Geometric and algebraic constraints of projected concentric circles and their applications to camera calibration

In this paper, we present a novel viewpoint of treating conks-based calibration as the algebraic and geometric constraints. From this viewpoint, we use four intersection points correspondence to conduct a unified algebraic constraint of Principal-Axes Aligned (PAA) conies which is a necessary and sufficient condition to recover the 2D Euclidean structure (ES). Under this unified constraint, we can establish the link to other existing approaches (such as concentric circles, confocal conies) and find some novel patterns. Meanwhile, the geometric interpretation that the quadrangle formed by PAA conies is actually a rectangle with one degree of freedom is shown. Then a framework is introduced to deal with various situations of PAA conies. Finally, we propose an optimization procedure to estimate the lens distortion which is discarded by previous methods. The experiments with linear method and optimization method show the good performance of our camera calibration algorithms.

We present a new algorithm for camera calibration using two concentric circles, which is a linear approach. In the calibration, a pinhole camera model is used. Different from previous methods, we take the projective equations of 3-D circles, which include the intrinsic parameter matrix of the camera, as the basis of our calibration approach. According to the special structure of the projective equations in algebra, we can get a linear equation system about the intrinsic parameters. After enough equations are constructed, the calibration can be easily finished. With at least three images of the two concentric circles, all five intrinsic parameters can be recovered. Experiments using computer simulated data and real data demonstrate the robustness and accuracy of our method.

In this paper, we present a new algorithm for camera calibration using concentric circles, which is a linear approach. Different from previous methods, we take the projective equations of three-dimensional circles, which include the intrinsic parameter matrix of the camera, as the basis of our calibration approach. According to the special structure of the projective equations in algebra, we can get a linear equation system about the intrinsic parameters. After enough equations constructed, the calibration can be easily finished. Our method needs three images of the two concentric circles at least, and all the five intrinsic parameters can be recovered. Experiments using computer simulated data demonstrate the robustness and accuracy of our method.

The accuracy of the results in stereo image-based 3D reconstruction is very sensitive to the intrinsic and extrinsic camera parameters determined during camera calibration. The existing camera calibration algorithms induce a significant amount of error due to poor estimation accuracies in camera parameters when they are used for long-range scenarios such as mapping civil infrastructure. This leads to unusable results, and may result in the failure of the whole reconstruction process. This paper proposes a novel way to address this problem. Instead of incremental improvements to the accuracy typically induced by new calibration algorithms, the authors hypothesize that a set of multiple calibrations created by videotaping a moving calibration pattern along a specific path can increase overall calibration accuracy. This is achieved by using conventional camera calibration algorithms to perform separate estimations for some predefined distance values. The result, which is a set of camera parameters for different distances, is then uniquely input in the Structure from Motion process to improve the Euclidean accuracy of the reconstruction. The proposed method has been tested on infrastructure scenes and the experimental analyses indicate the improved performance.

An automatic camera calibration scheme that utilizes a coordinate measuring machine (CMM) and a camera calibration algorithm is presented for a multiple-sensor integrated coordinate measurement system. In the proposed calibration scheme, the touch probe tip carried by the CMM is employed to automatically generate high-precision calibration target points for camera calibration and sensor integration. A camera calibration algorithm with analytical formulations is developed to calibrate camera parameters in three stages without nonlinear minimization procedures. Simulations and experiments were performed to verify the proposed camera calibration algorithm. The precision of the automatic camera calibration scheme is also evaluated.

Plane-based (2-D) camera calibration is becoming a hot research topic in recent years because of its flexibility. However, at least four image points are needed in every view to denote the coplanar feature in the 2-D camera calibration. Can we do the camera calibration by using the calibration object that only has three points? Some 1-D camera calibration techniques use the setup of three collinear points with known distances, but it is a kind of special conditions of calibration object setup. How about the general setup-three noncollinear points? We propose a new camera calibration algorithm based on the calibration objects with three noncollinear points. Experiments with simulated data and real images are carried out to verify the theoretical correctness and numerical robustness of our results. Because the objects with three noncollinear points have special properties in camera calibration, they are midway between 1-D and 2-D calibration objects. Our method is actually a new kind of camera calibration algorithm.

