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

Reconstruction of 3D Points From Uncalibrated Underwater Video

This thesis presents a 3D reconstruction software pipeline that is capable of generating point cloud data from uncalibrated underwater video. This research project was undertaken as a partnership with 2G Robotics, and the pipeline described in this thesis will become the 3D reconstruction engine for a software product that can generate photo-realistic 3D models from underwater video. The pipeline proceeds in three stages: video tracking, projective reconstruction, and autocalibration. Video tracking serves two functions: tracking recognizable feature points, as well as selecting well-spaced keyframes with a wide enough baseline to be used in the reconstruction. Video tracking is accomplished using Lucas-Kanade optical flow as implemented in the OpenCV toolkit. This simple and widely used method is well-suited to underwater video, which is taken by carefully piloted and slow-moving underwater vehicles. Projective reconstruction is the process of simultaneously calculating the motion of the cameras and the 3D location of observed points in the scene. This is accomplished using a geometric three-view technique. Results are presented showing that the projective reconstruction algorithm detailed here compares favourably to state-of-the-art methods. Autocalibration is the process of transforming a projective reconstruction, which is not suitable for visualization or measurement, into a metric space where it can be used. This is the most challenging part of the 3D reconstruction pipeline, and this thesis presents a novel autocalibration algorithm. Results are shown for two existing cost function-based methods in the literature which failed when applied to underwater video, as well as the proposed hybrid method. The hybrid method combines the best parts of its two parent methods, and produces good results on underwater video. Final results are shown for the 3D reconstruction pipeline operating on short under- water video sequences to produce visually accurate 3D point clouds of the scene, suitable for photorealistic rendering. Although further work remains to extend and improve the pipeline for operation on longer sequences, this thesis presents a proof-of-concept method for 3D reconstruction from uncalibrated underwater video

Projector Self-Calibration using the Dual Absolute Quadric

The applications for projectors have increased dramatically since their origins in cinema. These include augmented reality, information displays, 3D scanning, and even archiving and surgical intervention. One common thread between all of these applications is the nec- essary step of projector calibration. Projector calibration can be a challenging task, and requires significant effort and preparation to ensure accuracy and fidelity. This is especially true in large scale, multi-projector installations used for projection mapping. Generally, the cameras for projector-camera systems are calibrated off-site, and then used in-field un- der the assumption that the intrinsics have remained constant. However, the assumption of off-site calibration imposes several hard restrictions. Among these, is that the intrinsics remain invariant between the off-site calibration process and the projector calibration site. This assumption is easily invalidated upon physical impact, or changing of lenses. To ad- dress this, camera self-calibration has been proposed for the projector calibration problem. However, current proposed methods suffer from degenerate conditions that are easily en- countered in practical projector calibration setups, resulting in undesirable variability and a distinct lack of robustness. In particular, the condition of near-intersecting optical axes of the camera positions used to capture the scene resulted in high variability and significant error in the recovered camera focal lengths. As such, a more robust method was required. To address this issue, an alternative camera self-calibration method is proposed. In this thesis we demonstrate our method of projector calibration with unknown and uncalibrated cameras via autocalibration using the Dual Absolute Quadric (DAQ). This method results in a significantly more robust projector calibration process, especially in the presence of correspondence noise when compared with previous methods. We use the DAQ method to calibrate the cameras using projector-generated correspondences, by upgrading an ini- tial projective calibration to metric, and subsequently calibrating the projector using the recovered metric structure of the scene. Our experiments provide strong evidence of the brittle behaviour of existing methods of projector self-calibration by evaluating them in near-degenerate conditions using both synthetic and real data. Further, they also show that the DAQ can be used successfully to calibrate a projector-camera system and reconstruct the surface used for projection mapping robustly, where previous methods fail

3-D Scene Reconstruction from Aerial Imagery

3-D scene reconstructions derived from Structure from Motion (SfM) and Multi-View Stereo (MVS) techniques were analyzed to determine the optimal reconnaissance flight characteristics suitable for target reconstruction. In support of this goal, a preliminary study of a simple 3-D geometric object facilitated the analysis of convergence angles and number of camera frames within a controlled environment. Reconstruction accuracy measurements revealed at least 3 camera frames and a 6 convergence angle were required to achieve results reminiscent of the original structure. The central investigative effort sought the applicability of certain airborne reconnaissance flight profiles to reconstructing ground targets. The data sets included images collected within a synthetic 3-D urban environment along circular, linear and s-curve aerial flight profiles equipped with agile and non-agile sensors. S-curve and dynamically controlled linear flight paths provided superior results, whereas with sufficient data conditioning and combination of orthogonal flight paths, all flight paths produced quality reconstructions under a wide variety of operational considerations

