Automatic Reconstruction of Textured 3D Models

Three dimensional modeling and visualization of environments is an increasingly important problem. This work addresses the problem of automatic 3D reconstruction and we present a system for unsupervised reconstruction of textured 3D models in the context of modeling indoor environments. We present solutions to all aspects of the modeling process and an integrated system for the automatic creation of large scale 3D models

Automatic Reconstruction of Textured 3D Models

Three dimensional modeling and visualization of environments is an increasingly important problem. This work addresses the problem of automatic 3D reconstruction and we present a system for unsupervised reconstruction of textured 3D models in the context of modeling indoor environments. We present solutions to all aspects of the modeling process and an integrated system for the automatic creation of large scale 3D models

Monocular Pose Estimation Based on Global and Local Features

The presented thesis work deals with several mathematical and practical aspects of the monocular pose estimation problem. Pose estimation means to estimate the position and orientation of a model object with respect to a camera used as a sensor element. Three main aspects of the pose estimation problem are considered. These are the model representations, correspondence search and pose computation. Free-form contours and surfaces are considered for the approaches presented in this work. The pose estimation problem and the global representation of free-form contours and surfaces are defined in the mathematical framework of the conformal geometric algebra (CGA), which allows a compact and linear modeling of the monocular pose estimation scenario. Additionally, a new local representation of these entities is presented which is also defined in CGA. Furthermore, it allows the extraction of local feature information of these models in 3D space and in the image plane. This local information is combined with the global contour information obtained from the global representations in order to improve the pose estimation algorithms. The main contribution of this work is the introduction of new variants of the iterative closest point (ICP) algorithm based on the combination of local and global features. Sets of compatible model and image features are obtained from the proposed local model representation of free-form contours. This allows to translate the correspondence search problem onto the image plane and to use the feature information to develop new correspondence search criteria. The structural ICP algorithm is defined as a variant of the classical ICP algorithm with additional model and image structural constraints. Initially, this new variant is applied to planar 3D free-form contours. Then, the feature extraction process is adapted to the case of free-form surfaces. This allows to define the correlation ICP algorithm for free-form surfaces. In this case, the minimal Euclidean distance criterion is replaced by a feature correlation measure. The addition of structural information in the search process results in better conditioned correspondences and therefore in a better computed pose. Furthermore, global information (position and orientation) is used in combination with the correlation ICP to simplify and improve the pre-alignment approaches for the monocular pose estimation. Finally, all the presented approaches are combined to handle the pose estimation of surfaces when partial occlusions are present in the image. Experiments made on synthetic and real data are presented to demonstrate the robustness and behavior of the new ICP variants in comparison with standard approaches

Pose Estimation Revisited

The presented thesis deals with the 2D-3D pose estimation problem. Pose estimation means to estimate the relative position and orientation of a 3D object with respect to a reference camera system. The main focus concentrates on the geometric modeling and application of the pose problem. To deal with the different geometric spaces (Euclidean, affine and projective ones), a homogeneous model for conformal geometry is applied in the geometric algebra framework. It allows for a compact and linear modeling of the pose scenario. In the chosen embedding of the pose problem, a rigid body motion is represented as an orthogonal transformation whose parameters can be estimated efficiently in the corresponding Lie algebra. In addition, the chosen algebraic embedding allows the modeling of extended features derived from sphere concepts in contrast to point concepts used in classical vector calculus. For pose estimation, 3D object models are further treated two-fold, feature based and free-form based: While the feature based pose scenarios provide constraint equations to link different image and object entities, the free-form approach for pose estimation is achieved by applying extracted image silhouettes from objects on 3D free-form contours modeled by 3D Fourier descriptors. In conformal geometric algebra an extended scenario is derived, which deals beside point features with higher-order features such as lines, planes, circles, spheres, kinematic chains or cycloidal curves. This scenario is extended to general free-form contours by interpreting contours generated with 3D Fourier descriptors as n-times nested cycloidal curves. The introduced method for shape modeling links signal theory, geometry and kinematics and is applied advantageously for 2D-3D silhouette based free-form pose estimation. The experiments show the real-time capability and noise stability of the algorithms. Experiments of a running navigation system with visual self-localization are also presented