Camera calibration and image correction is an important step for most of the computer vision tasks, like 3D metric measurement and multi-view stereo. In this paper, we propose a novel algorithm for camera calibration and image correction. It considers the inaccuracy of 3D pattern (like chessboard) and the lens distortion effect on the feature point detection. After each iteration, the estimated parameters are used to undistorted the images to have better feature detection. The established 3D-2D points are more accurate for further camera calibration. A comparative study based on synthetic data, real image and data from our 3D scanner corrupted by reasonable levels of noise shows that the proposed algorithm successfully calibrated, corrected the distorted images and precisely reconstructed the captured laser stripes in 3D space.

In this paper, a new camera calibration algorithm is proposed, which is from the quasi-affine invariance of two parallel circles. Two parallel circles here mean two circles in one plane, or in two parallel planes. They are quite common in our life.Between two parallel circles and their images under a perspective projection, we set up a quasi-affine invariance. Especially, if their images under a perspective projection are separate, we find out an interesting distribution of the images and the virtual intersections of the images, and prove that it is a quasi-affine invariance.The quasi-affine invariance is very useful which is applied to identify the images of circular points. After the images of the circular points are identified, linear equations on the intrinsic parameters are established, from which a camera calibration algorithm is proposed. We perform both simulated and real experiments to verify it. The results validate this method and show its accuracy and robustness. Compared with the methods in the past literatures, the advantages of this calibration method are: it is from parallel circles with minimal number; it is simple by virtue of the proposed quasi-affine invariance; it does not need any matching.Excepting its application on camera calibration, the proposed quasi-affine invariance can also be used to remove the ambiguity of recovering the geometry of single axis motions by conic fitting method in [8] and [9]. In the two literatures, three conics are needed to remove the ambiguity of their method. While, two conics are enough to remove it if the two conics are separate and the quasi-affine invariance proposed by us is taken into account.KeywordsCamera CalibrationIntrinsic ParameterPinhole CameraAbsolute ConicCircular PointThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Accurate calibration of cameras in industrial production vision systems is a critical fundamental task. However, industrial visual measurement systems often face challenges such as large fields of view, shallow depths of field, and the use of imprecise large calibration templates. These factors make the task of accurate visual measurement in the industrial production environment a great challenge. This paper presents a camera calibration algorithm based on the eccentricity error of concentric circles and the fixed topological relationship constraints of the calibration board structure. In this calibration algorithm, the homography relationship of the calibration board targets is calculated to iteratively optimize the eccentricity error of the concentric circle patterns, providing stable and accurate feature point information for precise camera calibration in industrial settings. Additionally, during the iterative calibration process, deviation parameters are introduced for each feature point on the calibration board relative to the standard plane to account for the machining and geometric deformation errors of the calibration board. This approach addresses issues related to the imprecise calibration of large planar templates. These deviation parameters and eccentricity errors of the concentric circle feature points are optimized together with the camera calibration parameters to correct the positions of the feature points and enhance the camera calibration accuracy in complex industrial scenarios. The results of simulation and experiments validate the feasibility and operability of the proposed camera calibration method. It can fundamentally eliminate perspective transformation errors and improve the precision of camera parameters and target geometry.

This paper describes a method that detects two co-planar circular shaped objects having the same radius from an image with clutter background. We propose an unique RANSAC based method for detecting the candidates of ellipses that divides the circular region centered at the assumed ellipse center into N equal sectors, then fits the edge points selected randomly from each sector. We propose three geometrical constraints of a pair of co-planar circles having the same radius by considering the normal vectors of the supporting plane estimated from each ellipse and the 3D coordinates of the centers of the two circles. From the detected candidates of ellipses, we select the co-planar circle pairs having the same radius by checking how well they fit the proposed geometrical constraints. The output of this method can be used as inputs of many camera calibration and/or 3D structure recovery algorithms that require parallel or co-planar circles. Our method can also applied to the mobile robots to determine their position by monitoring the two co-planar circular objects in the environment.

