Robust convex optimisation techniques for autonomous vehicle vision-based navigation

This thesis investigates new convex optimisation techniques for motion and pose estimation. Numerous computer vision problems can be formulated as optimisation problems. These optimisation problems are generally solved via linear techniques using the singular value decomposition or iterative methods under an L2 norm minimisation. Linear techniques have the advantage of offering a closed-form solution that is simple to implement. The quantity being minimised is, however, not geometrically or statistically meaningful. Conversely, L2 algorithms rely on iterative estimation, where a cost function is minimised using algorithms such as Levenberg-Marquardt, Gauss-Newton, gradient descent or conjugate gradient. The cost functions involved are geometrically interpretable and can statistically be optimal under an assumption of Gaussian noise. However, in addition to their sensitivity to initial conditions, these algorithms are often slow and bear a high probability of getting trapped in a local minimum or producing infeasible solutions, even for small noise levels. In light of the above, in this thesis we focus on developing new techniques for finding solutions via a convex optimisation framework that are globally optimal. Presently convex optimisation techniques in motion estimation have revealed enormous advantages. Indeed, convex optimisation ensures getting a global minimum, and the cost function is geometrically meaningful. Moreover, robust optimisation is a recent approach for optimisation under uncertain data. In recent years the need to cope with uncertain data has become especially acute, particularly where real-world applications are concerned. In such circumstances, robust optimisation aims to recover an optimal solution whose feasibility must be guaranteed for any realisation of the uncertain data. Although many researchers avoid uncertainty due to the added complexity in constructing a robust optimisation model and to lack of knowledge as to the nature of these uncertainties, and especially their propagation, in this thesis robust convex optimisation, while estimating the uncertainties at every step is investigated for the motion estimation problem. First, a solution using convex optimisation coupled to the recursive least squares (RLS) algorithm and the robust H filter is developed for motion estimation. In another solution, uncertainties and their propagation are incorporated in a robust L convex optimisation framework for monocular visual motion estimation. In this solution, robust least squares is combined with a second order cone program (SOCP). A technique to improve the accuracy and the robustness of the fundamental matrix is also investigated in this thesis. This technique uses the covariance intersection approach to fuse feature location uncertainties, which leads to more consistent motion estimates. Loop-closure detection is crucial in improving the robustness of navigation algorithms. In practice, after long navigation in an unknown environment, detecting that a vehicle is in a location it has previously visited gives the opportunity to increase the accuracy and consistency of the estimate. In this context, we have developed an efficient appearance-based method for visual loop-closure detection based on the combination of a Gaussian mixture model with the KD-tree data structure. Deploying this technique for loop-closure detection, a robust L convex posegraph optimisation solution for unmanned aerial vehicle (UAVs) monocular motion estimation is introduced as well. In the literature, most proposed solutions formulate the pose-graph optimisation as a least-squares problem by minimising a cost function using iterative methods. In this work, robust convex optimisation under the L norm is adopted, which efficiently corrects the UAV’s pose after loop-closure detection. To round out the work in this thesis, a system for cooperative monocular visual motion estimation with multiple aerial vehicles is proposed. The cooperative motion estimation employs state-of-the-art approaches for optimisation, individual motion estimation and registration. Three-view geometry algorithms in a convex optimisation framework are deployed on board the monocular vision system for each vehicle. In addition, vehicle-to-vehicle relative pose estimation is performed with a novel robust registration solution in a global optimisation framework. In parallel, and as a complementary solution for the relative pose, a robust non-linear H solution is designed as well to fuse measurements from the UAVs’ on-board inertial sensors with the visual estimates. The suggested contributions have been exhaustively evaluated over a number of real-image data experiments in the laboratory using monocular vision systems and range imaging devices. In this thesis, we propose several solutions towards the goal of robust visual motion estimation using convex optimisation. We show that the convex optimisation framework may be extended to include uncertainty information, to achieve robust and optimal solutions. We observed that convex optimisation is a practical and very appealing alternative to linear techniques and iterative methods

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

Image Registration to Map Endoscopic Video to Computed Tomography for Head and Neck Radiotherapy Patients

