A stepwise camera calibration method incorporating compensation for eccentricity error

In visual measurement,high-precision camera calibration often employs circular targets.To address issues in mainstream methods,such as the eccentricity error of the circle from using the circle’s center for calibration,overfitting or local minimum from fullparameter optimization,and calibration errors due to neglecting the center of distortion,a stepwise camera calibration method incorporating compensation for eccentricity error was proposed to enhance monocular camera calibration precision.Initially,the multiimage distortion correction method calculated the common center of distortion and coefficients,improving precision,stability,and efficiency compared to single-image distortion correction methods.Subsequently,the projection point of the circle’s center was compared with the center of the contour’s projection to iteratively correct the eccentricity error,leading to more precise and stable calibration.Finally,nonlinear optimization refined the calibration parameters to minimize reprojection error and boosts precision.These processes achieved stepwise camera calibration,which enhanced robustness.In addition,the module comparison experiment showed that both the eccentricity error compensation and the camera parameter optimization could improve the calibration precision,but the latter had a greater impact.The combined use of the two methods further improved the precision and stability.Simulations and experiments confirmed that the proposed method achieved high precision,stability,and robustness,suitable for high-precision visual measurements.

GYRO BIAS ON-ORBIT CALIBRATION FOR MICRO SATELLITES

According to gyro application in micro-satellites, a new gyro bias real-time on-orbit calibration technology is presented and it is independent of any other sensors. The approach relies on gyro on-orbit measurements restricted by satellite attitude dynamics and estimates the gyro bias generated when the gyro is electrified. Observability of the calibration model is analyzed and applicable conditions of the technology are derived. Simulation results indicate that the calibration algorithm is accurate and robust at gyro sampling rate, and its convergence speed is fast. Within the given attitude dynamics model error, the convergence time is less than 100 s and the convergence accuracy is about 1.0 （°）/h. Calibration performance can meet requirements of spacecraft operations.

NEW VERSATILE CAMERA CALIBRATION TECHNIQUE BASED ON LINEAR RECTIFICATION

A new versatile camera calibration technique for machine vision usingoff-the-shelf cameras is described. Aimed at the large distortion of the off-the-shelf cameras, anew camera distortion rectification technology based on line-rectification is proposed. Afull-camera-distortion model is introduced and a linear algorithm is provided to obtain thesolution. After the camera rectification intrinsic and extrinsic parameters are obtained based onthe relationship between the homograph and absolute conic. This technology needs neither ahigh-accuracy three-dimensional calibration block, nor a complicated translation or rotationplatform. Both simulations and experiments show that this method is effective and robust.

The Calibration of High-Speed Camera Imaging System for ELMs Observation on EAST Tokamak

A tangential fast visible camera has been set up in EAST tokamak for the study of edge MHD instabilities such as ELM. To determine the 3-D information from CCD images, Tsai＇s two-stage technique was utilized to calibrate the high-speed camera imaging system for ELM study. By applying tiles of the passive stabilizers in the tokamak device as the calibration pattern, transformation parameters for transforming from a 3-D world coordinate system to a 2-D image coordinate system were obtained, including the rotation matrix, the translation vector, the focal length and the lens distortion. The calibration errors were estimated and the results indicate the reliability of the method used for the camera imaging system. Through the calibration, some information about ELM filaments, such as positions and velocities were obtained from images of H-mode CCD videos.

Non-Metric CCD Camera Calibration Algorithm in a Digital Photogrammetry System

Camera calibration is a critical process in photogrammetry and a necessary step to acquire 3D information from a 2D image. In this paper, a flexible approach for CCD camera calibration using 2D direct linear transformation （DLT） and bundle adjustment is proposed. The proposed approach assumes that the camera interior orientation elements are known, and addresses a new closed form solution in planar object space based on homogenous coordinate representation and matrix factorization. Homogeneous coordinate representation offers a direct matrix correspondence between the parameters of the 2D DLT and the collinearity equation. The matrix factorization starts by recovering the elements of the rotation matrix and then solving for the camera position with the collinearity equation. Camera calibration with high precision is addressed by bundle adjustment using the initial values of the camera orientation elements. The results show that the calibration precision of principal point and focal length is about 0.2 and 0.3 pixels respectivelv, which can meet the requirements of close-range photogrammetry with high accuracy.