Advances in 3D reconstruction

La tesi affronta il problema della ricostruzione di scene tridimensionali a partire da insiemi non strutturati di fotografie delle stesse. Lo stato dell'arte viene avanzato su diversi fronti: il primo contributo consiste in una formulazione robusta del problema di struttura e moto basata su di un approccio gerarchico, contrariamente a quello sequenziale prevalente in letteratura. Questa metodologia abbatte di un ordine di grandezza il costo computazionale complessivo, risulta inerentemente parallelizzabile, minimizza il progressivo accumulo degli errori e elimina la cruciale dipendenza dalla scelta della coppia di viste iniziale comune a tutte le formulazioni concorrenti. Un secondo contributo consiste nello sviluppo di una nuova procedura di autocalibrazione, particolarmente robusta e adatta al contesto del problema di moto e struttura. La soluzione proposta consiste in una procedura in forma chiusa per il recupero del piano all'infinito data una stima dei parametri intrinseci di almeno due camere. Questo metodo viene utilizzato per la ricerca esaustiva dei parametri interni, il cui spazio di ricerca Š strutturalmente limitato dalla finitezza dei dispositivi di acquisizione. Si Š indagato infine come visualizzare in maniera efficiente e gradevole i risultati di ricostruzione ottenuti: a tale scopo sono stati sviluppati algoritmi per il calcolo della disparit… stereo e procedure per la visualizzazione delle ricostruzione come insiemi di piani tessiturati automaticamente estratti, ottenendo una rappresentazione fedele, compatta e semanticamente significativa. Ogni risultato Š stato corredato da una validazione sperimentale rigorosa, con verifiche sia qualitative che quantitative.The thesis tackles the problem of 3D reconstruction of scenes from unstructured picture datasets. State of the art is advanced on several aspects: the first contribute consists in a robust formulation of the structure and motion problem based on a hierarchical approach, as opposed to the sequential one prevalent in literature. This methodology reduces the total computational complexity by one order of magnitude, is inherently parallelizable, minimizes the error accumulation causing drift and eliminates the crucial dependency from the choice of the initial couple of views which is common to all competing approaches. A second contribute consists in the discovery of a novel slef-calibration procedure, very robust and tailored to the structure and motion task. The proposed solution is a closed-form procedure for the recovery of the plane at infinity given a rough estimate of focal parameters of at least two cameras. This method is employed for the exaustive search of internal parameters, whise space is inherently bounded from the finiteness of acquisition devices. Finally, we inevstigated how to visualize in a efficient and compelling way the obtained reconstruction results: to this effect several algorithms for the computation of stereo disparity are presented. Along with procedures for the automatic extraction of support planes, they have been employed to obtain a faithful, compact and semantically significant representation of the scene as a collection of textured planes, eventually augmented by depth information encoded in relief maps. Every result has been verified by a rigorous experimental validation, comprising both qualitative and quantitative comparisons

Beyond Gr\"obner Bases: Basis Selection for Minimal Solvers

Many computer vision applications require robust estimation of the underlying geometry, in terms of camera motion and 3D structure of the scene. These robust methods often rely on running minimal solvers in a RANSAC framework. In this paper we show how we can make polynomial solvers based on the action matrix method faster, by careful selection of the monomial bases. These monomial bases have traditionally been based on a Gr\"obner basis for the polynomial ideal. Here we describe how we can enumerate all such bases in an efficient way. We also show that going beyond Gr\"obner bases leads to more efficient solvers in many cases. We present a novel basis sampling scheme that we evaluate on a number of problems

Autocalibration Region Extending Through Time: A Novel GRAPPA Reconstruction Algorithm to Accelerate 1H Magnetic Resonance Spectroscopic Imaging

Magnetic resonance spectroscopic imaging (MRSI) has the ability to noninvasively interrogate metabolism in vivo. However, excessively long scan times have thus far prevented its adoption into routine clinical practice. Generalized autocalibrating partially parallel acquisitions (GRAPPA) is a parallel imaging technique that allows one to reduce acquisition duration and use spatial sensitivity correlations to reconstruct the unsampled data points. The coil sensitivity weights are determined implicitly via a fully-sampled autocalibration region in k-space. In this dissertation, a novel GRAPPA-based algorithm is presented for the acceleration of 1H MRSI. Autocalibration Region extending Through Time (ARTT) GRAPPA instead extracts the coil weights from a region in k-t space, allowing for undersampling along each spatial dimension. This technique, by exploiting spatial-spectral correlations present in MRSI data, allows for a more accurate determination of the coil weights and subsequent parallel imaging reconstruction. This improved reconstruction accuracy can then be traded for more aggressive undersampling and a further reduction of acquisition duration. It is shown that the ARTT GRAPPA technique allows for approximately two-fold more aggressive undersampling than the conventional technique while achieving the same reconstruction accuracy. This accelerated protocol is then applied to acquire high-resolution brain metabolite maps in less than twenty minutes in three healthy volunteers at B0 = 7 T