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

Relative orientation with limited control in close range Photogrammetry

In close-range photogrammetry, situations can arise in which it is difficult or impossible to establish a network of control points as required for a conventional absolute orientation procedure. The thesis investigates the replacement of the traditional control network by a few control distances measured between well-defined artificial markers or natural feature points. The measured distances must then serve to reduce deformations suffered by the photogrammetric model in the orientation procedures. All investigations are based on analytical rather than analogue photogrammetry. After a review of the concepts of rotation matrices, least squares adjustment and the generation of synthetic image co-ordinate observations, the study is executed in three major steps. A test field of high precision is established by means of space intersection and a camera calibration method for close-range cameras is developed which combines perspective projection with geodetic observations of the lens system parameters. Thus a problem inherent in many camera calibration methods, namely the exact determination of the perspective centre, is largely overcome. Deformation characteristics related to error in elements of interior and relative orientation are determined by the controlled introduction of errors into these elements. The deformations are presented in tabular and diagrammatical form. An analysis of the deformation leads to the conclusions of theoretical and practical relevance for close-range photogrammetry. As a result of the deformation analysis mathematical models are introduced which utilise the measured distances for the reduction of model deformations. The efficiency of homogeneous scaling, affine scaling and convergency correction, as applied individually and in various combinations, is tested. A mathematical formulation of the converging correction as a restraining condition in a least squares adjustment is developed for this purpose. It is shown that a convergency error is less relevant to close-range photogrammetry than generally assumed and that characteristic model deformations in close-range photogrammetry have the character of affine scale errors. Throughout the thesis algorithms are developed which make it possible to execute all computations on computers with limited memory capacity. A program sample for the relative orientation adjustment is given in Appendix IV to demonstrate the memory saving techniques. Finally the results of the investigation are applied to the survey of shoulder height of African elephants in their natural habitat. Equipment and field work are described and results reported

Geometric Accuracy Testing, Evaluation and Applicability of Space Imagery to the Small Scale Topographic Mapping of the Sudan

The geometric accuracy, interpretabilty and the applicability of using space imagery for the production of small-scale topographic maps of the Sudan have been assessed. Two test areas have been selected. The first test area was selected in the central Sudan including the area between the Blue Nile and the White Nile and extending to Atbara in the Nile Province. The second test area was selected in the Red Sea Hills area which has modern 1:100,000 scale topographic map coverage and has been covered by six types of images, Landsat MSS TM and RBV; MOMS; Metric Camera (MC); and Large format Camera (LFC). Geometric accuracy testing has been carried out using a test field of well-defined control points whose terrain coordinates have been obtained from the existing maps. The same points were measured on each of the images in a Zeiss Jena Stereocomparator (Stecometer C II) and transformed into the terrain coordinate system using polynomial transformations in the case of the scanner and RBV images; and space resection/intersection, relative/absolute orientation and bundle adjustment in the case of the MC and LFC photographs. The two sets of coordinates were then compared. The planimetric accuracies (root mean square errors) obtained for the scanner and RBV images were: Landsat MSS +/-80 m; TM +/-45 m; REV +/-40 m; and MOMS +/-28 m. The accuracies of the 3-dimensional coordinates obtained from the photographs were: MC:-X=+/-16 m, Y=+/-16 m, Z=+/-30 m; and LFC:- X=+/-14 m, Y=+/-14 m, and Z=+/-20 m. The planimetric accuracy figures are compatible with the specifications for topographic maps at scales of 1:250,000 in the case of MSS; 1:125,000 scale in the case of TM and RBV; and 1:100,000 scale in the case of MOMS. The planimetric accuracies (vector =+/-20 m) achieved with the two space cameras are compatible with topographic mapping at 1:60,000 to 1:70,000 scale. However, the spot height accuracies of +/-20 to +/-30 m - equivalent to a contour interval of 50 to 60 m - fall short of the required heighting accuracies for 1:60,000 to 1:100,000 scale mapping. The interpretation tests carried out on the MSS, TM, and RBV images showed that, while the main terrain features (hills, ridges, wadis, etc.) can be mapped reasonably well, there was an almost complete failure to pick up the cultural features - towns, villages, roads, railways, etc. - present in the test areas. The high resolution MOMS images and the space photographs were much more satisfactory in this respect though still the cultural features are difficult to pick up due to the buildings and roads being built out of local material and exhibiting little contrast on the images