Konforme geometrische Algebra und deren Anwendungen auf stochastische Optimierungsprobleme im Bereich 3D-Vision

In the present work, the modeling capabilities of conformal geometric algebra (CGA) are harnessed to approach typical problems from the research field of 3D-vision. This increasingly popular methodology is then extended in a new fashion by the integration of a least squares technique into the framework of CGA. Specifically, choosing the linear Gauss-Helmert model as the basis, the most general variant of least squares adjustment can be brought into operation. The result is a new versatile parameter estimation, termed GH-method, that reconciles two different mathematical areas, that is algebra and stochastics, under the umbrella of geometry. The main concern of the thesis is to show up the advantages inhering with this combination. Monocular pose estimation, from the subject 3D-vision, is the applicational focus of this thesis; given a picture of a scene, position and orientation of the image capturing vision system with respect to an external coordinate system define the pose. The developed parameter estimation technique is applied to different variants of this problem. Parameters are encoded by the algebra elements, called multivectors. They can be geometric objects as a circle, geometric operators as a rotation or likewise the pose. In the conducted pose experiments, observations are image pixels with associated uncertainties. The high accuracy achieved throughout all experiments confirms the competitiveness of the proposed estimation technique. Central to this work is also the consideration of omnidirectional vision using a paracatadioptric imaging sensor. It is demonstrated that CGA provides the ideal framework to model the related image formation. Two variants of the perspective pose estimation problem are adapted to the omnidirectional case. A new formalization of the epipolar geometry of two images in terms of CGA is developed, from which new insights into the structures behind the essential and the fundamental matrix, respectively, are drawn. Renowned standard approaches are shown to implicitly make use of CGA. Finally, an invocation of the GH-method for estimating epipoles is presented. Experimental results substantiate the goodness of this approach. Next to the detailed elucidations on parameter estimation, this text also gives a comprehensive introduction to geometric algebra, its tensor representation, the conformal space and the respective conformal geometric algebra. A valuable contribution is especially the analytic investigation into the geometric capabilities of CGA.Die vorliegende Arbeit ist motiviert durch die im Forschungszweig Computer Vision (CV) der Informatik typisch auftretenden geometrischen Problemstellungen auf der Grundlage von digitalen Bildaufnahmen. Hierzu zählt die Berechnung einer optimal durch eine Menge von Bildpunkten verlaufende Kurve, die Bestimmung der Epipolargeometrie, das Schätzen der Pose eines Objektes oder die 3D-Rekonstruktion. Diese Klasse von Problemen lässt sich durch den Einsatz der geometrischen Algebra (GA) – so werden unter geometrischen Aspekten besonders interessante Clifford Algebren bezeichnet – in überaus prägnanter und geschlossener Form modellieren. Dieser mit wachsender Akzeptanz verfolgte Ansatz, der beständig durch den Lehrstuhl „Kognitive Systeme“ der Universität Kiel weiterentwickelt wird, ist zentraler Bestandteile der Dissertation. Speziell wird die „konforme geometrische Algebra“ (CGA), die auf einer nicht-linearen Einbettung des euklidischen 3D-Raumes in einen fünfdimensionalen projektiven konformen Raum beruht, eingesetzt. Die Elemente dieser Algebra erlauben die Repräsentation geometrischer Basisentitäten, im wesentlichen Punkte, Linien, Kreise, Kugeln und Ebenen. Eine Vielzahl von Operationen ist möglich; besonders interessant sind die Transformationen der enthaltenen konformen Gruppe sowie die Möglichkeit algebraisch mit Unterräumen zu rechnen, d.h. diese zu vergrößern, zu schneiden oder Inzidenzen abzufragen. Den zweiten wichtigen Bestandteil der Arbeit stellt ein für die oben genannten Problemstellungen typisches stochastischen Verfahren dar – die Ausgleichsrechnung nach der Methode der kleinsten Quadrate. Deren allgemeinste Form erwächst aus der Verwendung des aus der Geodäsie bekannten linearen Gauß-Helmert (GH) Modells. Der resultierende GH-Schätzer zeigt alle Optimalitätseigenschaften wie minimale Varianz und Erwartungstreue. Eine der geometrischen Algebra inhärente Tensordarstellung stellt eine geeignete numerische Schnittstelle zwischen CGA und der GH-Schätzmethode zur Verfügung. Aufgrund der Bilinearität des Algebraprodukts lässt sich so ebenfalls das Konzept der Fehlerfortpflanzung, ein wichtiges Instrument der Ausgleichsrechnung, mit hoher Genauigkeit auf die Operationen der Algebra ausdehnen. Im Ergebnis entsteht ein neues universelles Parameterschätzverfahren zur Bestimmung der des jeweiligen Problems zugrundeliegenden Variablen. Ziel der vorliegenden Arbeit ist es auch, die aus der Verbindung von Algebra und Stochastik entstehenden Vorteile anhand von typischen CV-Anwendungen herauszustellen. Den Schwerpunkt hierfür bildet die Schätzung der Pose (Position und Orientierung eines Objekts bezüglich eines objektfremden Koordinatensystems), z.B. die eines Roboters anhand eines vom Roboter aufgenommenen Kamerabildes. Es wird ebenfalls gezeigt, dass CGA den optimalen Rahmen zur Modellierung omnidirektionaler Bildgebungsverfahren bietet, falls diese auf einem katadioptrischen System mit parabolischem Spiegel beruhen. Als omnidirektionale Anwendungen werden Posenschätzung sowie die Bestimmung der Epipolargeometrie präsentiert. Die erreichte Güte der GH-Parameterschätzung in den einzelnen Anwendungen wird jeweils durch experimentell gewonnene Resultate untermauert. Neben den umfangreichen Ausführungen zur Parameterschätzung liefert diese Arbeit auch eine detaillierte Einführung und Herleitung der geometrischen Algebra. Besonderes Augenmerk ist auch auf die analytische Darlegung der konformen geometrischen Algebra zu richten