The purpose of this work was to explore the feasibility of registering endoscopic video to radiotherapy treatment plans for patients with head and neck cancer without physical tracking of the endoscope during the examination. Endoscopy-CT registration would provide a clinical tool that could be used to enhance the treatment planning process and would allow for new methods to study the incidence of radiation-related toxicity. Endoscopic video frames were registered to CT by optimizing virtual endoscope placement to maximize the similarity between the frame and the virtual image. Virtual endoscopic images were rendered using a polygonal mesh created by segmenting the airways of the head and neck with a density threshold. The optical properties of the virtual endoscope were matched to a calibrated model of the real endoscope. A novel registration algorithm was developed that takes advantage of physical constraints on the endoscope to effectively search the airways of the head and neck for the desired virtual endoscope coordinates. This algorithm was tested on rigid phantoms with embedded point markers and protruding bolus material. In these tests, the median registration accuracy was 3.0 mm for point measurements and 3.5 mm for surface measurements. The algorithm was also tested on four endoscopic examinations of three patients, in which it achieved a median registration accuracy of 9.9 mm. The uncertainties caused by the non-rigid anatomy of the head and neck and differences in patient positioning between endoscopic examinations and CT scans were examined by taking repeated measurements after placing the virtual endoscope in surface meshes created from different CT scans. Non-rigid anatomy introduced errors on the order of 1-3 mm. Patient positioning had a larger impact, introducing errors on the order of 3.5-4.5 mm. Endoscopy-CT registration in the head and neck is possible, but large registration errors were found in patients. The uncertainty analyses suggest a lower limit of 3-5 mm. Further development is required to achieve an accuracy suitable for clinical use

Line-constrained camera location estimation in multi-image stereomatching

Stereomatching is an effective way of acquiring dense depth information from a scene when active measurements are not possible. So-called lightfield methods take a snapshot from many camera locations along a defined trajectory (usually uniformly linear or on a regular grid—we will assume a linear trajectory) and use this information to compute accurate depth estimates. However, they require the locations for each of the snapshots to be known: the disparity of an object between images is related to both the distance of the camera to the object and the distance between the camera positions for both images. Existing solutions use sparse feature matching for camera location estimation. In this paper, we propose a novel method that uses dense correspondences to do the same, leveraging an existing depth estimation framework to also yield the camera locations along the line. We illustrate the effectiveness of the proposed technique for camera location estimation both visually for the rectification of epipolar plane images and quantitatively with its effect on the resulting depth estimation. Our proposed approach yields a valid alternative for sparse techniques, while still being executed in a reasonable time on a graphics card due to its highly parallelizable nature

Relating Multimodal Imagery Data in 3D

This research develops and improves the fundamental mathematical approaches and techniques required to relate imagery and imagery derived multimodal products in 3D. Image registration, in a 2D sense, will always be limited by the 3D effects of viewing geometry on the target. Therefore, effects such as occlusion, parallax, shadowing, and terrain/building elevation can often be mitigated with even a modest amounts of 3D target modeling. Additionally, the imaged scene may appear radically different based on the sensed modality of interest; this is evident from the differences in visible, infrared, polarimetric, and radar imagery of the same site. This thesis develops a `model-centric\u27 approach to relating multimodal imagery in a 3D environment. By correctly modeling a site of interest, both geometrically and physically, it is possible to remove/mitigate some of the most difficult challenges associated with multimodal image registration. In order to accomplish this feat, the mathematical framework necessary to relate imagery to geometric models is thoroughly examined. Since geometric models may need to be generated to apply this `model-centric\u27 approach, this research develops methods to derive 3D models from imagery and LIDAR data. Of critical note, is the implementation of complimentary techniques for relating multimodal imagery that utilize the geometric model in concert with physics based modeling to simulate scene appearance under diverse imaging scenarios. Finally, the often neglected final phase of mapping localized image registration results back to the world coordinate system model for final data archival are addressed. In short, once a target site is properly modeled, both geometrically and physically, it is possible to orient the 3D model to the same viewing perspective as a captured image to enable proper registration. If done accurately, the synthetic model\u27s physical appearance can simulate the imaged modality of interest while simultaneously removing the 3-D ambiguity between the model and the captured image. Once registered, the captured image can then be archived as a texture map on the geometric site model. In this way, the 3D information that was lost when the image was acquired can be regained and properly related with other datasets for data fusion and analysis

Generalizations of the projective reconstruction theorem

We present generalizations of the classic theorem of projective reconstruction as a tool for the design and analysis of the projective reconstruction algorithms. Our main focus is algorithms such as bundle adjustment and factorization-based techniques, which try to solve the projective equations directly for the structure points and projection matrices, rather than the so called tensor-based approaches. First, we consider the classic case of 3D to 2D projections. Our new theorem shows that projective reconstruction is possible under a much weaker restriction than requiring, a priori, that all estimated projective depths are nonzero. By completely specifying possible forms of wrong configurations when some of the projective depths are allowed to be zero, the theory enables us to present a class of depth constraints under which any reconstruction of cameras and points projecting into given image points is projectively equivalent to the true camera-point configuration. This is very useful for the design and analysis of different factorization-based algorithms. Here, we analyse several constraints used in the literature using our theory, and also demonstrate how our theory can be used for the design of new constraints with desirable properties. The next part of the thesis is devoted to projective reconstruction in arbitrary dimensions, which is important due to its applications in the analysis of dynamical scenes. The current theory, due to Hartley and Schaffalitzky, is based on the Grassmann tensor, generalizing the notions of Fundamental matrix, trifocal tensor and quardifocal tensor used for 3D to 2D projections. We extend their work by giving a theory whose point of departure is the projective equations rather than the Grassmann tensor. First, we prove the uniqueness of the Grassmann tensor corresponding to each set of image points, a question that remained open in the work of Hartley and Schaffalitzky. Then, we show that projective equivalence follows from the set of projective equations, provided that the depths are all nonzero. Finally, we classify possible wrong solutions to the projective factorization problem, where not all the projective depths are restricted to be nonzero. We test our theory experimentally by running the factorization based algorithms for rigid structure and motion in the case of 3D to 2D projections. We further run simulations for projections from higher dimensions. In each case, we present examples demonstrating how the algorithm can converge to the degenerate solutions introduced in the earlier chapters. We also show how the use of proper constraints can result in a better performance in terms of finding a correct solution