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

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

Map-Based Localization for Unmanned Aerial Vehicle Navigation

Unmanned Aerial Vehicles (UAVs) require precise pose estimation when navigating in indoor and GNSS-denied / GNSS-degraded outdoor environments. The possibility of crashing in these environments is high, as spaces are confined, with many moving obstacles. There are many solutions for localization in GNSS-denied environments, and many different technologies are used. Common solutions involve setting up or using existing infrastructure, such as beacons, Wi-Fi, or surveyed targets. These solutions were avoided because the cost should be proportional to the number of users, not the coverage area. Heavy and expensive sensors, for example a high-end IMU, were also avoided. Given these requirements, a camera-based localization solution was selected for the sensor pose estimation. Several camera-based localization approaches were investigated. Map-based localization methods were shown to be the most efficient because they close loops using a pre-existing map, thus the amount of data and the amount of time spent collecting data are reduced as there is no need to re-observe the same areas multiple times. This dissertation proposes a solution to address the task of fully localizing a monocular camera onboard a UAV with respect to a known environment (i.e., it is assumed that a 3D model of the environment is available) for the purpose of navigation for UAVs in structured environments. Incremental map-based localization involves tracking a map through an image sequence. When the map is a 3D model, this task is referred to as model-based tracking. A by-product of the tracker is the relative 3D pose (position and orientation) between the camera and the object being tracked. State-of-the-art solutions advocate that tracking geometry is more robust than tracking image texture because edges are more invariant to changes in object appearance and lighting. However, model-based trackers have been limited to tracking small simple objects in small environments. An assessment was performed in tracking larger, more complex building models, in larger environments. A state-of-the art model-based tracker called ViSP (Visual Servoing Platform) was applied in tracking outdoor and indoor buildings using a UAVs low-cost camera. The assessment revealed weaknesses at large scales. Specifically, ViSP failed when tracking was lost, and needed to be manually re-initialized. Failure occurred when there was a lack of model features in the cameras field of view, and because of rapid camera motion. Experiments revealed that ViSP achieved positional accuracies similar to single point positioning solutions obtained from single-frequency (L1) GPS observations standard deviations around 10 metres. These errors were considered to be large, considering the geometric accuracy of the 3D model used in the experiments was 10 to 40 cm. The first contribution of this dissertation proposes to increase the performance of the localization system by combining ViSP with map-building incremental localization, also referred to as simultaneous localization and mapping (SLAM). Experimental results in both indoor and outdoor environments show sub-metre positional accuracies were achieved, while reducing the number of tracking losses throughout the image sequence. It is shown that by integrating model-based tracking with SLAM, not only does SLAM improve model tracking performance, but the model-based tracker alleviates the computational expense of SLAMs loop closing procedure to improve runtime performance. Experiments also revealed that ViSP was unable to handle occlusions when a complete 3D building model was used, resulting in large errors in its pose estimates. The second contribution of this dissertation is a novel map-based incremental localization algorithm that improves tracking performance, and increases pose estimation accuracies from ViSP. The novelty of this algorithm is the implementation of an efficient matching process that identifies corresponding linear features from the UAVs RGB image data and a large, complex, and untextured 3D model. The proposed model-based tracker improved positional accuracies from 10 m (obtained with ViSP) to 46 cm in outdoor environments, and improved from an unattainable result using VISP to 2 cm positional accuracies in large indoor environments. The main disadvantage of any incremental algorithm is that it requires the camera pose of the first frame. Initialization is often a manual process. The third contribution of this dissertation is a map-based absolute localization algorithm that automatically estimates the camera pose when no prior pose information is available. The method benefits from vertical line matching to accomplish a registration procedure of the reference model views with a set of initial input images via geometric hashing. Results demonstrate that sub-metre positional accuracies were achieved and a proposed enhancement of conventional geometric hashing produced more correct matches - 75% of the correct matches were identified, compared to 11%. Further the number of incorrect matches was reduced by 80%

Large Area 3-D Reconstructions from Underwater Optical Surveys

Robotic underwater vehicles are regularly performing vast optical surveys of the ocean floor. Scientists value these surveys since optical images offer high levels of detail and are easily interpreted by humans. Unfortunately, the coverage of a single image is limited by absorption and backscatter while what is generally desired is an overall view of the survey area. Recent works on underwater mosaics assume planar scenes and are applicable only to situations without much relief. We present a complete and validated system for processing optical images acquired from an underwater robotic vehicle to form a 3D reconstruction of the ocean floor. Our approach is designed for the most general conditions of wide-baseline imagery (low overlap and presence of significant 3D structure) and scales to hundreds or thousands of images. We only assume a calibrated camera system and a vehicle with uncertain and possibly drifting pose information (e.g., a compass, depth sensor, and a Doppler velocity log). Our approach is based on a combination of techniques from computer vision, photogrammetry, and robotics. We use a local to global approach to structure from motion, aided by the navigation sensors on the vehicle to generate 3D sub-maps. These sub-maps are then placed in a common reference frame that is refined by matching overlapping sub-maps. The final stage of processing is a bundle adjustment that provides the 3D structure, camera poses, and uncertainty estimates in a consistent reference frame. We present results with ground truth for structure as well as results from an oceanographic survey over a coral reef.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86036/1/opizarro-12.pd