Practical Challenges to Calibrate a Heliostat with a Multi-Copter

Mechanical and Mechatronic Engineerin

Das "Surface Model" – Eine unsichere kontinuierliche Repräsentation des generischen Kameramodells und dessen Kalibrierung

Using digital cameras for measurement purposes requires the knowledge of the mapping between 3D world points and 2D positions on the image plane. There are many different mathematical models that provide this mapping for a specific imaging system. Grossberg and Nayar proposed a discrete generic camera model, which does not make any assumptions about the structure of this system. The model describes a digital camera by assigning an arbitrary viewing ray to each pixel of the camera image. This makes the model applicable to any kind of camera, especially also to non-central ones like onmidirectional catadioptrics. However, this model is difficult to use in practice, as there is no direct method for mapping a 3D point to the image or determining rays for subpixel image positions. In this work, the Surface Model, an uncertain continuous representation of the generic camera model, will be introduced. It uses a spline surface in 6D Plücker space to describe the camera. The interpolation abilities of the spline surface allow the viewing ray and its uncertainty for any (subpixel) position to be easily determined. Furthermore, the description facilitates the mapping from 3D world points to the image. The calibration of the generic model has to be performed pixel-wise and is technically involved and time-consuming. In this work, hand-held sparse planar chessboard patterns are used for calibration. The uncertainties of the corresponding image point measurements are taken into account and propagated during the complete calibration procedure to obtain an uncertain model. Simulations prove the validity of each step and the practical applicability of the procedure is shown by calibrating several real cameras of different types.Um digitale Kameras zu Vermessungszwecken einzusetzen muss der mathematische Zusammenhang zwischen 3D Weltpunkten und 2D Bildpunkten bekannt sein. Es existiert eine Vielzahl an mathematischen Modellen, welche diese Abbildung für spezifische Kamerasysteme beschreiben. Für deren Gültigkeit ist die Einhaltung der zugehörigen Randbedingungen, beispielsweise die hochgenaue Ausrichtung von Bildsensor, Linsen und Spiegeln, zwingend erforderlich. Andernfalls können fehlerhafte Messergebnisse die Folge sein. Um diese Problematik zu meiden, haben Grossberg und Nayar ein diskretes generisches Kameramodell vorgeschlagen, welches jedem einzelnen Pixel einen separaten Sehstrahl zuordnet. Somit kann jede erdenkliche Kamera beschrieben werden. Dies gilt auch für omnidirektionale catadioptrische Systeme, welche oftmals kein punktförmiges optisches Zentrum besitzen. Jedoch kann weder für jede beliebige Subpixel-Position ein Sehstrahl ermittelt werden, noch ist die Projektion eines beliebigen 3D-Punktes ins Kamerabild ohne weiteres möglich. In dieser Arbeit wird das "Surface Model" vorgestellt. Es dient als eine kontinuierliche Repräsentation des generischen Kameramodells, welche Modellunsicherheiten explizit berücksichtigt. Zur mathematischen Beschreibung wird eine Splineoberfläche im 6D Plücker-Raum genutzt. Deren Interpolationsfähigkeiten erlauben es, für jedwede Subpixel-Position direkt einen Sehstrahl zu ermitteln, sowie einen beliebigen 3D-Punkt ins Kamerabild zu projizieren. Die Kalibrierung des diskreten generischen Modells erfordert mehrere Messungen für jeden einzelnen Pixel. Um diesen aufwändigen Prozess zu vereinfachen, werden in dieser Arbeit von Hand platzierte planare Schachbrettmuster eingesetzt. Während der Kalibrierung treten unweigerlich Messungenauigkeiten auf. Beim hier vorgestellten Verfahren zur Parameterermittlung des Surface Models werden diese Unsicherheiten explizit zur Stabilisierung und Verbesserung der Genauigkeit genutzt. Dies resultiert in einem unsicheren Kameramodell, welches für die Anwendungen der Sehstrahlermittlung und der Punktprojektion Ergebnisunsicherheiten in Form von Kovarianzmatrizen zur Verfügung stellt. Mittels Simulationen wird die Anwendbarkeit sämtlicher vorgestellter Verfahren validiert. Durch die Kalibrierung verschiedener realer Kameras wird darüber hinaus deren praktische Nutzbarkeit aufgezeigt

