High-precision Calibration Method Research Articles

High-Precision Calibration Method and Error Analysis of Infrared Binocular Target Ranging Systems

Infrared binocular cameras, leveraging their distinct thermal imaging capabilities, are well-suited for visual measurement and 3D reconstruction in challenging environments. The precision of camera calibration is essential for leveraging the full potential of these infrared cameras. To overcome the limitations of traditional calibration techniques, a novel method for calibrating infrared binocular cameras is introduced. By creating a virtual target plane that closely mimics the geometry of the real target plane, the method refines the feature point coordinates, leading to enhanced precision in infrared camera calibration. The virtual target plane is obtained by inverse projecting the centers of the imaging ellipses, which are estimated at sub-pixel edge, into three-dimensional space, and then optimized using the RANSAC least squares method. Subsequently, the imaging ellipses are inversely projected onto the virtual target plane, where its centers are identified. The corresponding world coordinates of the feature points are then refined through a linear optimization process. These coordinates are reprojected onto the imaging plane, yielding optimized pixel feature points. The calibration procedure is iteratively performed to determine the ultimate set of calibration parameters. The method has been validated through experiments, demonstrating an average reprojection error of less than 0.02 pixels and a significant 24.5% improvement in calibration accuracy over traditional methods. Furthermore, a comprehensive analysis has been conducted to identify the primary sources of calibration error. Ultimately, this achieves an error rate of less than 5% in infrared stereo ranging within a 55-m range.

A Novel Dynamic Light-Section 3D Reconstruction Method for Wide-Range Sensing

Existing galvanometer-based laser-scanning systems are challenging to apply in multi-scale 3D reconstruction because of the difficulty in achieving a balance between a high reconstruction accuracy and a wide reconstruction range. This paper presents a novel method that synchronizes laser scanning by switching the field-of-view (FOV) of a camera using multi-galvanometers. Beyond the advanced hardware setup, we establish a comprehensive geometric model of the system by modeling dynamic camera, dynamic laser, and their combined interaction. Furthermore, since existing calibration methods mainly focus on either dynamic lasers or dynamic cameras and have certain limitations, we propose a novel high-precision and flexible calibration method by constructing an error model and minimizing the objective function. The performance of the proposed method was evaluated by scanning standard components. The results show that the proposed 3D reconstruction system achieves an accuracy of 0.3 mm when the measurement range is extended to 1100 mm × 1300 mm × 650 mm. This demonstrates that for meter-scale reconstruction ranges, a sub-millimeter measurement accuracy is achieved, indicating that the proposed method realizes multi-scale 3D reconstruction and simultaneously allows for high-precision and wide-range 3D reconstruction in industrial applications.

An Automatic High-Precision Calibration Method of Legs and Feet for Quadruped Robots Using Machine Vision and Artificial Neural Networks

Abstract Kinematics calibration for quadrupled robots is essential to ensuring motion accuracy and control stability. The angle of the leg joints of the quadruped robot is error-compensated to improve its position accuracy. This paper proposes a real-time high-precision kinematics calibration method for quadruped robots using machine vision and artificial neural networks to simplify the calibration process and improve calibration accuracy. The method includes two parts: identifying the markers fixed on the legs through target detection, calculating the center coordinates of the markers, and building an error model based on an artificial neural network to solve the angle error of each joint and compensate for it. A series of experiments have been carried out to verify the model’s accuracy. The experimental results show that, compared to traditional manual calibration, by adding an error correction model to the inverse kinematics neural network, the calibration efficiency can be significantly improved while the calibration accuracy is met.

A Stable, Efficient, and High-Precision Non-Coplanar Calibration Method: Applied for Multi-Camera-Based Stereo Vision Measurements.

