Interaktiv projicerad förstärkt verklighet är ett delområde inom projicerad förstärktverklighet, där interaktiviteten handlar om att projicera virtuelldata på en entitet somär rörlig. Denna projektion kan åstadkommas genom att använda en kalibrerad projektor-djupkamerasystem som detekterar entitet med hjälp av datorseende. Dettainteraktiva system har varierande antal tillämpningsområden, dock framkommer enkritisk problemformulering, vilket är noggrannheten för dessa system. Noggrannheten i detta fall är hur korrekt projektionen sker på den specifika entiteten, noggrannheten är därför en viktig aspekt för att validera ifall vissa tillämpningar är möjliga implementera. Lösningen för detta problem är att implementera interaktiv projicerad förstärkt verklighet och utföra prototyptester med det implementerade systemet och sedan vidare analysera noggrannheten med testdata. Prototypen kalibrerasmed befintliga verktyg från tidigare studier, detekterar med hjälp av positionsuppskattning och kan sedan projicera punkter på specifika kroppsdelar som även följerpersonen vid rörelse. Resultatet som framkom blev en prototyp som testades för noggrannheten. Testernasker med hjälp av datorseende för att extrahera mätdata såsom projicerade punktenoch förväntade punkten. Från analysen av testdata framkom det att projektionensnoggrannhet är lämplig för tillämpningar som inte kräver exceptionell noggrannhet,såsom nöje, konst, spel och med mera. Ytterligare forskning krävs för användningsområden som kräver exceptionell noggrannhet som tillämpningar inom sjukvård ochkirurgi. / Interactive projected augmented reality is a subfield within projected augmented reality, where the interactivity is about projecting virtual data onto an entity that canpotentially be in movement. This projection can be accomplished by using a calibrated projector-depth camera system that detects entities using computer vision.This interactive system has a varying number of application areas; however, a criticalproblem emerges, which is the accuracy of these systems. The accuracy in this caseis how correctly the projection takes place on the specific entity, the accuracy istherefore an important aspect to validate if certain applications are possible to implement correctly. The solution for this problem is by implementing interactive projectedaugmented reality and perform prototype tests with the implemented system andthen further analyzing the accuracy with test data. The prototype is calibrated withexisting tools from previous studies, detects using pose detection, which can thenproject points on specific body parts that also follows the person during movement.The result that got developed was a prototype that was tested for accuracy. The testsare done using computer vision to extract measurement data such as the projectedpoint and the expected point. The result from the analysis of the test data showedthat the accuracy of the projection is suitable for applications that do not requireexceptional accuracy, such as entertainment, art, games and so on. Further research is required for applications that require exceptional accuracy such ashealthcare and surgical applications.

Algebro-Differentialgleichungen (engl. differential-algebraic equations - DAEs) sind implizite singuläre gewöhnliche Differentialgleichungen, die restringierte dynamische Prozesse beschreiben. Sie unterscheiden sich von expliziten gewöhnlichen Differentialgleichungen dahingehend, dass Anfangswerte nicht beliebig vorgegeben werden können. Weiterhin sind in einer DAE neben Integrations- auch Differentiationsaufgaben involviert. Der Differentiationsindex gibt an, wieviele Differentiationen zur Lösung notwendig sind. Seit den 1980er Jahren wird vorwiegend an der Charakterisierung und Klassifizierung regulärer DAEs und der Konstruktion nebst Fundierung von Integrationsmethoden gearbeitet. I. Higueras, R. März und C. Tischendorf haben gezeigt, dass man lineare DAEs mit properem Hauptterm, A(t)(D(t)x(t))'' + B(t)x(t) = q(t), die regulär mit Traktabilitätsindex 2 sind, zuverlässig numerisch integrieren kann - im Unterschied zu linearen DAEs in Standardform. In Publikationen von R. Riaza und R. März wird die Klassifizierungen kritischer Punkten von linearen DAEs an die Verletzung bestimmter Rangbedingungen von Matrixfunktionen im Rahmen des Traktabilitätsindexes geknüpft. Im wesentlichen heißt ein kritischer Punkt harmlos, wenn der durch die inhärente Differentialgleichung beschriebene Fluß nicht tangiert ist. Gegenstand der vorliegenden Arbeit sind lineare quasi-proper formulierte DAEs. Es werden Index 2 DAEs mit harmlosen kritischen Punkten charakterisiert. Unter Verwendung von quasi-zulässigen Projektorfunktionen können neben DAEs, die fast überall gleiche charakteristische Werte haben, nun erstmalig auch solche mit Indexwechseln behandelt werden. Der Hauptteil der Arbeit besteht im Nachweis von Durchführbarkeit, Konvergenz und nur schwacher Instabilität von numerischen Integrationsmethoden (BDF, IRK(DAE)) für lineare Index 2 DAEs mit harmlosen kritischen Punkten, sowie in der Entwicklung von Fehlerschätzern und Schrittweitensteuerung. / Differential-algebraic equations (DAEs) are implicit singular ordinary differential equations, which describe dynamical processes that are restricted by some constraints. In contrast to explicit regular ordinary differential equations, for a DAE not any value can be imposed as an initial condition. Furthermore, DAEs involve not only integration problems but also differentiation problems. The differentiation index of a DAE indicates the number of differentiations required in order to solve a DAE. Since the 1980th, research focuses primarily on the characterization and classification of regular problem classes and the construction and foundation of integration methods for simulation software. I. Higueras, R. Maerz, and C. Tischendorf have shown that one can reliably integrate a general linear DAE with a properly stated leading term, A(t)(D(t)x(t))'' + B(t)x(t) = q(t), which is regular with tractability index 2 - in contrast to linear standard form DAEs. The first classification of critical points of linear DAEs has been published by R. Riaza and R. Maerz. Based on the tractability index, critical points are classified according to failures of certain rank conditions of matrix functions. Essentially, a critical point is said to be harmless, if the flow described by the inherent differential equation is not affected. The subject of this work are quasi-proper linear DAEs. Index-2 DAEs with harmless critical points are characterized. Under the application of quasi-admissible projector functions. Besides DAEs which have almost everywhere the same characteristic values, DAEs with index changes can now be discussed for the first time. The main part of the work is to provide a proof of feasibility, convergence, and only weak instability of numerical integration methods (BDF, IRK (DAE)) for linear index-2 DAEs with harmless critical points, as well as the development and testing of error estimators and stepsize control.

