Camera calibration method based on circular array calibration board

The line structure light three-dimensional reconstruction system is a kind of three-dimensional non-contact measurement system, which has the advantages of high precision, high speed, small damage to objects and strong adaptability. Camera calibration is a major factor that constrains the accuracy of 3D measurement systems. The camera calibration is based on the pinhole imaging model, and through a series of complex calculations, the camera’s internal parameters (focal length, distortion coefficient) and external parameters (rotation matrix and translation vector). The different calibration methods use different calibration targets, which can be divided into 3D calibration targets, 2D calibration targets, and one-dimensional calibration targets according to the characteristics of the calibration targets. This paper mainly discusses: calibration content and significance, calibration methods for different targets and evaluation methods for calibration of different targets. Firstly, the content and significance of calibration are expounded. Then, according to different calibration targets, the calibration algorithm is analyzed. Finally, the calibration algorithm is analyzed and summarized, and the development trends, advantages and disadvantages of different calibration methods are pointed out.

Traditional multi-camera calibration is usually on one side of the calibration board. If there are several cameras distributing on both sides of the calibration board, each camera needs to be calibrated on each side. Thus, the error accumulated from each calibration will have a non-ignorable impact on the results. In this paper, we presents a method that using transparent glass board to replace ordinary calibration board based on Zhang Zhengyou’s calibration method. We also introduce two new parameters (depth and refractive index of glass). Therefore, calibration of several cameras can be completed by one experiment. The calibration of camera in the front of the transparent glass board uses traditional calibration method and LM iterative algorithm to obtain the internal and external camera parameters. The calibration of camera on back side uses the traditional calibration model and the light refraction model, and the results without considering the refraction condition are served as the initial values. Th...

In order to achieve a comprehensive analysis of the influencing factors on the accuracy of the magnetic gradient full tensor measurement system, an orthogonal experimental design method is proposed to analyze the errors caused by the influencing factors. The influence of each factor on the accuracy of the measurement system is obtained more comprehensively. Furthermore, the relative degree of influence of the factor is obtained. Four factors including resolution, baseline length, measurement distance, and magnetic moment direction are selected for simulation calculation. The simulation results and analysis show that among the selected factors, the resolution has the greatest influence on the accuracy of the measurement system and the magnetic moment direction has the least influence. In the actual measurement system design, if the optimal configuration of the four factors cannot be satisfied, the former can be satisfied in priority in the order of resolution, measurement distance, baseline length, and magnetic moment direction.

A compact 3-D shape measurement system based on the combined stereovision and phase shifting method has been developed, which consists of a miniature projector and two small cameras arranged as a stereo pair. The projector projects sinusoidal phase shifted fringe patterns, which are captured by both cameras simultaneously. The two phase maps calculated are used for stereo matching. The 3-D shape of the object is then reconstructed by the triangulation method. This research focuses on improving the resolution and accuracy of the measurement system by using a sub-pixel stereo matching method, a multi-image averaging method, and an error compensation method. Experimental results are presented to show the effectiveness of the proposed methods in improving the resolution and accuracy of the system.

The accurate calibration for a 3D profile measurement system based on structured light projection is important to the precision measurement system; however, system calibration is always complicated and time-consuming. An improved fast method is proposed to calibrate the measurement system. First, LCD monitor, as a calibration plate, displays chessboard pattern designed by computer programming, and camera captures 1 image. Then LCD monitor displays white pattern, projector projects horizontal and vertical color-encoded fringes to the LCD monitor, and camera collects 2 images respectively. A Phase-shifting algorithm is used to establish a highly accurate correspondent relationship between camera pixels and projector pixels, and projector images are generated. Next, move the LCD monitor to other 8 places, get camera and projector images which are set for camera and projector calibration respectively using Zhang’s calibration method. Compared with ordinary techniques which use expensive equipments such as two or three orthogonal plates, LCD monitor is easy-to-use and flexible, and experiments show that calibration accuracy is improved by 5 times. In comparison with traditional projector calibration method, this method decreases the number of captured images from 8 to 2 in each place and increases the processing speed. Combining camera calibration and projector calibration, the complex calculation process of integrating traditional camera calibration and projector calibration can be simplified. Experiments have been performed based on the proposed technique and good results have been obtained.

The spatial response matrix in all directions needs to be measured for the traditional radiometer array calibration algorithm, and the reversed image can be blurred by missing partial spatial information. To solve this problem, an improved calibration algorithm with partial spatial information missing was proposed. Experimental results for the real scene show that the image blur can be restrained effectively by the improved calibration algorithm

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.

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.

