Robust Estimation of Motion Parameters and Scene Geometry : Minimal Solvers and Convexification of Regularisers for Low-Rank Approximation

In the dawning age of autonomous driving, accurate and robust tracking of vehicles is a quintessential part. This is inextricably linked with the problem of Simultaneous Localisation and Mapping (SLAM), in which one tries to determine the position of a vehicle relative to its surroundings without prior knowledge of them. The more you know about the object you wish to track—through sensors or mechanical construction—the more likely you are to get good positioning estimates. In the first part of this thesis, we explore new ways of improving positioning for vehicles travelling on a planar surface. This is done in several different ways: first, we generalise the work done for monocular vision to include two cameras, we propose ways of speeding up the estimation time with polynomial solvers, and we develop an auto-calibration method to cope with radially distorted images, without enforcing pre-calibration procedures.We continue to investigate the case of constrained motion—this time using auxiliary data from inertial measurement units (IMUs) to improve positioning of unmanned aerial vehicles (UAVs). The proposed methods improve the state-of-the-art for partially calibrated cases (with unknown focal length) for indoor navigation. Furthermore, we propose the first-ever real-time compatible minimal solver for simultaneous estimation of radial distortion profile, focal length, and motion parameters while utilising the IMU data.In the third and final part of this thesis, we develop a bilinear framework for low-rank regularisation, with global optimality guarantees under certain conditions. We also show equivalence between the linear and the bilinear framework, in the sense that the objectives are equal. This enables users of alternating direction method of multipliers (ADMM)—or other subgradient or splitting methods—to transition to the new framework, while being able to enjoy the benefits of second order methods. Furthermore, we propose a novel regulariser fusing two popular methods. This way we are able to combine the best of two worlds by encouraging bias reduction while enforcing low-rank solutions

An Enhanced Structure-from-Motion Paradigm based on the Absolute Dual Quadric and Images of Circular Points

International audienceThis work aims at introducing a new unified Structure-from-Motion (SfM) paradigm in which images of circular point-pairs can be combined with images of natural points. An imaged circular point-pair encodes the 2D Euclidean structure of a world plane and can easily be derived from the image of a planar shape, especially those including circles. A classical SfM method generally runs two steps: first a projective factorization of all matched image points (into projective cameras and points) and second a camera self-calibration that updates the obtained world from projective to Euclidean. This work shows how to introduce images of circular points in these two SfM steps while its key contribution is to provide the theoretical foundations for combining “classical” linear self-calibration constraints with additional ones derived from such images. We show that the two proposed SfM steps clearly contribute to better results than the classical approach. We validate our contributions on synthetic and real images

Video Processing with Additional Information

Cameras are frequently deployed along with many additional sensors in aerial and ground-based platforms. Many video datasets have metadata containing measurements from inertial sensors, GPS units, etc. Hence the development of better video processing algorithms using additional information attains special significance. We first describe an intensity-based algorithm for stabilizing low resolution and low quality aerial videos. The primary contribution is the idea of minimizing the discrepancy in the intensity of selected pixels between two images. This is an application of inverse compositional alignment for registering images of low resolution and low quality, for which minimizing the intensity difference over salient pixels with high gradients results in faster and better convergence than when using all the pixels. Secondly, we describe a feature-based method for stabilization of aerial videos and segmentation of small moving objects. We use the coherency of background motion to jointly track features through the sequence. This enables accurate tracking of large numbers of features in the presence of repetitive texture, lack of well conditioned feature windows etc. We incorporate the segmentation problem within the joint feature tracking framework and propose the first combined joint-tracking and segmentation algorithm. The proposed approach enables highly accurate tracking, and segmentation of feature tracks that is used in a MAP-MRF framework for obtaining dense pixelwise labeling of the scene. We demonstrate competitive moving object detection in challenging video sequences of the VIVID dataset containing moving vehicles and humans that are small enough to cause background subtraction approaches to fail. Structure from Motion (SfM) has matured to a stage, where the emphasis is on developing fast, scalable and robust algorithms for large reconstruction problems. The availability of additional sensors such as inertial units and GPS along with video cameras motivate the development of SfM algorithms that leverage these additional measurements. In the third part, we study the benefits of the availability of a specific form of additional information - the vertical direction (gravity) and the height of the camera both of which can be conveniently measured using inertial sensors, and a monocular video sequence for 3D urban modeling. We show that in the presence of this information, the SfM equations can be rewritten in a bilinear form. This allows us to derive a fast, robust, and scalable SfM algorithm for large scale applications. The proposed SfM algorithm is experimentally demonstrated to have favorable properties compared to the sparse bundle adjustment algorithm. We provide experimental evidence indicating that the proposed algorithm converges in many cases to solutions with lower error than state-of-art implementations of bundle adjustment. We also demonstrate that for the case of large reconstruction problems, the proposed algorithm takes lesser time to reach its solution compared to bundle adjustment. We also present SfM results using our algorithm on the Google StreetView research dataset, and several other datasets

Optical Flow in Mostly Rigid Scenes

The optical flow of natural scenes is a combination of the motion of the observer and the independent motion of objects. Existing algorithms typically focus on either recovering motion and structure under the assumption of a purely static world or optical flow for general unconstrained scenes. We combine these approaches in an optical flow algorithm that estimates an explicit segmentation of moving objects from appearance and physical constraints. In static regions we take advantage of strong constraints to jointly estimate the camera motion and the 3D structure of the scene over multiple frames. This allows us to also regularize the structure instead of the motion. Our formulation uses a Plane+Parallax framework, which works even under small baselines, and reduces the motion estimation to a one-dimensional search problem, resulting in more accurate estimation. In moving regions the flow is treated as unconstrained, and computed with an existing optical flow method. The resulting Mostly-Rigid Flow (MR-Flow) method achieves state-of-the-art results on both the MPI-Sintel and KITTI-2015 benchmarks.Comment: 15 pages, 10 figures; accepted for publication at CVPR 201

