. Finally, it is shown tat the proposed technique is computationally inexpensive, and that the models can be constructed 'on-the-fly', to accelerate simulation of the system response.
Singapore-MIT Alliance (SMA)

碩士
中正理工學院
應用物理學系研究所
86
The flight stability analysis is very important in design of projectiles. As for nonlinear aerodynamic characteristics of the projectiles, the linear theory may become invalid. The objective of the present work is to build a nonlinear model for analysis of the angular motion and the dynamic behaviors of projectiles. In the present study, firstly, a non-dimensionalized set of equations for governing the angular motion of projectiles is developed. To account for the nonlinearities of the system, the involved aerodynamic derivatives, i.e. static stability, aerodynamic damping and lagging, and Magnus moment derivatives are considered as functions of attitude angles. Time evolutions of angle-of-attack and side-slipping angle are obtained by solving nonlinear equations by using forth-order Runge-Kutta scheme. Phase diagrams, power spectra and water-fall diagrams are used as tools for analysis of dynamic behaviors of the system. By investigating a typical projectile, it is found that the results with the nonlinear aerodynamic derivatives may be different from those in the linear analysis at some conditions. The frequencies of the angular motion are strongly influenced by a dimensionless spin rate, while the other parameters only have little effects.

The aim of this work is to investigate projection operator method of deriva- tion of equations of motion for reduced density matrix and apply it to a model open quantum system. We gradually pass from quantum mechanical model of a molecule with one vibrational degree of freedom to an example of open quantum system relevant in the theory of nonlinear spectroscopy. In the thesis we present results of numerical simulations of the time evolution of the open quantum system performed with a program written for this purpose. We are specially concerned with simulations of the solution of the time-convolutionless generalized master equation up to the a second order of the perturbation expan- sion, and we show that under certain conditions it provides an exact solution of the problem. The text also contains derivation of the recurrence relations for the Franck-Condon factors for the most general case of two quantum harmonic oscillators in one space dimension, i. e. transformation matrix between two bases of the L2 (R) space determined by the solutions of the time-independent Schrödinger equation appropriate for these oscillators. 1

The goal of this thesis is two-fold. On the one hand, it pursues to provide a contribution to the conjugate duality by proposing a new duality concept, which can be understood as an umbrella for different meaningful perturbation methods. On the other hand, this thesis aims to investigate minimax location problems by means of the duality concept introduced in the first part of this work, followed by a numerical approach using epigraphical splitting methods. After summarizing some elements of the convex analysis as well as introducing important results needed later, we consider an optimization problem with geometric and cone constraints, whose objective function is a composition of n+1 functions. For this problem we propose a conjugate dual problem, where the functions involved in the objective function of the primal problem are decomposed. Furthermore, we formulate generalized interior point regularity conditions for strong duality and give necessary and sufficient optimality conditions. As applications of this approach we determine the formulae of the conjugate as well as the biconjugate of the objective function of the primal problem and analyze an optimization problem having as objective function the sum of reciprocals of concave functions. In the second part of this thesis we discuss in the sense of the introduced duality concept three classes of minimax location problems. The first one consists of nonlinear and linear single minimax location problems with geometric constraints, where the maximum of nonlinear or linear functions composed with gauges between pairs of a new and existing points will be minimized. The version of the nonlinear location problem is additionally considered with set-up costs. The second class of minimax location problems deals with multifacility location problems as suggested by Drezner (1991), where for each given point the sum of weighted distances to all facilities plus set-up costs is determined and the maximal value of these sums is to be minimized. As the last and third class the classical multifacility location problem with geometrical constraints is considered in a generalized form where the maximum of gauges between pairs of new facilities and the maximum of gauges between pairs of new and existing facilities will be minimized. To each of these location problems associated dual problems will be formulated as well as corresponding duality statements and necessary and sufficient optimality conditions. To illustrate the results of the duality approach and to give a more detailed characterization of the relations between the location problems and their corresponding duals, we consider examples in the Euclidean space. This thesis ends with a numerical approach for solving minimax location problems by epigraphical splitting methods. In this framework, we give formulae for the projections onto the epigraphs of several sums of powers of weighted norms as well as formulae for the projection onto the epigraphs of gauges. Numerical experiments document the usefulness of our approach for the discussed location problems.

The present dissertation develops an invariant framework for 3D gesture comparison studies. 3D gesture comparison without Lagrangian models is challenging not only because of the lack of prediction provided by physics, but also because of a dual geometry representation, spatial dimensionality and non-linearity associated to 3D-kinematics. In 3D spaces, it is difficult to compare curves without an alignment operator since it is likely that discrete curves are not synchronized and do not share a common point in space. One has to assume that each and every single trajectory in the space is unique. The common answer is to assert the similitude between two or more trajectories as estimating an average distance error from the aligned curves, provided that the alignment operator is found. In order to avoid the alignment problem, the method uses differential geometry for position and orientation curves. Differential geometry not only reduces the spatial dimensionality but also achieves view invariance. However, the nonlinear signatures may be unbounded or singular. Yet, it is shown that pattern recognition between intrinsic signatures using correlations is robust for position and orientation alike. A new mapping for orientation sequences is introduced in order to treat quaternion and Euclidean intrinsic signatures alike. The new mapping projects a 4D-hyper-sphere for orientations onto a 3D-Euclidean volume. The projection uses the quaternion invariant distance to map rotation sequences into 3D-Euclidean curves. However, quaternion spaces are sectional discrete spaces. The significance is that continuous rotation functions can be only approximated for small angles. Rotation sequences with large angle variations can only be interpolated in discrete sections. The current dissertation introduces two multi-scale approaches that improve numerical stability and bound the signal energy content of the intrinsic signatures. The first is a multilevel least squares curve fitting method similar to Haar wavelet. The second is a geodesic distance anisotropic kernel filter. The methodology testing is carried out on 3D-gestures for obstetrics training. The study quantitatively assess the process of skill acquisition and transfer of manipulating obstetric forceps gestures. The results show that the multi-scale correlations with intrinsic signatures track and evaluate gesture differences between experts and trainees.