Monocular pose estimation based on global and local features

The presented thesis work deals with several mathematical and practical aspects of the monocular pose estimation problem. Pose estimation means to estimate the position and orientation of a model object with respect to a camera used as a sensor element. Threemain aspects of the pose estimation problem are considered. These are themodel representations, correspondence search and pose computation. Free-form contours and surfaces are considered for the approaches presented in this work. The pose estimation problem and the global representation of free-form contours and surfaces are defined in the mathematical framework of the conformal geometric algebra (CGA), which allows a compact and linear modeling of the monocular pose estimation scenario. Additionally, a new local representation of these entities is presented which is also defined in CGA. Furthermore, it allows the extraction of local feature information of these models in 3D space and in the image plane. This local information is combined with the global contour information obtained from the global representations in order to improve the pose estimation algorithms. The main contribution of this work is the introduction of new variants of the iterative closest point (ICP) algorithm based on the combination of local and global features. Sets of compatible model and image features are obtained from the proposed local model representation of free-form contours. This allows to translate the correspondence search problem onto the image plane and to use the feature information to develop new correspondence search criteria. The structural ICP algorithm is defined as a variant of the classical ICP algorithm with additional model and image structural constraints. Initially, this new variant is applied to planar 3D free-form contours. Then, the feature extraction process is adapted to the case of free-form surfaces. This allows to define the correlation ICP algorithm for free-form surfaces. In this case, the minimal Euclidean distance criterion is replaced by a feature correlation measure. The addition of structural information in the search process results in better conditioned correspondences and therefore in a better computed pose. Furthermore, global information (position and orientation) is used in combination with the correlation ICP to simplify and improve the pre-alignment approaches for the monocular pose estimation. Finally, all the presented approaches are combined to handle the pose estimation of surfaces when partial occlusions are present in the image. Experiments made on synthetic and real data are presented to demonstrate the robustness and behavior of the new ICP variants in comparison with standard approaches

Visual Odometry and Sparse Scene Reconstruction for UAVs with a Multi-Fisheye Camera System