Ride comfort and handling qualities of a vehicle have attained much attention in the field of automobile. Vehicle manufacturers are trying to introduce as much ride comfort as possible without compromising handling qualities of vehicle. The two characteristics of the vehicle are linked with suspension system of vehicle. Good ride comfort means that the suspension system does not let road disturbance to reach the body of vehicle, while good handling qualities implies good road grip and maneuverability of the vehicle. Main objective to improve ride comfort is to elude physical fatigue and tiredness of driver while improvement in handling qualities will minimize chance of road accidents. Different suspension systems like passive, semi-active and active have been studied for long. Semi-active suspension system can provide change in damping coefficient to fulfill requirements of a good suspension system in a simple, easy and cost-effective way without requiring change in vehicle. Therefore, semi-active damper systems have gained more popularity in automobiles field. Designing control algorithm for semi-active suspension system is a complicated and challenging task. There have been many control algorithms to control damping coefficient, but no algorithm has utilized semi-active dampers to their full potential. This study investigates shortcomings of existing approaches, root cause of the problems and provides optimal solution to the problem. A suspension system involves different regions of operations that can be separated on the bases of operational constraints and stability of system. Existing methods do not use stability for designing their controllers or separating different regions. Furthermore, existing control strategies are based on linearized models and require gain adjustment and tuning to get better performance. Through analysis, it was found that there are three distinct regions. Damping force requirements for each region are different and critical. If wrong damping force is generated in any region, it may induce more acceleration/disturbance on vehicle, which is the main problem that existing methods suffer from. Proposed method generates right amount of force required at right time to suppress vibration by designing better control algorithm based on energy equations and dynamic equations. The proposed methods are validated by using simulations and experiments. For experimental validation of suspension system and attaining higher performance, accuracy of measurement system and parameters involved cannot be overlooked. Therefore, detailed investigations on accurate measurement system and parameter estimation methodology for suspension system were conducted. Thorough analysis on existing measurement system revealed critical errors in existing measurement system. To find out root cause of problems an analytical formula for evaluation of measurement system was derived. To overcome measurements issues it is required to use time, instead of encoders, as scalar base. This is not possible in existing methods, as sampling time of existing methods is dependent on other associated systems. Therefore, new measurement system is proposed, which uses high frequency clock and high sampling frequency to measure accurate time as soon as change in displacement occurs. This is same as using a stopwatch with a resolution as low as Nanoseconds. Simulations and experiments proved the proposed strategy and its effectiveness. The achieved accuracy from proposed method is comparable to the speed measurements system based on laser interferometer system. After having accurate measurement system for suspension system, accuracy of systems’ parameters is evaluated from accuracy point of view. The estimation problem is a mathematical problem in which number of independent equations are less than parameters to be estimated, which makes this problem unsolvable. Existing approaches use excitation method to generate additional equations and convert system to an overdetermined system and hence to be solved and an optimization problem. Getting overdetermined system is not a solution to the problem as independent equations are still the same. Furthermore, existing methods do not take care of coupling effects, eliminating or isolating noise and parameters from each other. Therefore, parameters estimation is not accurate. This motivated to develop an algorithm to estimate parameters with more accuracy and reliability. The proposed method converts estimation problem into a control problem and the parameters are updated by generating step-by-step update based on state feedback and projecting input on error of states or their functions. Properly designed desired trajectories for different parameters are used to decouple the parameter from other parameters. A systematic way of updating one parameter at a time in different cycles ensured convergence of parameters to true value even if absolute decoupling between parameters is not possible for complicate and nonlinear systems. The proposed method is validated, for linear and nonlinear problems by simulations and experiments.

The microwave sounding unit (MSU) prelaunch thermal‐vacuum chamber test data for eight MSU flight models that flew on TIROS‐N, NOAA 7 through NOAA 12, and NOAA 14 were reanalyzed using an improved calibration algorithm, originally designed for the advanced microwave sounding unit‐A (AMSU‐A) operations. The new calibration algorithm can automatically adjust for any channel gain shift in operation. Adoption of this calibration algorithm as the MSU calibration procedure in the recalibration project will make the data sets from the MSU and the AMSU‐A more consistent. This will be useful for future blending of the climate trends generated from the MSU and AMSU‐A data. A single nonlinearity parameter u, which appears in the new calibration algorithm, was obtained for each channel from analysis of the prelaunch calibration test data. A software package for implementing this new calibration algorithm was developed and applied to calculate the MSU time series for improvement of the accuracy of the climate record. Sample calculations of MSU antenna temperatures with the new calibration algorithm were made for two satellites and are compared with similar results obtained from the old MSU calibration algorithm. Significant differences are observed, and strong evidence indicates that the new calibration procedure will provide a more accurate quantification of climate trends.