Traditional non-coplanar calibration methods, represented by Tsai's method, are difficult to apply in multi-camera-based stereo vision measurements because of insufficient calibration accuracy, inconvenient operation, etc. Based on projective theory and matrix transformation theory, a novel mathematical model is established to characterize the transformation from targets' 3D affine coordinates to cameras' image coordinates. Then, novel non-coplanar calibration methods for both monocular and binocular camera systems are proposed in this paper. To further improve the stability and accuracy of calibration methods, a novel circular feature points extraction method based on region Otsu algorithm and radial section scanning method is proposed to precisely extract the circular feature points. Experiments verify that our novel calibration methods are easy to operate, and have better accuracy than several classical methods, including Tsai's and Zhang's methods. Intrinsic and extrinsic parameters of multi-camera-systems can be calibrated simultaneously by our methods. Our novel circular feature points extraction algorithm is stable, and with high precision can effectively improve calibration accuracy for coplanar and non-coplanar methods. Real stereo measurement experiments demonstrate that the proposed calibration method and feature extraction method have high accuracy and stability, and can further serve for complicated shape and deformation measurements, for instance, stereo-DIC measurements, etc.

A 3D reconstruction method based on one-dimensional galvanometer laser scanning system

The line-structured light galvanometer scanning system projects the laser light strip onto the object by swinging the mirror to realize the 3D profile measurement of the object. It has the advantages of compact structure, fast measurement speed and strong adaptability to complex environments. In this paper, a three-dimensional scanning system based on a line laser, a one-dimensional galvanometer and an industrial camera is constructed, and a new mathematical model of one-dimensional galvanometer laser scanner is derived. On this basis, a high-precision and simple calibration method of the laser scanning system is proposed. Compared with other methods, this method takes into account the rotation angle error caused by the installation of the galvanometer. The whole calibration process only needs a freely moving chessboard instead of a precision electric stage for operation, which is very easy and convenient for on-site use. The experimental results show that the measurement system calibrated by the proposed method has an average relative deviation of 0.14% for the distance measurement of ceramic balls, and successfully achieved 3D reconstruction of plaster objects with complex surfaces and metal parts with high or low reflectivity.

A non-coplanar high-precision calibration method for cameras based on an affine coordinate correction model

Traditional non-coplanar calibration methods such as Tsai’s method have many problems, such as insufficient calibration accuracy, inconvenient operation, inaccurate models, etc. This paper proposes a new high-precision non-coplanar calibration method that aims to solve these problems. Like Tsai’s method, the proposed calibration method utilizes a one-dimensional displacement stage and a two-dimensional plane target to generate a virtual 3D feature point sequence. As an improvement, an affine coordinate correction model is applied to ensure the accuracy and orthogonality of the obtained virtual 3D coordinates. A novel and accurate camera calibration model is further established. Compared with Tsai’s model, which uses a radial alignment constraint and ignores the orthonormal constraint of the rotation matrix, the proposed calibration model fully considers the degrees of freedom of the camera’s parameters to be calibrated, as well as the lens’s nonlinear distortion parameters. More accurate analytical solutions of intrinsic and extrinsic parameters can be obtained with the proposed calibration model. Finally, a novel high-precision non-coplanar calibration method is proposed based on the proposed calibration model. The reprojection experiment proves that the calibration accuracy of this calibration method is better than that of Tsai’s and Zhang’s calibration methods under the same calibration conditions. As a supplement, a novel binocular camera system extrinsic parameter calibration method with known intrinsic parameters is proposed. With accurate intrinsic and extrinsic parameters, the binocular camera system’s relative measurement accuracy could be within 1/10 000. Overall, this method can be used in experimental and industrial applications that require high-precision calibration parameters.

