An Improved Outdoor Camera Calibration Method Based On EKF

A common problem in vanishing-point-based camera calibration methods is that they are ill-conditioned when the parallel lines for calibration in the world coordinates also appear to be parallel or near-parallel in the image coordinates. Then the camera parameters are not calculable or incur substantial error because one of the vanishing points approaches infinity. We propose a new method that overcomes the ill-conditioning. Using lane markings on a road to form a rectangular calibration pattern with two vanishing points, we first derive a set of equations based on one vanishing point without assuming any extrinsic parameters being known a priori. Because only one vanishing point can approach infinity at any one time, ill-conditioning can be avoided completely by selecting the vanishing point that does not suffer from it. This enables us to produce a set of extrinsic camera parameters that maps the world and image coordinates accurately. Simulation and real image tests show that the proposed method conquers ill-conditioning successfully and is insensitive to pixel offset on the calibration pattern.

Calibration of the transformation between two planes, the image plane and the 2D platform, is important for applications where 2D metric information on the image plane is used to compute the 3D information in a world coordinate system. Efforts have been taken in computer vision literature to perform a full-scale camera calibration, including intrinsic and extrinsic parameters. For some applications, calibration of intrinsic parameters is not required as often as that of the extrinsic parameters. This paper addresses the problem of calibrating a camera's extrinsic parameters with respect to a 2D platform to which a camera is observing. A rational approximation method is proposed. Simulation and experimental results show that the proposed rational approximation method achieves comparable accuracy with the well-known homography-based approach. This work is motivated by our mobile sensor network project. Other relevant applications include vision-based metrology.

Camera calibration is an important issue in computer vision. In this paper, we propose an improved camera auto-calibration algorithm from sequential images based on VP (vanishing point) and EKF (extended Kalman filter) to determine camera intrinsic parameters. This is the first vanishing point-based auto-calibration algorithm, which only uses a sequence of monocular images as input without any other information. According to geometry constraints of projective projection, we compute the vanishing points in three orthogonal directions by observing an object moving in one direction from an image sequence. Afterwards intrinsic parameters can be calculated. The extended Kalman filter is used to track the feature points in the image sequence rapidly and accurately. Compared with existing methods based on vanishing point, our approach simplifies calibration process, gets rid of calibration objects and manual intervention, avoids correspondences between 2D image and 3D world features and reduces errors to a large extent. Simulations and real image experiments validate the proposed approach and indicate that it is accurate and robust to noise. As a result, it could be applied to almost all real scenes like on-orbit camera calibration, autonomous vehicle navigation, space vehicle rendezvous and docking.

This paper presents a new algorithm of traditional camera calibration which is based on Extended Kalman Filter. The Extended Kalman Filter is a set of mathematical equations that provides an efficient way to estimate the state of a process. The technique of camera calibration can be divided into three kinds in practice, among which the traditional camera calibration has the highest precision. The substance of camera calibration is to figure out the intrinsic and extrinsic parameters of a camera for its further application in computer vision. In this paper, the image coordinates of the characteristics and the corresponding world coordinates are taken as the filter's inputs, the estimate value of these parameters are taken as the filter's outputs. Simulation and experiments results show the well optimization of this method.

Many approaches for camera and LiDAR calibration are presented in literature but none of them estimates all intrinsic and extrinsic parameters simultaneously and therefore optimally in a probabilistic sense.In this work, we present a method to simultaneously estimate intrinsic and extrinsic parameters of cameras and LiDARs in a unified problem. We derive a probabilistic formulation that enables flawless integration of different measurement types without hand-tuned weights. An arbitrary number of cameras and LiDARs can be calibrated simultaneously. Measurements are not required to be time-synchronized. The method is designed to work with any camera model.In evaluation, we show that additional LiDAR measurements significantly improve intrinsic camera calibration. Further, we show on real data that our method achieves state-of-the-art calibration precision with high reliability.

This paper introduces a simultaneous estimation method of the extrinsic parameters of multiple fish-eye cameras using simple calibration markers. Precise extrinsic parameters of cameras mounted on a car are important, for example, to provide a seamless overhead view image to the driver. Calibration markers are set in the area that are observable from adjacent two cameras. Extrinsic parameters of each camera are estimated individually and then combined and refined using a geometric constraint. Cube markers are chosen as the calibration markers. The method is evaluated by simulation and experiments using a real car. It is shown that extrinsic parameters are obtained by the proposed method and suggested that the errors of intrinsic parameters affect the estimation of extrinsic parameters.

Accurately estimating the 3D position of underwater objects is of great interest when doing research on marine animals. An inherent problem of 3D reconstruction of underwater positions is the presence of refraction which invalidates the assumption of a single viewpoint. Three ways of performing 3D reconstruction on underwater objects are compared in this work: an approach relying solely on in-air camera calibration, an approach with the camera calibration performed under water and an approach based on ray tracing with Snell's law. As expected, the in-air camera calibration showed to be the most inaccurate as it does not take refraction into account. The precision of the estimated 3D positions based on the underwater camera calibration and the ray tracing based approach were, on the other hand, almost identical. However, the ray tracing based approach is found to be advantageous as it is far more flexible in terms of the calibration procedure due to the decoupling of the intrinsic and extrinsic camera parameters.

We present a camera calibration technique to determine the focal length and the extrinsic parameters of a camera merely by using one perspective view of two coplanar circles with arbitrary radii and topological configuration. We believe our effort is valuable, in that the position of a camera and its focal length are frequently adjusted in many vision applications. In contrast to the iterative optimization technique in previous work, whose convergence relies heavily on proper initialization, we propose a closed-form solution on the basis of simple matrix operations, which turns out to be computationally efficient. It can also be used to initialize existing algorithms for higher accuracy and speed. Our method is based on the projective equation of a circle, first presented here, which naturally encodes the intrinsic and extrinsic camera parameters and the degenerate conic envelope spanned by the image of circular points. Extensive experiments with both synthetic data and real images verify the efficiency and robustness of our technique.

