Autocalibration with the Minimum Number of Cameras with Known Pixel Shape

In 3D reconstruction, the recovery of the calibration parameters of the cameras is paramount since it provides metric information about the observed scene, e.g., measures of angles and ratios of distances. Autocalibration enables the estimation of the camera parameters without using a calibration device, but by enforcing simple constraints on the camera parameters. In the absence of information about the internal camera parameters such as the focal length and the principal point, the knowledge of the camera pixel shape is usually the only available constraint. Given a projective reconstruction of a rigid scene, we address the problem of the autocalibration of a minimal set of cameras with known pixel shape and otherwise arbitrarily varying intrinsic and extrinsic parameters. We propose an algorithm that only requires 5 cameras (the theoretical minimum), thus halving the number of cameras required by previous algorithms based on the same constraint. To this purpose, we introduce as our basic geometric tool the six-line conic variety (SLCV), consisting in the set of planes intersecting six given lines of 3D space in points of a conic. We show that the set of solutions of the Euclidean upgrading problem for three cameras with known pixel shape can be parameterized in a computationally efficient way. This parameterization is then used to solve autocalibration from five or more cameras, reducing the three-dimensional search space to a two-dimensional one. We provide experiments with real images showing the good performance of the technique.Comment: 19 pages, 14 figures, 7 tables, J. Math. Imaging Vi

Self-calibration of turntable sequences from silhouettes

This paper addresses the problem of recovering both the intrinsic and extrinsic parameters of a camera from the silhouettes of an object in a turntable sequence. Previous silhouette-based approaches have exploited correspondences induced by epipolar tangents to estimate the image invariants under turntable motion and achieved a weak calibration of the cameras. It is known that the fundamental matrix relating any two views in a turntable sequence can be expressed explicitly in terms of the image invariants, the rotation angle, and a fixed scalar. It will be shown that the imaged circular points for the turntable plane can also be formulated in terms of the same image invariants and fixed scalar. This allows the imaged circular points to be recovered directly from the estimated image invariants, and provide constraints for the estimation of the imaged absolute conic. The camera calibration matrix can thus be recovered. A robust method for estimating the fixed scalar from image triplets is introduced, and a method for recovering the rotation angles using the estimated imaged circular points and epipoles is presented. Using the estimated camera intrinsics and extrinsics, a Euclidean reconstruction can be obtained. Experimental results on real data sequences are presented, which demonstrate the high precision achieved by the proposed method. © 2009 IEEE.published_or_final_versio