Autonomously operating UAVs demand a fast localization for navigation, to actively explore unknown areas and to create maps. For pose estimation, many UAV systems make use of a combination of GPS receivers and inertial sensor units (IMU). However, GPS signal coverage may go down occasionally, especially in the close vicinity of objects, and precise IMUs are too heavy to be carried by lightweight UAVs. This and the high cost of high quality IMU motivate the use of inexpensive vision based sensors for localization using visual odometry or visual SLAM (simultaneous localization and mapping) techniques. The first contribution of this thesis is a more general approach to bundle adjustment with an extended version of the projective coplanarity equation which enables us to make use of omnidirectional multi-camera systems which may consist of fisheye cameras that can capture a large field of view with one shot. We use ray directions as observations instead of image points which is why our approach does not rely on a specific projection model assuming a central projection. In addition, our approach allows the integration and estimation of points at infinity, which classical bundle adjustments are not capable of. We show that the integration of far or infinitely far points stabilizes the estimation of the rotation angles of the camera poses. In its second contribution, we employ this approach to bundle adjustment in a highly integrated system for incremental pose estimation and mapping on light-weight UAVs. Based on the image sequences of a multi-camera system our system makes use of tracked feature points to incrementally build a sparse map and incrementally refines this map using the iSAM2 algorithm. Our system is able to optionally integrate GPS information on the level of carrier phase observations even in underconstrained situations, e.g. if only two satellites are visible, for georeferenced pose estimation. This way, we are able to use all available information in underconstrained GPS situations to keep the mapped 3D model accurate and georeferenced. In its third contribution, we present an approach for re-using existing methods for dense stereo matching with fisheye cameras, which has the advantage that highly optimized existing methods can be applied as a black-box without modifications even with cameras that have field of view of more than 180 deg. We provide a detailed accuracy analysis of the obtained dense stereo results. The accuracy analysis shows the growing uncertainty of observed image points of fisheye cameras due to increasing blur towards the image border. Core of the contribution is a rigorous variance component estimation which allows to estimate the variance of the observed disparities at an image point as a function of the distance of that point to the principal point. We show that this improved stochastic model provides a more realistic prediction of the uncertainty of the triangulated 3D points.Autonom operierende UAVs benötigen eine schnelle Lokalisierung zur Navigation, zur Exploration unbekannter Umgebungen und zur Kartierung. Zur Posenbestimmung verwenden viele UAV-Systeme eine Kombination aus GPS-Empfängern und Inertial-Messeinheiten (IMU). Die Verfügbarkeit von GPS-Signalen ist jedoch nicht überall gewährleistet, insbesondere in der Nähe abschattender Objekte, und präzise IMUs sind für leichtgewichtige UAVs zu schwer. Auch die hohen Kosten qualitativ hochwertiger IMUs motivieren den Einsatz von kostengünstigen bildgebenden Sensoren zur Lokalisierung mittels visueller Odometrie oder SLAM-Techniken zur simultanen Lokalisierung und Kartierung. Im ersten wissenschaftlichen Beitrag dieser Arbeit entwickeln wir einen allgemeineren Ansatz für die Bündelausgleichung mit einem erweiterten Modell für die projektive Kollinearitätsgleichung, sodass auch omnidirektionale Multikamerasysteme verwendet werden können, welche beispielsweise bestehend aus Fisheyekameras mit einer Aufnahme einen großen Sichtbereich abdecken. Durch die Integration von Strahlrichtungen als Beobachtungen ist unser Ansatz nicht von einem kameraspezifischen Abbildungsmodell abhängig solange dieses der Zentralprojektion folgt. Zudem erlaubt unser Ansatz die Integration und Schätzung von unendlich fernen Punkten, was bei klassischen Bündelausgleichungen nicht möglich ist. Wir zeigen, dass durch die Integration weit entfernter und unendlich ferner Punkte die Schätzung der Rotationswinkel der Kameraposen stabilisiert werden kann. Im zweiten Beitrag verwenden wir diesen entwickelten Ansatz zur Bündelausgleichung für ein System zur inkrementellen Posenschätzung und dünnbesetzten Kartierung auf einem leichtgewichtigen UAV. Basierend auf den Bildsequenzen eines Mulitkamerasystems baut unser System mittels verfolgter markanter Bildpunkte inkrementell eine dünnbesetzte Karte auf und verfeinert diese inkrementell mittels des iSAM2-Algorithmus. Unser System ist in der Lage optional auch GPS Informationen auf dem Level von GPS-Trägerphasen zu integrieren, wodurch sogar in unterbestimmten Situation - beispielsweise bei nur zwei verfügbaren Satelliten - diese Informationen zur georeferenzierten Posenschätzung verwendet werden können. Im dritten Beitrag stellen wir einen Ansatz zur Verwendung existierender Methoden für dichtes Stereomatching mit Fisheyekameras vor, sodass hoch optimierte existierende Methoden als Black Box ohne Modifzierungen sogar mit Kameras mit einem Gesichtsfeld von mehr als 180 Grad verwendet werden können. Wir stellen eine detaillierte Genauigkeitsanalyse basierend auf dem Ergebnis des dichten Stereomatchings dar. Die Genauigkeitsanalyse zeigt, wie stark die Genauigkeit beobachteter Bildpunkte bei Fisheyekameras zum Bildrand aufgrund von zunehmender Unschärfe abnimmt. Das Kernstück dieses Beitrags ist eine Varianzkomponentenschätzung, welche die Schätzung der Varianz der beobachteten Disparitäten an einem Bildpunkt als Funktion von der Distanz dieses Punktes zum Hauptpunkt des Bildes ermöglicht. Wir zeigen, dass dieses verbesserte stochastische Modell eine realistischere Prädiktion der Genauigkeiten der 3D Punkte ermöglicht

