Global Calibration of Multi-Cameras Based on Refractive Projection and Ray Tracing

Multi-cameras system is widely applied in 3D computer vision especially when multiple cameras are distributed on both sides of the measured object. The calibration methods of multi-cameras system are critical to the accuracy of vision measurement and the key is to find an appropriate calibration target. In this paper, a high-precision camera calibration method for multi-cameras system based on transparent glass checkerboard and ray tracing is described, which is used to calibrate multiple cameras distributed on both sides of the glass checkerboard. Firstly, the intrinsic parameters of each camera is obtained by Zhang’s calibration method. Then, multiple cameras capture several images from the front and back of the glass checkerboard with different orientations, and all images contain distinct grid corners. As the cameras on one side are not affected by the refraction of glass checkerboard, extrinsic parameters can be directly calculated. However, the cameras on another side are influenced by the refraction of glass checkerboard, and the direct use of projection model will produce calibration error. A multi-cameras calibration method using refractive projection model and ray tracing is developed to eliminate this error. Furthermore, both synthetic and real data are employed to validate the proposed approach. The experimental results of refractive calibration show that the error of the 3D reconstruction is smaller than 0.2 mm, the relative errors of both rotation and translation are less than 0.014%, and the mean and standard deviation of reprojection error of 4-cameras system are 0.00007 and 0.4543 pixel. The proposed method is flexible, high accurate, and simple to carry out.

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A Nonlinear Calibration Method Based on Sinusoidal Excitation and DFT Transformation for High-Precision Power Analyzers

Journal of Sensors ◽

10.1155/2021/5578361 ◽

2021 ◽

Vol 2021 ◽

pp. 1-9

Author(s):

Wenjian Zhou ◽

Sheng Yang ◽

Li Wang ◽

Hanmin Sheng ◽

Yang Deng

Keyword(s):

High Precision ◽

Interpolation Method ◽

Spline Interpolation ◽

Calibration Method ◽

Calibration Error ◽

Initial Moment ◽

Calibration Process ◽

Calibration Methods ◽

Nonlinear Calibration ◽

Sinusoidal Excitation

For most high-precision power analyzers, the measurement accuracy may be affected due to the nonlinear relationship between the input and output signal. Therefore, calibration before measurement is important to ensure accuracy. However, the traditional calibration methods usually have complicated structures, cumbersome calibration process, and difficult selection of calibration points, which is not suitable for situations with many measurement points. To solve these issues, a nonlinear calibration method based on sinusoidal excitation and DFT transformation is proposed in this paper. By obtaining the effective value data of the current sinusoidal excitation from the calibration source, the accurate calibration process can be done, and the calibration efficiency can be improved effectively. Firstly, through Fourier transform, the phase value at the initial moment of the fundamental frequency is calculated. Then, the mapping relationship between the sampling value and the theoretical calculation value is established according to the obtained theoretical discrete expression, and a cubic spline interpolation method is used to further reduce the calibration error. Simulations and experiments show that the calibration method presented in this paper achieves high calibration accuracy, and the results are compensation value after calibration with a deviation of ± 3 × 10 − 4 .

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On-Site Calibration Method for Line-Structured Light Sensor-Based Railway Wheel Size Measurement System

Sensors ◽

10.3390/s21206717 ◽

2021 ◽

Vol 21 (20) ◽

pp. 6717

Author(s):

Yunfeng Ran ◽

Qixin He ◽

Qibo Feng ◽

Jianying Cui

Keyword(s):

Structured Light ◽

Field Tests ◽

Calibration Method ◽

Field Application ◽

Calibration Error ◽

Epipolar Constraint ◽

Calibration Process ◽

Calibration Methods ◽

Calibration Accuracy ◽

Calibration Time

Line-structured light has been widely used in the field of railway measurement, owing to its high capability of anti-interference, fast scanning speed and high accuracy. Traditional calibration methods of line-structured light sensors have the disadvantages of long calibration time and complicated calibration process, which is not suitable for railway field application. In this paper, a fast calibration method based on a self-developed calibration device was proposed. Compared with traditional methods, the calibration process is simplified and the calibration time is greatly shortened. This method does not need to extract light strips; thus, the influence of ambient light on the measurement is reduced. In addition, the calibration error resulting from the misalignment was corrected by epipolar constraint, and the calibration accuracy was improved. Calibration experiments in laboratory and field tests were conducted to verify the effectiveness of this method, and the results showed that the proposed method can achieve a better calibration accuracy compared to a traditional calibration method based on Zhang’s method.

