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

3D Reconstruction with Uncalibrated Cameras Using the Six-Line Conic Variety

We present new algorithms for the recovery of the Euclidean structure from a projective calibration of a set of cameras with square pixels but otherwise arbitrarily varying intrinsic and extrinsic parameters. Our results, based on a novel geometric approach, include a closed-form solution for the case of three cameras and two known vanishing points and an efficient one-dimensional search algorithm for the case of four cameras and one known vanishing point. In addition, an algorithm for a reliable automatic detection of vanishing points on the images is presented. These techniques fit in a 3D reconstruction scheme oriented to urban scenes reconstruction. The satisfactory performance of the techniques is demonstrated with tests on synthetic and real data

Self-Calibration of Cameras with Euclidean Image Plane in Case of Two Views and Known Relative Rotation Angle

The internal calibration of a pinhole camera is given by five parameters that are combined into an upper-triangular $3\times 3$ calibration matrix. If the skew parameter is zero and the aspect ratio is equal to one, then the camera is said to have Euclidean image plane. In this paper, we propose a non-iterative self-calibration algorithm for a camera with Euclidean image plane in case the remaining three internal parameters --- the focal length and the principal point coordinates --- are fixed but unknown. The algorithm requires a set of $N \geq 7$ point correspondences in two views and also the measured relative rotation angle between the views. We show that the problem generically has six solutions (including complex ones). The algorithm has been implemented and tested both on synthetic data and on publicly available real dataset. The experiments demonstrate that the method is correct, numerically stable and robust.Comment: 13 pages, 7 eps-figure

Towards A Self-calibrating Video Camera Network For Content Analysis And Forensics

Due to growing security concerns, video surveillance and monitoring has received an immense attention from both federal agencies and private firms. The main concern is that a single camera, even if allowed to rotate or translate, is not sufficient to cover a large area for video surveillance. A more general solution with wide range of applications is to allow the deployed cameras to have a non-overlapping field of view (FoV) and to, if possible, allow these cameras to move freely in 3D space. This thesis addresses the issue of how cameras in such a network can be calibrated and how the network as a whole can be calibrated, such that each camera as a unit in the network is aware of its orientation with respect to all the other cameras in the network. Different types of cameras might be present in a multiple camera network and novel techniques are presented for efficient calibration of these cameras. Specifically: (i) For a stationary camera, we derive new constraints on the Image of the Absolute Conic (IAC). These new constraints are shown to be intrinsic to IAC; (ii) For a scene where object shadows are cast on a ground plane, we track the shadows on the ground plane cast by at least two unknown stationary points, and utilize the tracked shadow positions to compute the horizon line and hence compute the camera intrinsic and extrinsic parameters; (iii) A novel solution to a scenario where a camera is observing pedestrians is presented. The uniqueness of formulation lies in recognizing two harmonic homologies present in the geometry obtained by observing pedestrians; (iv) For a freely moving camera, a novel practical method is proposed for its self-calibration which even allows it to change its internal parameters by zooming; and (v) due to the increased application of the pan-tilt-zoom (PTZ) cameras, a technique is presented that uses only two images to estimate five camera parameters. For an automatically configurable multi-camera network, having non-overlapping field of view and possibly containing moving cameras, a practical framework is proposed that determines the geometry of such a dynamic camera network. It is shown that only one automatically computed vanishing point and a line lying on any plane orthogonal to the vertical direction is sufficient to infer the geometry of a dynamic network. Our method generalizes previous work which considers restricted camera motions. Using minimal assumptions, we are able to successfully demonstrate promising results on synthetic as well as on real data. Applications to path modeling, GPS coordinate estimation, and configuring mixed-reality environment are explored

A Self-Calibration Method of Zooming Camera

In this article we proposed a novel approach to self- calibrate a camera with variable focal length. We show that the estimation of camera’s intrinsic parameters is possible from only two points of an unknown planar scene. The projection of these points by using the projection matrices in two images only permit us to obtain a system of equations according to the camera’s intrinsic parameters . From this system we formulated a nonlinear cost function which its minimization allows us to estimate the camera’s intrinsic parameters in each view. The results on synthetic and real data justify the robustness of our method in term of reliability and convergence

Cavlectometry: Towards Holistic Reconstruction of Large Mirror Objects

We introduce a method based on the deflectometry principle for the reconstruction of specular objects exhibiting significant size and geometric complexity. A key feature of our approach is the deployment of an Automatic Virtual Environment (CAVE) as pattern generator. To unfold the full power of this extraordinary experimental setup, an optical encoding scheme is developed which accounts for the distinctive topology of the CAVE. Furthermore, we devise an algorithm for detecting the object of interest in raw deflectometric images. The segmented foreground is used for single-view reconstruction, the background for estimation of the camera pose, necessary for calibrating the sensor system. Experiments suggest a significant gain of coverage in single measurements compared to previous methods. To facilitate research on specular surface reconstruction, we will make our data set publicly available

Extrinsic Parameter Calibration for Line Scanning Cameras on Ground Vehicles with Navigation Systems Using a Calibration Pattern

Line scanning cameras, which capture only a single line of pixels, have been increasingly used in ground based mobile or robotic platforms. In applications where it is advantageous to directly georeference the camera data to world coordinates, an accurate estimate of the camera's 6D pose is required. This paper focuses on the common case where a mobile platform is equipped with a rigidly mounted line scanning camera, whose pose is unknown, and a navigation system providing vehicle body pose estimates. We propose a novel method that estimates the camera's pose relative to the navigation system. The approach involves imaging and manually labelling a calibration pattern with distinctly identifiable points, triangulating these points from camera and navigation system data and reprojecting them in order to compute a likelihood, which is maximised to estimate the 6D camera pose. Additionally, a Markov Chain Monte Carlo (MCMC) algorithm is used to estimate the uncertainty of the offset. Tested on two different platforms, the method was able to estimate the pose to within 0.06 m / 1.05$^{\circ}$ and 0.18 m / 2.39$^{\circ}$. We also propose several approaches to displaying and interpreting the 6D results in a human readable way.Comment: Published in MDPI Sensors, 30 October 201

Omnidirectional video

Omnidirectional video enables direct surround immersive viewing of a scene by warping the original image into the correct perspective given a viewing direction. However, novel views from viewpoints off the camera path can only be obtained if we solve the 3D motion and calibration problem. In this paper we address the case of a parabolic catadioptric camera – a paraboloidal mirror in front of an orthographic lens – and we introduce a new representation, called the circle space, for points and lines in such images. In this circle space, we formulate an epipolar constraint involving a 4x4 fundamental matrix. We prove that the intrinsic parameters can be inferred in closed form from the 2D subspace of the new fundamental matrix from two views if they are constant or from three views if they vary. Three dimensional motion and structure can then be estimated from the decomposition of the fundamental matrix