Autonomous Pick-and-Place Procedure with an Industrial Robot Using Multiple 3D Sensors for Object Detection and Obstacle Avoidance

Master's thesis in Mechatronics (MAS500)This thesis proposes a full pipeline autonomous pick-and-place procedure, integrating perception, planning, grasping and control for execution of tasks towards long term industrial automation. Within perception, we demonstrate the detection of a large object (target) including position and orientation (pose) estimation in 3D world. Further on, obstacles in the work area are mapped with proposed filtering prior to motion planning and navigation of an industrial robot to the target’s pose. The target is then picked using a custom built motorized 3D printed end gripper, and placed at a desired location in the robot’s reachable environment. Point cloud based model-free obstacle avoidance is performed throughout the whole process. The complete pipeline is targeted towards typical tasks in various industries including offshore, logistics and warehouse domain with scanning of the scene, picking and placing of a bulky object from one position to another without or with minimal human intervention

Relative Pose Estimation Using Non-overlapping Multicamera Clusters

This thesis considers the Simultaneous Localization and Mapping (SLAM) problem using a set of perspective cameras arranged such that there is no overlap in their fields-of-view. With the known and fixed extrinsic calibration of each camera within the cluster, a novel real-time pose estimation system is presented that is able to accurately track the motion of a camera cluster relative to an unknown target object or environment and concurrently generate a model of the structure, using only image-space measurements. A new parameterization for point feature position using a spherical coordinate update is presented which isolates system parameters dependent on global scale, allowing the shape parameters of the system to converge despite the scale parameters remaining uncertain. Furthermore, a flexible initialization scheme is proposed which allows the optimization to converge accurately using only the measurements from the cameras at the first time step. An analysis is presented identifying the configurations of the cluster motions and target structure geometry for which the optimization solution becomes degenerate and the global scale is ambiguous. Results are presented that not only confirm the previously known critical motions for a two-camera cluster, but also provide a complete description of the degeneracies related to the point feature constellations. The proposed algorithms are implemented and verified in experiments with a camera cluster constructed using multiple perspective cameras mounted on a quadrotor vehicle and augmented with tracking markers to collect high-precision ground-truth motion measurements from an optical indoor positioning system. The accuracy and performance of the proposed pose estimation system are confirmed for various motion profiles in both indoor and challenging outdoor environments