Calibration and Reconstruction in Non-Central Axial Catadioptric Systems

Tese de doutoramento em Engenharia Electrotécnica e de Computadores, no ramo de Automação e Robótica, apresentada ao Departamento de Engenharia Eletrotécnica e de Computadores da Faculdade de Ciências e Tecnologia da Universidade de CoimbraEsta tese de doutoramento estuda sistemas de visão axiais catadióptricos nãocentrais, ou seja, sistemas com um espelho de simetria axial e uma câmara pinhole com o centro ótico pertencente ao eixo do espelho. São propostos métodos originais para calibração e reconstrução 3D usando a imagem de pontos e retas. Por “calibração” entende-se a reconstrução da geometria do sistema de visão, em termos da forma do espelho e da posição e orientação relativa camera/espelho. Para além disso, também se pretende estimar a pose da câmara em relação ao sistema de coordenadas do mundo, ou seja, a estimação dos parâmetros extrínsecos. Assume-se que a câmara pinhole está calibrada internamente a priori. Os algoritmos baseiam-se na utilização da imagem de um padrão de calibração planar, por exemplo, um padrão em xadrez. São propostos cinco algoritmos distintos. Um método estima a posição do eixo do espelho na imagem (de modo a determinar a orientação relativa câmara/ espelho) usando a invariância do cross-ratio. Outro método estima os parâmetros extrínsecos e a distância câma-ra/espelho, dado o conhecimento da forma do espelho. Baseia-se no estabelecimento de uma relação linear 3D/1D entre pontos do mundo e elementos da imagem, e na utilização do algoritmo Direct-Linear-Transformation (DLT) de modo a determinar um subconjunto dos parâmetros do sistema. Os parâmetros restantes são estimados usando procedimentos de otimização não-linear, numa variável de cada vez. Como uma extensão ao método anterior, também é proposta a estimação da forma do espelho como parte do processo de calibração. Este método utiliza a imagem de pontos e retas. Aproveita o facto de que todos os pontos num círculo da imagem centrado na origem possuem raios de retroprojeção que se intersetam num único ponto, formando um sistema de projeção central. Também é proposto um algoritmo para o caso particular de sistemas catadióptricos com espelhos esféricos, onde a calibração é alcançada através do ajuste de curvas quárticas às imagens de retas de um padrão de calibração. É derivada uma solução analítica, que é seguidamente refinada através de um procedimento de otimização não-linear. v Finalmente, considerando o caso de um sistema axial catadióptrico completamente calibrado, é feita a reconstrução da posição 3D de uma reta através de uma única imagem dessa mesma reta (que é possível devido ao facto de o sistema ser não-central). A reta é reconstruída a partir de 3 ou mais pontos na imagem, conhecendo o rácio da distância entre 3 pontos na reta (o que é uma assunção admissível em, por exemplo, ambientes estruturados com objetos arquitetónicos repetitivos, como janelas ou ladrilhos). É usada a invariância do cross-ratio de modo a restringir a localização da reta e, seguidamente, é feita a reconstrução a partir de um conjunto de pontos na imagem através de otimização não-linear. São apresentadas experiências com imagens reais e simuladas de modo a avaliar a precisão e robustez dos métodos.This PhD thesis focuses on non-central axial catadioptric vision systems, i.e. systems with an axial symmetrical mirror and a pinhole camera with its optical center located on the mirror axis. We propose novel methods to achieve calibration and 3D reconstruction from the image of points and lines. By “calibration” we mean the reconstruction of the vision system geometry, in terms of mirror shape and mirror/camera relative position and orientation. We also aim at the estimation of the pose of the camera w.r.t. the world coordinates frame, i.e. the estimation of the extrinsic parameters. We assume that the pinhole camera is internally calibrated a priori. The algorithms rely on the image of a planar calibration pattern, e.g. a checkerboard. We propose five distinct algorithms. One method aims at estimating the position of the mirror axis in the image (to determine camera/mirror relative orientation) using the cross-ratio as an invariant. Another method estimates the extrinsic parameters and camera/mirror distance given the knowledge of the mirror shape. It relies on establishing a 3D/1D linear relation between world points and image features, and using the Direct- Linear-Transformation (DLT) algorithm to obtain a subset of the system parameters. The remaining parameters are estimated using non-linear optimization, on a single variable at a time. As an extension to the previous method, we propose the estimation of the mirror shape as part of the calibration process. This method requires the image of points and lines. It uses the fact that all points in any image circle centered at the origin have backprojection rays that intersect at a single point, effectively becoming a central projection system. We also propose an algorithm for the particular case of catadioptric systems with spherical mirrors, where the calibration is achieved by fitting quartic curves to the images of lines in a calibration pattern. An analytical solution is derived, which is later refined by a non-linear optimization procedure. Finally, we consider the case of a fully calibrated non-central axial catadioptric system, and aim at the reconstruction of the 3D position of a line from a single vii image of that line (which is possible because the system is non-central). The line is reconstructed from 3 or more image points, given the knowledge of the distance ratio of 3 points in the line (a fair assumption in, for example, structured environments with repetitive architectural features, like windows or tiles). We use cross-ratio as an invariant to constrain the line localization and then perform the reconstruction from a set of image points through non-linear optimization. Experiments with simulated and real images are performed to evaluate the accuracy and robustness of the methods.FCT - PROTEC SFRH/BD/50281/200