Self-Calibration of Multi-Camera Systems for Vehicle Surround Sensing

Multikamerasysteme werden heute bereits in einer Vielzahl von Fahrzeugen und mobilen Robotern eingesetzt. Die Anwendungen reichen dabei von einfachen Assistenzfunktionen wie der Erzeugung einer virtuellen Rundumsicht bis hin zur Umfelderfassung, wie sie für teil- und vollautomatisches Fahren benötigt wird. Damit aus den Kamerabildern metrische Größen wie Distanzen und Winkel abgeleitet werden können und ein konsistentes Umfeldmodell aufgebaut werden kann, muss das Abbildungsverhalten der einzelnen Kameras sowie deren relative Lage zueinander bekannt sein. Insbesondere die Bestimmung der relativen Lage der Kameras zueinander, die durch die extrinsische Kalibrierung beschrieben wird, ist aufwendig, da sie nur im Gesamtverbund erfolgen kann. Darüber hinaus ist zu erwarten, dass es über die Lebensdauer des Fahrzeugs hinweg zu nicht vernachlässigbaren Veränderungen durch äußere Einflüsse kommt. Um den hohen Zeit- und Kostenaufwand einer regelmäßigen Wartung zu vermeiden, ist ein Selbstkalibrierungsverfahren erforderlich, das die extrinsischen Kalibrierparameter fortlaufend nachschätzt. Für die Selbstkalibrierung wird typischerweise das Vorhandensein überlappender Sichtbereiche ausgenutzt, um die extrinsische Kalibrierung auf der Basis von Bildkorrespondenzen zu schätzen. Falls die Sichtbereiche mehrerer Kameras jedoch nicht überlappen, lassen sich die Kalibrierparameter auch aus den relativen Bewegungen ableiten, die die einzelnen Kameras beobachten. Die Bewegung typischer Straßenfahrzeuge lässt dabei jedoch nicht die Bestimmung aller Kalibrierparameter zu. Um die vollständige Schätzung der Parameter zu ermöglichen, lassen sich weitere Bedingungsgleichungen, die sich z.B. aus der Beobachtung der Bodenebene ergeben, einbinden. In dieser Arbeit wird dazu in einer theoretischen Analyse gezeigt, welche Parameter sich aus der Kombination verschiedener Bedingungsgleichungen eindeutig bestimmen lassen. Um das Umfeld eines Fahrzeugs vollständig erfassen zu können, werden typischerweise Objektive, wie zum Beispiel Fischaugenobjektive, eingesetzt, die einen sehr großen Bildwinkel ermöglichen. In dieser Arbeit wird ein Verfahren zur Bestimmung von Bildkorrespondenzen vorgeschlagen, das die geometrischen Verzerrungen, die sich durch die Verwendung von Fischaugenobjektiven und sich stark ändernden Ansichten ergeben, berücksichtigt. Darauf aufbauend stellen wir ein robustes Verfahren zur Nachführung der Parameter der Bodenebene vor. Basierend auf der theoretischen Analyse der Beobachtbarkeit und den vorgestellten Verfahren stellen wir ein robustes, rekursives Kalibrierverfahren vor, das auf einem erweiterten Kalman-Filter aufbaut. Das vorgestellte Kalibrierverfahren zeichnet sich insbesondere durch die geringe Anzahl von internen Parametern, sowie durch die hohe Flexibilität hinsichtlich der einbezogenen Bedingungsgleichungen aus und basiert einzig auf den Bilddaten des Multikamerasystems. In einer umfangreichen experimentellen Auswertung mit realen Daten vergleichen wir die Ergebnisse der auf unterschiedlichen Bedingungsgleichungen und Bewegungsmodellen basierenden Verfahren mit den aus einer Referenzkalibrierung bestimmten Parametern. Die besten Ergebnisse wurden dabei durch die Kombination aller vorgestellten Bedingungsgleichungen erzielt. Anhand mehrerer Beispiele zeigen wir, dass die erreichte Genauigkeit ausreichend für eine Vielzahl von Anwendungen ist

Self-Calibration of Multi-Camera Systems for Vehicle Surround Sensing

Multi-camera systems are being deployed in a variety of vehicles and mobile robots today. To eliminate the need for cost and labor intensive maintenance and calibration, continuous self-calibration is highly desirable. In this book we present such an approach for self-calibration of multi-Camera systems for vehicle surround sensing. In an extensive evaluation we assess our algorithm quantitatively using real-world data

Accelerated volumetric reconstruction from uncalibrated camera views

While both work with images, computer graphics and computer vision are inverse problems. Computer graphics starts traditionally with input geometric models and produces image sequences. Computer vision starts with input image sequences and produces geometric models. In the last few years, there has been a convergence of research to bridge the gap between the two fields. This convergence has produced a new field called Image-based Rendering and Modeling (IBMR). IBMR represents the effort of using the geometric information recovered from real images to generate new images with the hope that the synthesized ones appear photorealistic, as well as reducing the time spent on model creation. In this dissertation, the capturing, geometric and photometric aspects of an IBMR system are studied. A versatile framework was developed that enables the reconstruction of scenes from images acquired with a handheld digital camera. The proposed system targets applications in areas such as Computer Gaming and Virtual Reality, from a lowcost perspective. In the spirit of IBMR, the human operator is allowed to provide the high-level information, while underlying algorithms are used to perform low-level computational work. Conforming to the latest architecture trends, we propose a streaming voxel carving method, allowing a fast GPU-based processing on commodity hardware