THREE-DIMENSIONAL VISION FOR STRUCTURE AND MOTION ESTIMATION

1997/1998Questa tesi, intitolata Visione Tridimensionale per la stima di Struttura e Moto, tratta di tecniche di Visione Artificiale per la stima delle proprietà geometriche del mondo tridimensionale a partire da immagini numeriche. Queste proprietà sono essenziali per il riconoscimento e la classificazione di oggetti, la navigazione di veicoli mobili autonomi, il reverse engineering e la sintesi di ambienti virtuali. In particolare, saranno descritti i moduli coinvolti nel calcolo della struttura della scena a partire dalle immagini, e verranno presentati contributi originali nei seguenti campi. Rettificazione di immagini steroscopiche. Viene presentato un nuovo algoritmo per la rettificazione, il quale trasforma una coppia di immagini stereoscopiche in maniera che punti corrispondenti giacciano su linee orizzontali con lo stesso indice. Prove sperimentali dimostrano il corretto comportamento del metodo, come pure la trascurabile perdita di accuratezza nella ricostruzione tridimensionale quando questa sia ottenuta direttamente dalle immagini rettificate. Calcolo delle corrispondenze in immagini stereoscopiche. Viene analizzato il problema della stereovisione e viene presentato un un nuovo ed efficiente algoritmo per l'identificazione di coppie di punti corrispondenti, capace di calcolare in modo robusto la disparità stereoscopica anche in presenza di occlusioni. L'algoritmo, chiamato SMW, usa uno schema multi-finestra adattativo assieme al controllo di coerenza destra-sinistra per calcolare la disparità e l'incertezza associata. Gli esperimenti condotti con immagini sintetiche e reali mostrano che SMW sortisce un miglioramento in accuratezza ed efficienza rispetto a metodi simili Inseguimento di punti salienti. L'inseguitore di punti salienti di Shi-Tomasi- Kanade viene migliorato introducendo uno schema automatico per lo scarto di punti spuri basato sulla diagnostica robusta dei campioni periferici ( outliers ). Gli esperimenti con immagini sintetiche e reali confermano il miglioramento rispetto al metodo originale, sia qualitativamente che quantitativamente. Ricostruzione non calibrata. Viene presentata una rassegna ragionata dei metodi per la ricostruzione di un modello tridimensionale della scena, a partire da una telecamera che si muove liberamente e di cui non sono noti i parametri interni. Il contributo consiste nel fornire una visione critica e unificata delle più recenti tecniche. Una tale rassegna non esiste ancora in letterarura. Moto tridimensionale. Viene proposto un algoritmo robusto per registrate e calcolare le corrispondenze in due insiemi di punti tridimensionali nei quali vi sia un numero significativo di elementi mancanti. Il metodo, chiamato RICP, sfrutta la stima robusta con la Minima Mediana dei Quadrati per eliminare l'effetto dei campioni periferici. Il confronto sperimentale con una tecnica simile, ICP, mostra la superiore robustezza e affidabilità di RICP.This thesis addresses computer vision techniques estimating geometrie properties of the 3-D world /rom digital images. Such properties are essential for object recognition and classification, mobile robots navigation, reverse engineering and synthesis of virtual environments. In particular, this thesis describes the modules involved in the computation of the structure of a scene given some images, and offers original contributions in the following fields. Stereo pairs rectification. A novel rectification algorithm is presented, which transform a stereo pair in such a way that corresponding points in the two images lie on horizontal lines with the same index. Experimental tests prove the correct behavior of the method, as well as the negligible decrease oLthe accuracy of 3-D reconstruction if performed from the rectified images directly. Stereo matching. The problem of computational stereopsis is analyzed, and a new, efficient stereo matching algorithm addressing robust disparity estimation in the presence of occlusions is presented. The algorithm, called SMW, is an adaptive, multi-window scheme using left-right consistency to compute disparity and its associated uncertainty. Experiments with both synthetic and real stereo pairs show how SMW improves on closely related techniques for both accuracy and efficiency. Features tracking. The Shi-Tomasi-Kanade feature tracker is improved by introducing an automatic scheme for rejecting spurious features, based on robust outlier diagnostics. Experiments with real and synthetic images confirm the improvement over the original tracker, both qualitatively and quantitatively. 111 Uncalibrated vision. A review on techniques for computing a three-dimensional model of a scene from a single moving camera, with unconstrained motion and unknown parameters is presented. The contribution is to give a critical, unified view of some of the most promising techniques. Such review does not yet exist in the literature. 3-D motion. A robust algorithm for registering and finding correspondences in two sets of 3-D points with significant percentages of missing data is proposed. The method, called RICP, exploits LMedS robust estimation to withstand the effect of outliers. Experimental comparison with a closely related technique, ICP, shows RICP's superior robustness and reliability.XI Ciclo1968Versione digitalizzata della tesi di dottorato cartacea

Hierarchical structure-and-motion recovery from uncalibrated images

This paper addresses the structure-and-motion problem, that requires to find camera motion and 3D struc- ture from point matches. A new pipeline, dubbed Samantha, is presented, that departs from the prevailing sequential paradigm and embraces instead a hierarchical approach. This method has several advantages, like a provably lower computational complexity, which is necessary to achieve true scalability, and better error containment, leading to more stability and less drift. Moreover, a practical autocalibration procedure allows to process images without ancillary information. Experiments with real data assess the accuracy and the computational efficiency of the method.Comment: Accepted for publication in CVI

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

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