The assembly platform of complex structures with a variety of CNC tools can achieve automated clamping, riveting, drilling, seamless calibration docking, and can also realize connecting engineering of complex assembly. In this paper, to solve the issue of digital measurement positioning technology in complex-structure assembly platform, an industrial robot-assisted laser scanning system is designed, and its kinematics model is established. At the same time, the trajectory of the robot rotation scan is planned. Finally, the measurement accuracy of the system we have established proves to meet the ac- tual demands by assembling experiment. In the assembly of complex-structure, digitized measurement positioning technology is an important standard of assembly quality. The technology can be realized by the robots equipped with vision meas- urement system, which is real-time scanning, high measuring accuracy and efficiency. In the 1960s, there were researches of combining visual measurement systems and robot in the world. In 1969, Nilsson developed the first intelligent mobile robot named shakey equipped with a camera, rangefinder, and contact sensors at Stanford SRI Institute, and its task was automatic obstacle avoidance and target motion tracking. In the late 1990s, machine vision measurement technology be- gan to develop rapidly in China. Harbin Institute of Technology achieved a fully autonomous soccer robot navigation with heterogeneous binocular active vision systems, analyzed fusion method of foot- ball robot's navigation data based on the binocular coordination, and proposed the binocular coordina- tion navigation model and target implementation strategy based on its behavior (1). National University of Defense Technology studied surgical instrument tracking and positioning technology based on bin- ocular vision (2). Currently, machine vision technology is widely used in various aspects, especially in industrial production and assembly. The machine vision measurement technology has become increas- ingly mature, but the study of improving the measurement accuracy of vision measurement system is still a main direction that we need to further study. In this paper, through analyzing the complex-structure assembly and detection system, a laser scan- ning measurement system is built by the Swedish ABB robot equipped with a CCD(Charge-coupled Device) high-speed camera. The system proves to be large measurement range, high accuracy and real- time.

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.

Camera calibration is an avoidable process for computational vision applications, such as 3D reverse engineering, industrial robot calibration, optic-pattern recognition, simultaneous localization and mapping, autonomous visual-driving and photogrammetric vision. The camera calibration problem is too complex, nonlinear and multimodal. Traditional camera calibration methods using gradient-based optimization often trap to one of the many local solutions available. Accurate computation ability of traditional camera calibration methods is limited since they use gradient-based optimization methods. Since evolutionary computing algorithms can avoid local solutions of numerical problems, they have the potential to accurately compute the required camera calibration parameters for high-precision computational vision applications. In this paper, the camera calibration parameters are computed by using 11 evolutionary computing algorithms, i.e., WDE, ABC, PSO, COBIDE, DE, CS, GWO, TLBO, MVMO, FOA and LSHADE. In order to make unbiased evaluation of the camera calibration results provided by the related evolutionary computing algorithms, two gradient-based traditional camera calibration methods, i.e., Zhang and Bouguet, have been used in the conducted experiments in this paper. The camera calibration results of the related methods were used to model a 3D physical test scene by using Structure from Motion photogrammetry method. The reference data set of the related 3D physical scene has been captured by using a 3D terrestrial laser scanner. Statistical comparison of the camera calibration results exposed that WDE supplies statistically better results than other comparison algorithms.

Camera calibration is an important step for vision-based measurement applications. A well-known flexible camera calibration method is analyzed that uses the checkerboard pattern plane and in which the camera can be moved freely. When using a perspective projection camera model, characteristics of both the objective plane and the image plane are utilized and accurate results can be obtained. However, the method's results may fail when the rotation angles of the planar pattern are small, and the distortion coefficients obtained under the perspective projection model can not be used for a real-time vision application. We solve the ill-conditioned equations using the genetic algorithm, and the correct camera parameters are always obtained. We compute the distortion coefficients of the inverse projection model, which can be used for general vision applications. The influence of the corner detection precision is taken into consideration. Simulation shows that the best results may be obtained when the planar pattern is placed in a close range and its rotation angle is small. Simulations and real-world experiments illustrate that the improved calibration algorithm can always obtain robust and accurate results.

The accuracy and stability of excitation source determine the measurement accuracy of passive sensor measurement system, but the implementation of high-precision excitation source (especially AC excitation source) is difficult or costly in design and process. For this purpose, this paper proposes a systematic proportional method. In this method, the DC voltage converted by the excitation signal is taken as the reference voltage of the ADC used in this system. And then the ratio of the measured signal to the excitation signal is obtained by using the transmission characteristics of the ADC, therefore the amplitude fluctuation of the excitation signal is compensated. The method can greatly suppress the measurement error caused by the amplitude fluctuation of the excitation signal and the fluctuation of the ADC reference voltage, and effectively improve the measurement accuracy of the measurement system. To verify the effectiveness of the proposed method, the Wheatstone bridge measurement circuit is designed. The experimental results show that when the amplitude of the excitation signal changes 50%, the measurement result of the measurement system using non-proportional method changes about 50%, while that of the measurement system using proportional method only changes about 1%. To further improve the measurement accuracy, the DC bias voltage compensation circuit is added, and the maximum variation error of the measurement result after compensation is only 0.3%. More importantly, the method can also be extended to other linear measurement systems with excitation source in principle, which has greater application value.