Camera’s internal parameter calibration is an important problem in computer vision. The moment, a precise targets like checkboard is required when camera calibration is performed. But this method is not suitable for a telephoto lens. In order to overcome this problem, a new camera calibration model is constructed by installing the debugged telephoto camera on an accurate two-dimensional rotating platform. Let the camera move around the rotating axis of the rotating platform. The camera takes pictures of distant objects directly. Then, the next picture is get by rotating the two-dimensional platform. The image coordinates , of the same point in space, in different images are obtained by image matching. The motion matrix of the camera is calculated from the readings of the two-dimensional rotating platform. Last, the optimization equation can be enumerated to solve the internal parameters. The experimental results show that the internal parameters obtained by the algorithm can satisfy the calculation accuracy.

An analytical method to calibrate a camera's extrinsic parameters and effective focal lengths is presented. We used a single image with four coplanar control lines. Unique solutions of the camera's extrinsic parameters and the two effective focal lengths are derived linearly and analytically. If the effective focal lengths are known, unique solutions of the extrinsic parameters can be derived more easily. Our method can easily be implemented and has better precision than the analogous method by use of control points. The results of simulated experiments are presented.

Purpose: A prototype mobile C‐arm capable of kV cone beam CT has been proposed to evaluate patient setup accuracy. To facilitate this, the location of the C‐arm's reconstructed image volume in the treatment room must be known. Method and Materials: A calibration procedure to make the necessary transformation between image coordinates and room coordinates has been developed using a commercial optical tracking system. Markers are placed on both the C‐arm and a calibration phantom. After the initial calibration procedure, only the markers on the C‐arm need to be located at the time of image acquisition to make the final transformation. The calibration procedure was evaluated using the optical tracking system and a phantom with attached reflective markers. After imaging, the markers were located in the reconstruction and then transformed into world coordinates. These positions were then compared to the markers location according to the tracking system (assumed true world coordinates). Movements were made to the C‐arm, subsequent images acquired, and the analysis was repeated. Calibrations done on different days were also used to analyze the same data set. Results: The max error of any of the markers after the movements was below 1.4 mm, the mean absolute error below 0.9 mm, and the RMS error below 1.0 mm. The other calibrations had slightly larger errors but no marker out of any of the calibrations had a max error greater then 2.3 mm, a mean absolute error greater then 1.6 mm, or an RMS error greater then 1.6 mm. Conclusion:.2160 2005 AAPM Meeting Program 2160 Medical Physics, Vol. 32, No. 6, June 2005 The results show that using an optical tracking system can provide an accurate transformation of the reconstructed coordinates of a mobile C‐arm into room coordinates. This work supported in part by Research Scholar Grant ♯ 03‐028‐01‐CCE from the American Cancer Society and Siemens.

Camera calibration using one-dimensional information and its applications in both controlled and uncontrolled environments

A multi‐camera rig calibration algorithm based on a double sided planar target is proposed. Due to their inherently simple realisation, low cost and accuracy, planar calibration targets came out as one of the most largely adopted calibration tools both for intrinsic and extrinsic camera parameters. However, concerning the estimation of extrinsic parameters, one of the major drawbacks of these targets is their requirement for distinct target visibility from both cameras. This prevents many configurations from being adopted where, e.g. two cameras are facing each other. An inexpensive solution could be based on printing/pasting a planar pattern on both target sides, however, the relative misalignment between the patterns on the two sides and the target thickness could be unknown. The authors propose a solution where double‐sided target displacement error is estimated together with the extrinsic parameters allowing the reuse of all the available planar calibration tools in less constrained configurations. To assess their approach the authors tested the system in two scenarios, one using two professional 4K cameras and one using two smartphones.

The process of solving camera intrinsic and extrinsic parameters has been presented by using geometric techniques. In contrast with traditional method, which is a pure algebra process, the geometric technique accomplishes the camera parameters more intuitively and easily. If the perspective projection matrix is given, according to the geometric meaning of perspective projection camera model, the coordinates of optical centre can be directly estimated in the world coordinate system. Then rotation matrix and translation vector can be obtained from the matrix. Finally, we can derive camera intrinsic parameters. During the process of derivation, for any given 3 by 4 matrix, the constraint conditions have been discussed in another way when the matrix could be described as a perspective projection transformation. Although it has the same result as pure algebra progress, it's of great significance to understand the geometric meaning among the intrinsic and extrinsic camera parameters

Stereo-vision devices have rigorous requirements for extrinsic parameter calibration. In Stereo Visual Inertial Odometry (VIO), inaccuracy in or changes to camera extrinsic parameters may lead to serious degradation in estimation performance. In this manuscript, we propose an online calibration method for stereo VIO extrinsic parameters correction. In particular, we focus on Multi-State Constraint Kalman Filter (MSCKF [1]) framework to implement our method. The key component is to formulate stereo extrinsic parameters as part of the state variables and model the Jacobian of feature reprojection error with respect to stereo extrinsic parameters as sub-block of update Jacobian. Therefore we can estimate stereo extrinsic parameters simultaneously with inertial measurement unit (IMU) states and camera poses. Experiments on EuRoC dataset and real-world outdoor dataset demonstrate that the proposed algorithm produce higher positioning accuracy than the original S-MSCKF [2], and the noise of camera extrinsic parameters are self-corrected within the system.