La composition interne de notre planète est un vaste sujet d’étude auquel participent de nombreuses disciplines scientifiques. Les conditions extrêmes de pression et de température qui règnent à l’intérieur du noyau (constitué principalement de fer et de nickel) et du manteau terrestre (à base de pérovskites) rendent très difficile la détermination de leur compositions exactes. Ce projet de thèse contribue aux études récentes dont l’enjeu est de déterminer plus précisément le chimisme des minéraux présents. Il a pour objet le développement d’un outil de calcul des vitesses de propagation des ondes sismiques a l’aide d’une méthode fondée sur les simulations ab initio. Ces vitesses sont déduites du tenseur élastique complet, incluant la relaxation atomique et les modifications induites du champ cristallin. Nous utilisons l’approche de la théorie de perturbation de la fonctionnelle de la densité (DFPT) qui permet de s'affranchir des incertitudes numériques qu’impliquent les méthodes classiques basées sur des différences finies. Nous combinons cette approche avec le formalisme « Projector Augmented-Wave » (PAW) qui permet, avec un coût de calcul faible, de prendre en compte tous les électrons du système. Nous avons appliqué la méthode sur des matériaux du noyau et du manteau terrestre. Nous avons déterminé les effets de différents éléments légers (Si, S, C, O et H) sur les vitesses de propagation des ondes sismiques dans le fer pur ainsi que celui de l’aluminium dans la pérovskite MgSiO3. / The internal composition of our planet is a large topic of study and involves many scientific disciplines. The extreme conditions of pressure and temperature prevailing inside the core (consisting primarily of iron and nickel) and the mantle (consisting mainly of perovskites) make the determination of the exact compositions very difficult. This thesis contributes to recent studies whose aim is to determine more accurately the chemistry of these minerals. Its purpose is the development of a tool for the calculation of seismic wave velocities within methods based on ab-initio simulations. These velocities are calculated from the full elastic tensor, including the atomic relaxation and induced changes in the crystal field. We use the approach of the density functional perturbation theory (DFPT) to eliminate numerical uncertainties induced by conventional methods based on finite differences. We combine this approach with the « Projector Augmented-Wave » (PAW) formalism that takes into account all the electrons of the system with a low computational cost. We apply the method on core and mantle materials and we determine the effects of various lights elements (Si, S, C, O and H) on the seismic wave velocities of pure iron, as well as the effect of aluminum in the perovskite MgSiO3.