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A Decoupled Calibration Method for Camera Intrinsic Parameters and Distortion Coefficients

Mathematical Problems in Engineering ◽

10.1155/2016/1392832 ◽

2016 ◽

Vol 2016 ◽

pp. 1-12 ◽

Cited By ~ 5

Author(s):

Kun Yan ◽

Hong Tian ◽

Enhai Liu ◽

Rujin Zhao ◽

Yuzhen Hong ◽

...

Keyword(s):

Real Data ◽

Calibration Method ◽

Intrinsic Parameters ◽

Radial Distortion ◽

Vision Measurement ◽

Field Of Vision ◽

Marquardt Algorithm ◽

Calibration Accuracy ◽

Camera Intrinsic Parameters ◽

Division Model

Camera calibration is a necessary process in the field of vision measurement. In this paper, we propose a flexible and high-accuracy method to calibrate a camera. Firstly, we compute the center of radial distortion, which is important to obtain optimal results. Then, based on the radial distortion of the division model, the camera intrinsic parameters and distortion coefficients are solved in a linear way independently. Finally, the intrinsic parameters of the camera are optimized via the Levenberg-Marquardt algorithm. In the proposed method, the distortion coefficients and intrinsic parameters are successfully decoupled; calibration accuracy is further improved through the subsequent optimization process. Moreover, whether it is for relatively small image distortion or distortion larger image, utilizing our method can get a good result. Both simulation and real data experiment demonstrate the robustness and accuracy of the proposed method. Experimental results show that the proposed method can be obtaining a higher accuracy than the classical methods.

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Calibration and Noise Identification of a Rolling Shutter Camera and a Low-Cost Inertial Measurement Unit

Sensors ◽

10.3390/s18072345 ◽

2018 ◽

Vol 18 (7) ◽

pp. 2345 ◽

Cited By ~ 3

Author(s):

Chang-Ryeol Lee ◽

Ju Yoon ◽

Kuk-Jin Yoon

Keyword(s):

Inertial Measurement Unit ◽

Unscented Kalman Filter ◽

Low Cost ◽

Real Data ◽

Calibration Method ◽

Measurement Unit ◽

Sensor Calibration ◽

Calibration Error ◽

Inertial Measurement ◽

Noise Density

A low-cost inertial measurement unit (IMU) and a rolling shutter camera form a conventional device configuration for localization of a mobile platform due to their complementary properties and low costs. This paper proposes a new calibration method that jointly estimates calibration and noise parameters of the low-cost IMU and the rolling shutter camera for effective sensor fusion in which accurate sensor calibration is very critical. Based on the graybox system identification, the proposed method estimates unknown noise density so that we can minimize calibration error and its covariance by using the unscented Kalman filter. Then, we refine the estimated calibration parameters with the estimated noise density in batch manner. Experimental results on synthetic and real data demonstrate the accuracy and stability of the proposed method and show that the proposed method provides consistent results even with unknown noise density of the IMU. Furthermore, a real experiment using a commercial smartphone validates the performance of the proposed calibration method in off-the-shelf devices.

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A Multi Camera and Multi Laser Calibration Method for 3D Reconstruction of Revolution Parts

Sensors ◽

10.3390/s21030765 ◽

2021 ◽

Vol 21 (3) ◽

pp. 765

Author(s):

Hugo Álvarez ◽

Marcos Alonso ◽

Jairo R. Sánchez ◽

Alberto Izaguirre

Keyword(s):

3D Reconstruction ◽

Calibration Method ◽

Laser Plane ◽

Calibration Methods ◽

Laser Calibration ◽

Calibration Object ◽

Focus Plane ◽

Chessboard Pattern ◽

Line Patterns

This paper describes a method for calibrating multi camera and multi laser 3D triangulation systems, particularly for those using Scheimpflug adapters. Under this configuration, the focus plane of the camera is located at the laser plane, making it difficult to use traditional calibration methods, such as chessboard pattern-based strategies. Our method uses a conical calibration object whose intersections with the laser planes generate stepped line patterns that can be used to calculate the camera-laser homographies. The calibration object has been designed to calibrate scanners for revolving surfaces, but it can be easily extended to linear setups. The experiments carried out show that the proposed system has a precision of 0.1 mm.