A new technique for high precision sub-regional camera calibration based on checkerboard pattern

Camera calibration is critical in computer vision measurement system, affecting the accuracy of the whole system. Many camera calibration methods have been proposed, but they cannot consider precision and operation complexity at the same time. In this paper, a new technique is proposed to calibrate camera. Firstly, the global calibration method is described in de-tail. It requires the camera to observe a checkerboard pattern shown at a few different orientations. The checkerboard corners are obtained by Harris algorithm. With direct linear transformation and non-linear optimal algorithm, the global calibration pa-rameters are obtained. Then, a sub-regional method is proposed. Those corners are divided into two groups, middle corners and edge corners, which are used to calibrate the corresponding area to get two sets of calibration parameters. Finally, some experimental images are used to test the proposed method. Experimental results demonstrate that the average projection error of sub-region method is decreased at least 16% compared with the global calibration method. The proposed technique is simple and accurate. It is suitable for the industrial computer vision measurement.

Development and calibration of the Moon-based EUV camera for Chang'e-3

The process of development and calibration for the first Moon-based ex- treme ultraviolet （EUV） camera to observe Earth＇s plasmasphere is introduced and the design, test and calibration results are presented. The EUV camera is composed of a multilayer film mirror, a thin film filter, a photon-counting imaging detector, a mech- anism that can adjust the direction in two dimensions, a protective cover, an electronic unit and a thermal control unit. The center wavelength of the EUV camera is 30.2 nm with a bandwidth of 4.6nm. The field of view is 14.7° with an angular resolution of 0.08°, and the sensitivity of the camera is 0.11 count s-1 Rayleigh-1. The geomet- ric calibration, the absolute photometric calibration and the relative photometric cal- ibration are carried out under different temperatures before launch to obtain a matrix that can correct geometric distortion and a matrix for relative photometric correction, which are used for in-orbit correction of the images to ensure their accuracy.

GF-5 VIMI On-Orbit Calibration Instrument and Performance

The Visible and Infrared Multispectral Imager (VIMI) is one of the main payloads of the GF-5 satellite. It has 12 spectral bands covering the wavelength from visible light to thermal infrared. The imager designed life is 8 years. In order to monitor and correct the radiometric performance of the imager for a long time and meet the user’s demand for the quantitative remote sensing application, the expandable diffuser used for calibration in full FOV and full optical path method is designed. The solar diffuser is installed on the front side of the optical system and does not affect the normal imaging of VIMI. When VIMI need calibration, the diffuser is expand to the front of optical system via the driving mechanism. According to the characteristics of the GF-5 satellite orbit, the requirement of the calibration energy and the installation matrix of the imager relative to the satellite, the expansion angle of the diffuser is 39 degrees. The 430 mm × 430 mm large-size PTEE diffuser is manufactured to ensure full FOV and full optical path calibration. The diffuser’s directional hemispherical reflectance is higher than 95% from 420 nm to 2400 nm and variation of BRDF in the direction of imager observation is better than 2.5%. The diffuser stability monitoring radiometer is designed to monitor the on-orbit attenuation performance of the diffuser. Results of ground simulation experiments and preliminary on-board calibration experiments were introduced.

Effective Self-calibration for Camera Parameters and Hand-eye Geometry Based on Two Feature Points Motions

A novel and effective self-calibration approach for robot vision is presented, which can effectively estimate both the camera intrinsic parameters and the hand-eye transformation at the same time. The proposed calibration procedure is based on two arbitrary feature points of the environment, and three pure translational motions and two rotational motions of robot endeffector are needed. New linear solution equations are deduced, and the calibration parameters are finally solved accurately and effectively. The proposed algorithm has been verified by simulated data with different noise and disturbance. Because of the need of fewer feature points and robot motions, the proposed method greatly improves the efficiency and practicality of the calibration procedure. © 2017 Chinese Association of Automation.