Multicamera System for Automatic Positioning of Objects in Game Sports

Garantir um sistema com múltiplas câmaras que seja capaz de extrair dados 3D da posição de uma bola durante um evento desportivo, através da análise e teste de técnicas de visão computacional (calibração de câmaras e reconstrução 3D)

Localización por visión omnidireccional para asistencia personal

El objetivo de este proyecto es el desarrollo de una aplicación SLAM para una cámara omnidireccional a partir de una aplicación EKF-SLAM Monocular en tiempo real, programada en C++ y diseñada para su uso con cámaras convencionales. Para ello, se han realizado modificaciones sobre dos aspectos básicos: el modelo de proyección y el descriptor de puntos característicos. El modelo de proyección debe ser adaptado a uno apropiado para sistemas omnidireccionales. Se toma el Modelo de la Esfera, un modelo no lineal que permite calcular la proyección de puntos del espacio en puntos de la imagen omnidireccional, y de puntos en la imagen en rayos tridimensionales en los que se encuentra el punto. El descriptor de puntos característicos permite identificar los puntos en una imagen. Las imágenes omnidireccionales conllevan un modelo de proyección más complejo, así como una importante deformación y una escala variable en la imagen debido al cambio de resolución a lo largo de la dirección radial. Por lo tanto, se implementa un nuevo descriptor de puntos para cámaras omnidireccionales que los haga invariantes a cambios de escala y rotación en la imagen. Finalmente se han llevado a cabo varios experimentos divididos en dos fases. En la primera fase se han utilizado datos facilitados por Rawseeds para hacer una comparación entre el nuevo descriptor implementado y el descriptor normal. Los resultados de estos experimentos muestran que el nuevo descriptor tiene un mejor rendimiento en el emparejamiento, que se traduce en una mejora de rendimiento en el SLAM. En la segunda fase se ha experimentado con secuencias tomadas en el Campus Río Ebro con un casco-cámara del Grupo de Robótica, Visión y Tiempo Real, comparando los resultados obtenidos a partir de la aplicación SLAM utilizando el nuevo descriptor con los obtenidos con un dispositivo GPS. Los resultados muestran una gran precisión en la estimación de la trayectoria en un recorrido corto, mientras que en un recorrido largo, la precisión disminuye considerablemente. Además de la deriva del error propia del algoritmo EKF-SLAM por tratarse de un algoritmo incremental, se han establecido dos posibles causas de esta disminución de la precisión, ambas consecuencia de la inobservabilidad de la escala de un SLAM monocular: por un lado, la deriva de escala a lo largo del recorrido debido a la gran longitud de este, y por otro lado, la existencia de zonas del entorno con diferentes escalas alrededor de una misma localización y que afectaría en especial a cámaras omnidireccionales por su gran ángulo de visión

Laser-plasma interactions as tools for studying processes in quantum electrodynamics