Affine multi-view modelling for close range object measurement

In photogrammetry, sensor modelling with 3D point estimation is a fundamental topic of research. Perspective frame cameras offer the mathematical basis for close range modelling approaches. The norm is to employ robust bundle adjustments for simultaneous parameter estimation and 3D object measurement. In 2D to 3D modelling strategies image resolution, scale, sampling and geometric distortion are prior factors. Non-conventional image geometries that implement uncalibrated cameras are established in computer vision approaches; these aim for fast solutions at the expense of precision. The projective camera is defined in homogeneous terms and linear algorithms are employed. An attractive sensor model disembodied from projective distortions is the affine. Affine modelling has been studied in the contexts of geometry recovery, feature detection and texturing in vision, however multi-view approaches for precise object measurement are not yet widely available. This project investigates affine multi-view modelling from a photogrammetric standpoint. A new affine bundle adjustment system has been developed for point-based data observed in close range image networks. The system allows calibration, orientation and 3D point estimation. It is processed as a least squares solution with high redundancy providing statistical analysis. Starting values are recovered from a combination of implicit perspective and explicit affine approaches. System development focuses on retrieval of orientation parameters, 3D point coordinates and internal calibration with definition of system datum, sensor scale and radial lens distortion. Algorithm development is supported with method description by simulation. Initialization and implementation are evaluated with the statistical indicators, algorithm convergence and correlation of parameters. Object space is assessed with evaluation of the 3D point correlation coefficients and error ellipsoids. Sensor scale is checked with comparison of camera systems utilizing quality and accuracy metrics. For independent method evaluation, testing is implemented over a perspective bundle adjustment tool with similar indicators. Test datasets are initialized from precise reference image networks. Real affine image networks are acquired with an optical system (~1M pixel CCD cameras with 0.16x telecentric lens). Analysis of tests ascertains that the affine method results in an RMS image misclosure at a sub-pixel level and precisions of a few tenths of microns in object space

Towards Reliable and Accurate Global Structure-from-Motion

Reconstruction of objects or scenes from sparse point detections across multiple views is one of the most tackled problems in computer vision. Given the coordinates of 2D points tracked in multiple images, the problem consists of estimating the corresponding 3D points and cameras\u27 calibrations (intrinsic and pose), and can be solved by minimizing reprojection errors using bundle adjustment. However, given bundle adjustment\u27s nonlinear objective function and iterative nature, a good starting guess is required to converge to global minima. Global and Incremental Structure-from-Motion methods appear as ways to provide good initializations to bundle adjustment, each with different properties. While Global Structure-from-Motion has been shown to result in more accurate reconstructions compared to Incremental Structure-from-Motion, the latter has better scalability by starting with a small subset of images and sequentially adding new views, allowing reconstruction of sequences with millions of images. Additionally, both Global and Incremental Structure-from-Motion methods rely on accurate models of the scene or object, and under noisy conditions or high model uncertainty might result in poor initializations for bundle adjustment. Recently pOSE, a class of matrix factorization methods, has been proposed as an alternative to conventional Global SfM methods. These methods use VarPro - a second-order optimization method - to minimize a linear combination of an approximation of reprojection errors and a regularization term based on an affine camera model, and have been shown to converge to global minima with a high rate even when starting from random camera calibration estimations.This thesis aims at improving the reliability and accuracy of global SfM through different approaches. First, by studying conditions for global optimality of point set registration, a point cloud averaging method that can be used when (incomplete) 3D point clouds of the same scene in different coordinate systems are available. Second, by extending pOSE methods to different Structure-from-Motion problem instances, such as Non-Rigid SfM or radial distortion invariant SfM. Third and finally, by replacing the regularization term of pOSE methods with an exponential regularization on the projective depth of the 3D point estimations, resulting in a loss that achieves reconstructions with accuracy close to bundle adjustment

Using Geometric Constraints for Camera Calibration and Positioning and 3D Scene Modelling

International audienceThis work concerns the incorporation of geometric information in camera calibration and 3D modelling. Using geometric constraints enables stabler results and allows to perform tasks with fewer images. Our approach is interactive; the user defines geometric primitives and constraints between them. It is based on the observation that constraints such as coplanarity, parallelism or orthogonality, are easy to delineate by a user, and are well adapted to model the main structure of e.g. architectural scenes. We propose methods for camera calibration, camera position estimation and 3D scene reconstruction, all based on such geometric constraints. Various approaches exist for calibration and positioning from constraints, often based on vanishing points. We generalize this by considering composite primitives based on triplets of vanishing points. These are frequent in architectural scenes and considering composites of vanishing points makes computations more stable. They are defined by depicting in the images points belonging to parallelepipedic structures (e.g. appropriate points on two connected walls). Constraints on angles or length ratios on these structures can then be easily imposed. A method is proposed that "collects" all these data for all considered images, and computes simultaneously the calibration and pose of all cameras via matrix factorization. 3D scene reconstruction is then performed using many more geometric constraints, i.e. not only those encapsulated by parallelepipedic structures. A method is proposed that reconstructs the whole scene in iterations, solving a linear equation system at each iteration, and which includes an analysis of the parts of the scene that can/cannot be reconstructed at the current stage. The complete approach is validated by various experimental results, for cases where a single or several views are available