On-orbit Geometric Calibration of Linear Push-broom Optical Satellite Based on Sparse GCPs

The paper presents a geometric calibration method based on the sparse ground control points (GCPs), aiming to the linear push-broom optical satellite. This method can achieve the optimal estimate of internal and external parameters with two overlapped image pair along the charge-coupled device (CCD), and sparse GCPs in the image region, further get rid of the dependence on the expensive calibration site data. With the calibrated parameters, the line of sight (LOS) of all CCD detectors can be recovered. This paper firstly establishes the rigorous imaging model of linear push-broom optical satellite based on its imaging mechanism. And then the calibration model is constructed by improving the internal sensor model with a viewing-angle model after an analysis on systematic errors existing in the imaging model is performed. A step-wise solution is applied aiming to the optimal estimate of external and internal parameters. At last, we conduct a set of experiments on the ZY-3 NAD camera and verify the accuracy and effectiveness of the presented method by comparison.

Multi-camera calibration method based on minimizing the difference of reprojection error vectors

In order to achieve a high precision in three-dimensional（3D） multi-camera measurement system, an efficient multi-cameracalibration method is proposed. A stitching method of large scalecalibration targets is deduced, and a fundamental of multi-cameracalibration based on the large scale calibration target is provided.To avoid the shortcomings of the method, the vector differencesof reprojection error with the presence of the constraint conditionof the constant rigid body transformation is modelled, and mini-mized by the Levenberg-Marquardt （LM） method. Results of thesimulation and observation data calibration experiment show thatthe accuracy of the system calibrated by the proposed methodreaches 2 mm when measuring distance section of 20 000 mmand scale section of 7 000 mm × 7 000 mm. Consequently, theproposed method of multi-camera calibration performs better thanthe fundamental in stability. This technique offers a more uniformerror distribution for measuring large scale space.

Calibration chain design based on integrating sphere transfer radiometer for SI-traceable on-orbit spectral radiometric calibration and its uncertainty analysis

In order to satisfy the requirement of SI-traceable on-orbit absolute radiation calibration transfer with high accuracy for satellite remote sensors,a transfer chain consisting of a fiber coupling monochromator（FBM） and an integrating sphere transfer radiometer（ISTR） was designed in this paper.Depending on the Sun,this chain based on detectors provides precise spectral radiometric calibration and measurement to spectrometers in the reflective solar band（RSB） covering 300–2500 nm with a spectral bandwidth of 0.5–6 nm.It shortens the traditional chain based on lamp source and reduces the calibration uncertainty from 5% to 0.5% by using the cryogenic radiometer in space as a radiometric benchmark and trap detectors as secondary standard.This paper also gives a detailed uncertainty budget with reasonable distribution of each impact factor,including the weak spectral signal measurement with uncertainty of 0.28%.According to the peculiar design and comprehensive uncertainty analysis,it illustrates that the spectral radiance measurement uncertainty of the ISTR system can reach to 0.48%.The result satisfies the requirements of SI-traceable on-orbit calibration and has wider significance for expanding the application of the remote sensing data with high-quality.

A Review of RGB-D Camera Calibration Methods

RGB-D camera is a new type of sensor,which can obtain the depth and texture information in an unknown 3D scene simultaneously,and they have been applied in various fields widely.In fact,when implementing such kinds of applications using RGB-D camera,it is necessary to calibrate it first.To the best of our knowledge,at present,there is no existing a systemic summary related to RGB-D camera calibration methods.Therefore,a systemic review of RGB-D camera calibration is concluded as follows.Firstly,the mechanism of obtained measurement and the related principle of RGB-D camera calibration methods are presented.Subsequently,as some specific applications need to fuse depth and color information,the calibration methods of relative pose between depth camera and RGB camera are introduced in Section 2.Then the depth correction models within RGB-D cameras are summarized and compared respectively in Section 3.Thirdly,considering that the angle of the view field of RGB-D camera is smaller and limited to some specific applications,we discuss the calibration models of relative pose among multiple RGB-D cameras in Section 4.At last,the direction and trend of RGB-D camera calibration are prospected and concluded.

Camera Calibration for 3D Color Scanning System Using Virtual 3D Model

Instead of traditionally using a 3D physical model with many control points on it, a calibration plate with printed chess grid and movable along its normal direction is implemented to provide large area 3D control points with variable Z values. Experiments show that the approach presented is effective for reconstructing 3D color objects in computer vision system.