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Calibration of Camera and Flash LiDAR System with a Triangular Pyramid Target

Applied Sciences ◽

10.3390/app11020582 ◽

2021 ◽

Vol 11 (2) ◽

pp. 582

Author(s):

Zean Bu ◽

Changku Sun ◽

Peng Wang ◽

Hang Dong

Keyword(s):

Simulated Data ◽

Real Data ◽

Calibration Method ◽

Multiple Sensors ◽

Triangular Pyramid ◽

World Coordinate System ◽

Flash Lidar ◽

Novel Method ◽

3D Information ◽

Incremental Validation

Calibration between multiple sensors is a fundamental procedure for data fusion. To address the problems of large errors and tedious operation, we present a novel method to conduct the calibration between light detection and ranging (LiDAR) and camera. We invent a calibration target, which is an arbitrary triangular pyramid with three chessboard patterns on its three planes. The target contains both 3D information and 2D information, which can be utilized to obtain intrinsic parameters of the camera and extrinsic parameters of the system. In the proposed method, the world coordinate system is established through the triangular pyramid. We extract the equations of triangular pyramid planes to find the relative transformation between two sensors. One capture of camera and LiDAR is sufficient for calibration, and errors are reduced by minimizing the distance between points and planes. Furthermore, the accuracy can be increased by more captures. We carried out experiments on simulated data with varying degrees of noise and numbers of frames. Finally, the calibration results were verified by real data through incremental validation and analyzing the root mean square error (RMSE), demonstrating that our calibration method is robust and provides state-of-the-art performance.

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Stable Calibrations of Six-DOF Serial Robots by Using Identification Models with Equalized Singular Values

Robotica ◽

10.1017/s0263574721000229 ◽

2021 ◽

pp. 1-22

Author(s):

Zhouxiang Jiang ◽

Min Huang

Keyword(s):

Industrial Robot ◽

Singular Values ◽

Calibration Method ◽

Identification Accuracy ◽

Condition Numbers ◽

Measurement Instruments ◽

Unknown Parameters ◽

Calibration Methods ◽

Six Dof ◽

The Stability

SUMMARY In typical calibration methods (kinematic or non-kinematic) for serial industrial robot, though measurement instruments with high resolutions are adopted, measurement configurations are optimized, and redundant parameters are eliminated from identification model, calibration accuracy is still limited under measurement noise. This might be because huge gaps still exist among the singular values of typical identification Jacobians, thereby causing the identification models ill conditioned. This paper addresses such problem by using new identification models established in two steps. First, the typical models are divided into the submodels with truncated singular values. In this way, the unknown parameters corresponding to the abnormal singular values are removed, thereby reducing the condition numbers of the new submodels. However, these models might still be ill conditioned. Therefore, the second step is to further centralize the singular values of each submodel by using a matrix balance method. Afterward, all submodels are well conditioned and obtain much higher observability indices compared with those of typical models. Simulation results indicate that significant improvements in the stability of identification results and the identifiability of unknown parameters are acquired by using the new identification submodels. Experimental results indicate that the proposed calibration method increases the identification accuracy without incurring additional hardware setup costs to the typical calibration method.

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Vicarious Radiometric Calibration of Ocean Color Bands for FY-3D/MERSI-II at Lake Qinghai, China

Sensors ◽

10.3390/s21010139 ◽

2020 ◽

Vol 21 (1) ◽

pp. 139

Author(s):

Shengli Chen ◽

Xiaobing Zheng ◽

Xin Li ◽

Wei Wei ◽

Shenda Du ◽

...

Keyword(s):

Infrared Imaging ◽

Large Deviation ◽

Ocean Color ◽

Calibration Method ◽

Surface Measurement ◽

Radiometric Calibration ◽

Lake Qinghai ◽

Vicarious Calibration ◽

Calibration Methods ◽

Spectral Imager

To calibrate the low signal response of the ocean color (OC) bands and test the stability of the Fengyun-3D (FY-3D)/Medium Resolution Spectral Imager II (MERSI-II), an absolute radiometric calibration field test of FY-3D/MERSI-II at the Lake Qinghai Radiometric Calibration Site (RCS) was carried out in August 2018. The lake surface and atmospheric parameters were mainly measured by advanced observation instruments, and the MODerate spectral resolution atmospheric TRANsmittance algorithm and computer model (MODTRAN4.0) was used to simulate the multiple scattering radiance value at the altitude of the sensor. The results showed that the relative deviations between bands 9 and 12 are within 5.0%, while the relative deviations of bands 8, and 13 are 17.1%, and 12.0%, respectively. The precision of the calibration method was verified by calibrating the Aqua/Moderate-resolution Imaging Spectroradiometer (MODIS) and National Polar-orbiting Partnership (NPP)/Visible Infrared Imaging Radiometer (VIIRS), and the deviation of the calibration results was evaluated with the results of the Dunhuang RCS calibration and lunar calibration. The results showed that the relative deviations of NPP/VIIRS were within 7.0%, and the relative deviations of Aqua/MODIS were within 4.1% from 400 nm to 600 nm. The comparisons of three on-orbit calibration methods indicated that band 8 exhibited a large attenuation after launch and the calibration results had good consistency at the other bands except for band 13. The uncertainty value of the whole calibration system was approximately 6.3%, and the uncertainty brought by the field surface measurement reached 5.4%, which might be the main reason for the relatively large deviation of band 13. This study verifies the feasibility of the vicarious calibration method at the Lake Qinghai RCS and provides the basis and reference for the subsequent on-orbit calibration of FY-3D/MERSI-II.