Cette thèse porte sur la reconstruction active de modèles 3D à l’aide d’une caméra et d’un projecteur. Les méthodes de reconstruction standards utilisent des motifs de lumière codée qui ont leurs forces et leurs faiblesses. Nous introduisons de nouveaux motifs basés sur la lumière non structurée afin de pallier aux manques des méthodes existantes. Les travaux présentés s’articulent autour de trois axes : la robustesse, la précision et finalement la comparaison des patrons de lumière non structurée aux autres méthodes. Les patrons de lumière non structurée se différencient en premier lieu par leur robustesse aux interréflexions et aux discontinuités de profondeur. Ils sont conçus de sorte à homogénéiser la quantité d’illumination indirecte causée par la projection sur des surfaces difficiles. En contrepartie, la mise en correspondance des images projetées et capturées est plus complexe qu’avec les méthodes dites structurées. Une méthode d’appariement probabiliste et efficace est proposée afin de résoudre ce problème. Un autre aspect important des reconstructions basées sur la lumière non structurée est la capacité de retrouver des correspondances sous-pixels, c’est-à-dire à un niveau de précision plus fin que le pixel. Nous présentons une méthode de génération de code de très grande longueur à partir des motifs de lumière non structurée. Ces codes ont l’avantage double de permettre l’extraction de correspondances plus précises tout en requérant l’utilisation de moins d’images. Cette contribution place notre méthode parmi les meilleures au niveau de la précision tout en garantissant une très bonne robustesse. Finalement, la dernière partie de cette thèse s’intéresse à la comparaison des méthodes existantes, en particulier sur la relation entre la quantité d’images projetées et la qualité de la reconstruction. Bien que certaines méthodes nécessitent un nombre constant d’images, d’autres, comme la nôtre, peuvent se contenter d’en utiliser moins aux dépens d’une qualité moindre. Nous proposons une méthode simple pour établir une correspondance optimale pouvant servir de référence à des fins de comparaison. Enfin, nous présentons des méthodes hybrides qui donnent de très bons résultats avec peu d’images. / This thesis deals with active 3D reconstruction from camera-projector systems. Standard reconstruction methods use coded light patterns that come with their strengths and weaknesses. We introduce unstructured light patterns that feature several improvements compared to the current state of the art. The research presented revolves around three main axes : robustness, precision and comparison of existing unstructured light patterns to existing methods. Unstructured light patterns stand out first and foremost by their robustness to interreflections and depth discontinuities. They are specifically designed to homogenize the indirect lighting generated by their projection on hard to scan surfaces. The downside of these patterns is that matching projected and captured images is not straightforward anymore. A probabilistic correspondence method is formulated to solve this problem efficiently. Another important aspect of reconstruction obtained with unstructured light pat- terns is their ability to recover subpixel correspondences, that is with a precision finer than the pixel level. We present a method to produce long codes using unstructured light. These codes enable us to extract more precise correspondences while requiring less patterns. This contribution makes our method one of the most accurate - yet robust to standard challenges - method of active reconstruction in the domain. Finally, the last part of this thesis adresses the comparison of existing reconstruction methods on several aspects, but mainly on the impact of using less and less patterns on the quality of the reconstruction. While some methods need a fixed number of images, some, like ours, can accommodate fewer patterns in exchange for some quality loss. We devise a simple method to capture an optimal correspondence map that can be used as a groundtruth for comparison purposes. Last, we present several hybrid methods that perform quite well even with few images.

Quantum mechanics became a foundation for incessant development of versatile computational methods for analysis of chemical and physical properties of molecules and crystals. A huge progress has been made in the fifield of density functional theory, since nowadays this theory offers the best compromise between precision of results and efficiency fiof computation. The chemical bonding analysis can be easily performed with real space methods based on chemical concepts introduced via partitioning of real space into chemically meaningful domains, since the orbital based approach is not well applicable due to the delocalized nature of plane waves. However the practical usage of those methods often requires a signifificant amount of computational resources. Some methods require the evaluation of so called domain overlap matrices, that is a formidable task for complex and low-symmetry systems. In the present research the author enables the investigation of complex solid compounds with real space chemical bonding indicators by introducing the derivation of the expression for the evaluation of the domain overlap matrix elements from the projected-augmented wave method. The corresponding program module was developed, which is capable to perform the real space chemical bonding analysis with a number of methods, like electron localizability indicators, electron localization function, localization/delocalization indices and domain averaged Fermi hole orbitals. The efficiency and the accuracy of the developed implementation is demonstrated by the comparison with the domain overlap matrix elements evaluation from the full-potential linearized augmented plane wave method on a set of simple compounds with three atoms per primitive cell at most. A set of complex periodic structures is analyzed and the capability of the present implementation to unravel intricate chemical bonding patterns is demonstrated.

A programmable illuminating system (PIS) uses a commercial multimedia projector together with a suitable optical relay system in order to illuminate specimens under microscope with transmitted light. The theoretical part of the diploma thesis describes some methods used in the optical transmission microscopy. All of these methods employ physical masks placed in the condenser front focal plane. In the case of the traditional methods the masks are used to enhance contrast (e.g. dark-field illumination) and resolution (oblique illumination). One of the methods (a condenser with rotating aperture) provides the information about the three-dimensionality of the specimen. The next part of the thesis contains the theory and the basic classification of the illuminating systems used in the optical transmission microscopy. An optical and mechanical design of the optical relay system used for PIS is introduced. The experimental part shows the results made with two different PIS arrangements. It was shown on two different specimens that the PIS provides the same illumination as the classical methods. It was also proved that the PIS can simulate the rotating aperture in the condenser front focal plane and thus to give the information about the three-dimensionality of the specimen. Some new static and dynamic illuminating methods were introduced.