An Easy Camera Calibration Technique

This paper describes a method for estimating intrinsic and extrinsic parameters of a camera,including horizonal scale factor caused by imperfect match between computer image acquisition hardware and camera hardware,coordinates of image center(c x ,c y) and lense radical distortion parameter k,which calculates extrinsic parameters by a tetrahedra pose estimation algorithm and then get all other parameters by nonlinear optimization in two steps,and simulations show this method is easy and reliable.

Flexible Planar-Scene Camera Calibration Technique

A flexible camera calibration technique using 2D-DLT and bundle adjustment with planar scenes is proposed. The equation of principal line under image coordinate system represented with 2D-DLT parameters is educed using the correspondence between collinearity equations and 2D-DLT. A novel algorithm to obtain the initial value of principal point is put forward. Proof of Critical Motion Sequences for calibration is given in detail. The practical decomposition algorithm of exterior parameters using initial values of principal point, focal length and 2D-DLT parameters is discussed elaborately. Planar\|scene camera calibration algorithm with bundle adjustment is addressed. Very good results have been obtained with both computer simulations and real data calibration. The calibration result can be used in some high precision applications, such as reverse engineering and industrial inspection.

A Robust Estimation Method for Camera Calibration with Known Rotation

Imagine that hundreds of video streams, taken by mobile phones during a rock concert, are uploaded to a server. One attractive application of such prominent dataset is to allow a user to create his own video with a deliberately chosen but virtual camera trajectory. In this paper we present algorithms for the main sub-tasks (spatial calibration, image interpolation) related to this problem. Calibration: Spatial calibration of individual video streams is one of the most basic tasks related to creating such a video. At its core, this requires to estimate the pairwise relative geometry of images taken by different cameras. It is also known as the relative pose problem [1], and is fundamental to many computer vision algorithms. In practice, efficiency and robustness are of highest relevance for big data applications such as the ones addressed in the EU-FET_SME project SceneNet. In this paper, we present an improved algorithm that exploits additional data from inertial sensors, such as accelerometer, magnetometer or gyroscopes, which by now are available in most mobile phones. Experimental results on synthetic and real data demonstrate the accuracy and efficiency of our algorithm. Interpolation: Given the calibrated cameras, we present a second algorithm that generates novel synthetic images along a predefined specific camera trajectory. Each frame is produced from two “neighboring” video streams that are selected from the data base. The interpolation algorithm is then based on the point cloud reconstructed in the spatial calibration phase and iteratively projects triangular patches from the existing images into the new view. We present convincing images synthesized with the proposed algorithm.

Overview of Camera Calibration

This paper introduce several commonly used camera calibration method include their advantages and disadvantages.The traditional methods of camera calibration need to know precise structural information of calibration object and they are accurate.Camera calibration based on active vision get the camera calibration through the controlling of some parameters of camera.Self-calibration of camera don't need to use the calibration block and get the camera calibration through the corresponding relationship among multiple images.

Camera Calibration from Profile of Revolution

This paper focuses on the problem of calibrating a pinhole camera from images of profile of a revolution. In this paper, the symmet ry of images of profiles of revolution has been extensively exploited and a prac tical and accurate technique of camera calibration from profiles alone has been developed. Compared with traditional techniques for camera calibration, for inst ance, it may involve taking images of some precisely machined calibration patter n (such as a calibration grid), or edge detection for determining vanish points which are often far from images center or even do not physically exist, or calcu lation of fundamental matrix and Kruppa equations which can be numerically unsta ble, the method presented here uses just profiles of revolution, which are commo nly found in daily life (e.g. bowls and vases), to make the process easier as a result of the reduced cost and increased accessibility of the calibration object s. This paper firstly analyzes the relationship between the symmetry property of profile of revolution and the intrinsic parameters of a camera, and then shows how to use images of profile of revolution to provide enough information for det ermining intrinsic parameters. During the process, high-accurate profile extrac tion algorithm has also been used. Finally, results from real data are presented , demonstrating the efficiency and accuracy of the proposed methods.