With 3D vision measuring, camera calibration is necessary for extracting metric information from 2D images. We present a new algorithm for camera calibration that only requires a spatial triangle with known size. In our method, the camera is fixed while the triangle is rotated freely at one of its vertices. By taking a few (at least two) pictures of the rotating object at an identical camera view position and direction, the camera intrinsic matrix can be obtained. It advances other traditional methods in that the extrinsic parameters are separated from the intrinsic ones, which simplifies the problem with more efficiency and accuracy. Experiments also show that our method is robust and results in high resolution.

Camera calibration is used to establish a mathematical model and solve the parameters of the camera through the correspondence between a series of scene points and pixel points. How to establish this mapping relationship is a key issue that needs to be solved in camera calibration. Various algorithms of calibration have been proposed by domestic and foreign scholars, including traditional visual calibration algorithm, camera self-calibration algorithm, and active-vision-based calibration algorithm. This paper focuses on some of the most widely used camera calibration algorithms and compares them.

In the picking robot binocular vision systems research, the camera calibration is often an indispensable step and these basements to locate the target of the object and rebuild the three-dimensional construction based on the robot stereo vision for the follow-up study. So, searching for a high accuracy and simple camera calibration algorithm is of great significance and necessary. However, For most of these camera calibration algorithms, it is necessary to establish a reference object, namely the target, in front of the camera at present, but posing the target is very not convenient or almost impossible in some cases. Therefore, a picking robot online calibration algorithm based on the vision scene was proposed by studying the work environment characteristics of the picking robot binocular vision system and the invariant projective geometry. The experimental results showed that this algorithm’s calibration accuracy and precision good meets to the requirement of the robot binocular vision system camera calibration in the complex environment.

The conventional calibration methods based on a perspective camera model are not suitable for the underground camera with two-layer glasses, which is specially designed for explosion proof and dust removal in a coal mine. Underground camera modeling and calibration algorithms are urgently needed to improve the precision and reliability of underground visual measurement systems. This article presents a novel geometrically driven underground camera calibration algorithm for a boom-type roadheader. The underground camera model is established under coplanarity constraints, considering explicitly the impact of refraction triggered by the two-layer glasses and deriving the geometrical relationship of equivalent collinearity equations. On this basis, we perform parameters calibration based on a geometrically driven calibration model, which are 2D-2D correspondences between the image points and object coordinates of the planar target. A hybrid Levenberg-Marqurdt (LM) and particle swarm optimization (PSO) algorithm is further proposed in terms of the dynamic combination of the LM and PSO, which optimizes the underground camera calibration results by minimizing the error of the nonlinear underground camera model. The experimental results demonstrate that the pose errors caused by the two-layer glass refraction are well corrected by the proposed method. The accuracy of the cutting-head pose estimation has increased by 55.73%, meeting the requirements of underground excavations.

It is proposed a method for camera calibration that could be used in stereo systems as well as in stereo head navigation in this paper. A pinhole camera model and two-dimensional planar target are considered. An Iterated Extended Kalman Filter (IEKF) is used to estimate camera parameters. The met hod takes the observed feature points of images as the filter input and the estimated value of the intrinsic and extrinsic camera parameters as the filter output. Both computer simulation and real data experiments have been used to test the proposed method, and good results have been obtained. The RMS error of absolute distance between reprojection feature points is about 0.09 pixels in real experiments. The experimental results show IEKF is also a feasible optimization algorithm for on-line camera calibration. Key words: Camera Calibration, Iterated Extended Kalman Filter, planar target 1. INTRODUCTION Camera calibration is a crucial phase in most vision systems and a first step in 3D reconstruction. It has been broadly applied in machine vision, virtual reality, and three-dimensional reconstruction and so on. Generally, in order to obtain higher calibration precision, in trinsic and extrinsic camera para meters are estimated through nonlinear optimization methods with information acquired from images. Starting from the simplest method we could mention the Least Square Error (LSE)