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Improving the performance of a radio-frequency localization system in adverse outdoor applications

EURASIP Journal on Wireless Communications and Networking ◽

10.1186/s13638-021-02001-6 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Marcelo N. de Sousa ◽

Ricardo Sant’Ana ◽

Rigel P. Fernandes ◽

Julio Cesar Duarte ◽

José A. Apolinário ◽

...

Keyword(s):

Random Forest ◽

Ray Tracing ◽

Real World ◽

Practical Implication ◽

Real Life ◽

Simulated Data ◽

Real Data ◽

Gradient Boosting ◽

Real World Data ◽

Localization Accuracy

AbstractIn outdoor RF localization systems, particularly where line of sight can not be guaranteed or where multipath effects are severe, information about the terrain may improve the position estimate’s performance. Given the difficulties in obtaining real data, a ray-tracing fingerprint is a viable option. Nevertheless, although presenting good simulation results, the performance of systems trained with simulated features only suffer degradation when employed to process real-life data. This work intends to improve the localization accuracy when using ray-tracing fingerprints and a few field data obtained from an adverse environment where a large number of measurements is not an option. We employ a machine learning (ML) algorithm to explore the multipath information. We selected algorithms random forest and gradient boosting; both considered efficient tools in the literature. In a strict simulation scenario (simulated data for training, validating, and testing), we obtained the same good results found in the literature (error around 2 m). In a real-world system (simulated data for training, real data for validating and testing), both ML algorithms resulted in a mean positioning error around 100 ,m. We have also obtained experimental results for noisy (artificially added Gaussian noise) and mismatched (with a null subset of) features. From the simulations carried out in this work, our study revealed that enhancing the ML model with a few real-world data improves localization’s overall performance. From the machine ML algorithms employed herein, we also observed that, under noisy conditions, the random forest algorithm achieved a slightly better result than the gradient boosting algorithm. However, they achieved similar results in a mismatch experiment. This work’s practical implication is that multipath information, once rejected in old localization techniques, now represents a significant source of information whenever we have prior knowledge to train the ML algorithm.

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Cobot User Frame Calibration: Evaluation and Comparison between Positioning Repeatability Performances Achieved by Traditional and Vision-Based Methods

Robotics ◽

10.3390/robotics10010045 ◽

2021 ◽

Vol 10 (1) ◽

pp. 45

Author(s):

Roberto Pagani ◽

Cristina Nuzzi ◽

Marco Ghidelli ◽

Alberto Borboni ◽

Matteo Lancini ◽

...

Keyword(s):

Quantitative Analysis ◽

Production Line ◽

Calibration Method ◽

Fiducial Marker ◽

Positioning System ◽

Local Calibration ◽

Calibration Methods ◽

Robot Positioning ◽

Good Repeatability ◽

Calibration Time

Since cobots are designed to be flexible, they are frequently repositioned to change the production line according to the needs; hence, their working area (user frame) needs to be often calibrated. Therefore, it is important to adopt a fast and intuitive user frame calibration method that allows even non-expert users to perform the procedure effectively, reducing the possible mistakes that may arise in such contexts. The aim of this work was to quantitatively assess the performance of different user frame calibration procedures in terms of accuracy, complexity, and calibration time, to allow a reliable choice of which calibration method to adopt and the number of calibration points to use, given the requirements of the specific application. This has been done by first analyzing the performances of a Rethink Robotics Sawyer robot built-in user frame calibration method (Robot Positioning System, RPS) based on the analysis of a fiducial marker distortion obtained from the image acquired by the wrist camera. This resulted in a quantitative analysis of the limitations of this approach that only computes local calibration planes, highlighting the reduction of performances observed. Hence, the analysis focused on the comparison between two traditional calibration methods involving rigid markers to determine the best number of calibration points to adopt to achieve good repeatability performances. The analysis shows that, among the three methods, the RPS one resulted in very poor repeatability performances (1.42 mm), while the three and five points calibration methods achieve lower values (0.33 mm and 0.12 mm, respectively) which are closer to the reference repeatability (0.08 mm). Moreover, comparing the overall calibration times achieved by the three methods, it is shown that, incrementing the number of calibration points to more than five, it is not suggested since it could lead to a plateau in the performances, while increasing the overall calibration time.

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