Efficient 2D SLAM for a Mobile Robot with a Downwards Facing Camera

As digital cameras become cheaper and better, computers more powerful, and robots more abundant the merging of these three techniques also becomes more common and capable. The combination of these techniques is often inspired by the human visual system and often strives to give machines the same capabilities that humans already have, such as object identification, navigation, limb coordination, and event detection. One such field that is particularly popular is that of SLAM, or Simultaneous Localization and Mapping, which has high-profile applications in self-driving cars and delivery drones. This thesis proposes and describes an online SLAM algorithm for a specific scenario: that of a robot with a downwards facing camera exploring a flat surface (e.g., a floor). The method is based on building homographies from robot odometry data, which are then used to rectify the images so that the tilt of the camera with regards to the floor is eliminated, thereby moving the problem from 3D to 2D. The 2D pose of the robot in the plane is estimated using registrations of SURF features, and then a bundle adjustment algorithm is used to consolidate the most recent measurements with the older ones in order to optimize the map. The algorithm is implemented and tested with an AR.Drone 2.0 quadcopter. The results are mixed, but hardware seems to be the limiting factor: the algorithm performs well and runs at 5-20 Hz on a i5 desktop computer; but the bad quality, high compression and low resolution of the drone’s bottom camera makes the algorithm unstable and this cannot be overcome, even with several tiers of outlier filtering.För att robotar skall vara praktiska behöver de ha en flexibel uppfattning om sin omgivning och deras egen position i den, men de metoder som finns för detta idag är ofta väldigt krävande. I det här projektet har en förenklad metod för kartläggning i realtid med en drönare utvecklats. Algoritmen behandlar ett enklare problem än de vanliga tredimensionella problemen - istället för att titta framåt i rummet tittar drönaren neråt och försöker bygga en karta genom att pussla ihop bilder av golvet. Metoden är effektiv, men kvalitén på drönarens kamera som användes är för dålig för att metoden skall ge pålitliga resultat

Towards high-accuracy augmented reality GIS for architecture and geo-engineering

L’architecture et la géo-ingénierie sont des domaines où les professionnels doivent prendre des décisions critiques. Ceux-ci requièrent des outils de haute précision pour les assister dans leurs tâches quotidiennes. La Réalité Augmentée (RA) présente un excellent potentiel pour ces professionnels en leur permettant de faciliter l’association des plans 2D/3D représentatifs des ouvrages sur lesquels ils doivent intervenir, avec leur perception de ces ouvrages dans la réalité. Les outils de visualisation s’appuyant sur la RA permettent d’effectuer ce recalage entre modélisation spatiale et réalité dans le champ de vue de l’usager. Cependant, ces systèmes de RA nécessitent des solutions de positionnement en temps réel de très haute précision. Ce n’est pas chose facile, spécialement dans les environnements urbains ou sur les sites de construction. Ce projet propose donc d’investiguer les principaux défis que présente un système de RA haute précision basé sur les panoramas omnidirectionels.Architecture and geo-engineering are application domains where professionals need to take critical decisions. These professionals require high-precision tools to assist them in their daily decision taking process. Augmented Reality (AR) shows great potential to allow easier association between the abstract 2D drawings and 3D models representing infrastructure under reviewing and the actual perception of these objects in the reality. The different visualization tools based on AR allow to overlay the virtual models and the reality in the field of view of the user. However, the architecture and geo-engineering context requires high-accuracy and real-time positioning from these AR systems. This is not a trivial task, especially in urban environments or on construction sites where the surroundings may be crowded and highly dynamic. This project investigates the accuracy requirements of mobile AR GIS as well as the main challenges to address when tackling high-accuracy AR based on omnidirectional panoramas

Reconstruction of Specular Reflective Surfaces using Auto-Calibrating Deflectometry

This thesis discusses deflectometry as a reconstruction method for highly reflecting surfaces. It focuses on deflectometry alone and does not use other reconstruction techniques to supplement with additional data. It explains the measurement process and principle and provides a crash course into an efficient mathematical representation of the principles involved. Using this, it reformulates existing three-dimensional reconstructing methods, expands upon them and develops new ones