Conventional particle accelerators and astronomical observations have long been some of the only tools for studying processes in high energy physics. The development of laser-plasma sources and high gradient accelerators will therefore be a key asset to these studies. In particular, laser-plasma accelerators have favourable spatial and temporal properties for studies into intense processes, and can be readily coupled to a wide array of other laser-plasma sources creating unique environments. Here, coupling to an X-ray source and intense laser focus were used to study processes in quantum electrodynamics. To study the linear Breit-Wheeler process, a 40 ps laser was used to drive a volumetric X-ray emitter. Line emission from a thin-foil Ge target, produced a highly efficient (3.4%), dense source of 1.3 − 1.9 keV X-rays, with 3 ± 1 (stat.) ±0.4 (sys.) ×10^{12} photons/eV/sphere. These X-rays were collided with bremsstrahlung gamma rays (with energies up to 800 MeV) to investigate electron-positron pair production. The X-ray source was well-optimised for studying this interaction, and would allow the detection of Breit-Wheeler pairs if used with a moderately improved electron beam for generating bremsstrahlung (3× the highest electron energy and 5× the total charge, as achieved previously). This would constitute the first laser-plasma photon- photon collider with low virtuality (energy off mass-shell ≈ 10^{−20} MeV^2). In order to differentiate between competing models of electron radiation reaction in strong field quantum electrodynamics, a narrow energy-spread electron beam was studied. By utilising shock injection into a laser wakefield accelerator, a high energy (1260±40 MeV), narrow energy- spread (4.1±0.9 %) beam was generated. This is one of only a few studies that have successfully achieved these electron beam properties. While the shot-to-shot reproducibility of the electron beam was limited to 60%, the relative energy-spread was sufficiently small that differentiation of radiation reaction models could be readily achieved in future experiments. With the upcoming commissioning of many multi-PW laser facilities, these studies demonstrate how active research into quantum electrodynamics can be achieved on the smaller, more accessible, laser-laboratory scale.Open Acces

A NEW METHOD OF WAVELENGTH SCANNING INTERFEROMETRY FOR INSPECTING SURFACES WITH MULTI-SIDE HIGH-SLOPED FACETS

With the development of modern advanced manufacturing technologies, the requirements for ultra-precision structured surfaces are increasing rapidly for both high value-added products and scientific research. Examples of the components encompassing the structures include brightness enhancement film (BEF), optical gratings and so forth. Besides, specially designed structured surfaces, namely metamaterials can lead to specified desirable coherence, angular or spatial characteristics that the natural materials do not possess. This promising field attracts a large amount of funding and investments. However, owing to a lack of effective means of inspecting the structured surfaces, the manufacturing process is heavily reliant on the experience of fabrication operators adopting an expensive trial-and-error approach, resulting in high scrap rates up to 50-70% of the manufactured items. Therefore, overcoming this challenge becomes increasingly valuable. The thesis proposes a novel methodology to tackle this challenge by setting up an apparatus encompassing multiple measurement probes to attain the dataset for each facet of the structured surface and then blending the acquired datasets together, based on the relative location of the probes, which is achieved via the system calibration. The method relies on wavelength scanning interferometry (WSI), which can achieve areal measurement with axial resolutions approaching the nanometre without the requirement for the mechanical scanning of either the sample or optics, unlike comparable techniques such as coherence scanning interferometry (CSI). This lack of mechanical scanning opens up the possibility of using a multi-probe optics system to provide simultaneous measurement with multi adjacent fields of view. The thesis presents a proof-of-principle demonstration of a dual-probe wavelength scanning interferometry (DPWSI) system capable of measuring near-right-angle V-groove structures in a single measurement acquisition. The optical system comprises dual probes, with orthogonal measurement planes. For a given probe, a range of V-groove angles is measurable, limited by the acceptance angle of the objective lenses employed. This range can be expanded further by designing equivalent probe heads with varying angular separation. More complicated structured surfaces can be inspected by increasing the number of probes. The fringe analysis algorithms for WSI are discussed in detail, some improvements are proposed, and experimental validation is conducted. The scheme for calibrating the DPSWI system and obtaining the relative location between the probes to achieve the whole topography is implemented and presented in full. The appraisal of the DPWSI system is also carried out using a multi-step diamond-turned specimen and a sawtooth brightness enhancement film (BEF). The results showed that the proposed method could achieve the inspection of the near-right-angle V-groove structures with submicrometre scale vertical resolution and micrometre level lateral resolution

3rd International Workshop on Instrumentation for Planetary Missions : October 24–27, 2016, Pasadena, California

The purpose of this workshop is to provide a forum for collaboration, exchange of ideas and information, and discussions in the area of the instruments, subsystems, and other payload-related technologies needed to address planetary science questions. The agenda will compose a broad survey of the current state-of-the-art and emerging capabilities in instrumentation available for future planetary missions.Universities Space Research Association (USRA); Lunar and Planetary Institute (LPI); Jet Propulsion Laboratory (JPL)Conveners: Sabrina Feldman, Jet Propulsion Laboratory, David Beaty, Jet Propulsion Laboratory ; Science Organizing Committee: Carlton Allen, Johnson Space Center (retired) [and 12 others