A novel method for 3D reconstruction in tight and restricted space based on improved line-structured light

Three-dimensional (3D) reconstruction techniques have been widely employed in many fields. But precise endoscopic 3D measurement inside of objects, especially in tight and restricted spaces, is still a challenge since there is no easy access for measurement tools. Endoscope with 2D-view function has been widely used. However, the precise measurement technology of the inner surface of small hollow objects has not been widely researched. The components of the existing endoscope three-dimensional measuring probe are complex, expensive and not performed well in accuracy. Thus, a novel method and a miniaturized endoscopic 3D sensor is introduced. To be suit in tight and restricted space, the sensor probe prototype has a maximum 6 mm in thickness. The miniatured sensor prototype is mainly based on improved line-structured light, which performs better in robustness and measurement accuracy than coded projection. Especially, the components are inexpensive and easily available, which reduces the manufacturing cost thus making it easily to popularize in industry. Correspondingly, to ensure the sensor measurement accuracy, we also proposed a calibration method for a miniature line-structured light system based on specially designed planar targets. It should be noted that the 3D extension of the line-structured light system relies on the movement of the translation stage. Taking full account of the characteristics of the sensor prototype, a high-precision direction calibration method of the translation stage based on joint multi-calibration position noise estimation is proposed. Finally, the accuracy experiment is carried out on the gauge block to verify that the measurement method proposed can achieve high-precision 3D reconstruction in a restricted space, and that the 3D reconstruction error is less than 10µm.

Geometric calibration of helicopter-borne wide-angle SAR imagery based on the range Doppler model

ABSTRACT Helicopter-borne wide-angle synthetic aperture radar (SAR) can be used in a wide range of military and civil applications because of their high resolution and mobility. The absolute geometric positioning accuracy is an important index for SAR image quality assessment. However, the effectiveness of using traditional geometric calibration methods with helicopter-borne SAR images obtained by time-domain imaging algorithms remains to be verified. Based on the range-Doppler model, a high-precision geometric calibration method for helicopter-borne SAR is proposed in this study and verified by experiments using real data with different resolutions. The results show that after calibration, the positioning accuracy of SAR images with 20 m and 1 m resolutions is improved from 51.33 m to 4.71 m and from 62.49 m to 3.03 m, respectively. These results verify the effectiveness of the proposed method.

A low-cost calibration method for the infrared sensor array for quantitative analysis of natural gas

Infrared-based measurement technology is a promising approach to natural gas analysis, and high-precision calibration models for infrared sensor arrays require sufficient calibration data, which is costly. Therefore, we propose a calibration-transfer-based low-cost calibration method for infrared gas sensor arrays. We construct four identical infrared sensor arrays, one as the master array and three as slave arrays. A dedicated multi-layer perceptual neural network undertakes the data space mapping between the slave array and the master array. Thus, the slave sensor arrays can reuse the existing high-precision calibration model of the master array, reducing the calibration cost. The root mean squared errors of methane, ethane, and propane of the calibrated slave array are 2.87%(detection range: 0%–100%), 1.56%(detection range: 0%–24%), and 1.54%(detection range: 0%–12%), respectively, which are close to the accuracy level of the master array. The results show that our approach outperforms related algorithms in infrared sensor array calibration. In addition, experimental results on actual natural gas samples validate the method. The proposed low-cost and high-precision calibration method provides a basis for the generalization of infrared sensor arrays for mixed gas concentration monitoring. Furthermore, the reported scheme can be extended to quantitative analysis of other gas mixtures.

High-precision visual imaging model and calibration method for multi-depth-of-field targets

In the field of high-precision large-depth 3D reconstruction, some bottlenecks exist in the improvement of visual measurement accuracy. This is because traditional vision measurement methods simplify the imaging model of a fixed-focus camera to a pinhole imaging model with fixed parameters accompanied by various distortion information. In fact, according to the optical properties of camera imaging, the position of the optical center in the pinhole imaging model varies with the depth of the imaging target. In this paper, in order to achieve the objective of improving visual measurement accuracy, a high-precision visual imaging model for multi-depth-of-field targets and the corresponding camera parameters calibration method are proposed based on the optical properties of camera imaging. When using this imaging model for 3D measurements, different pixel points in the image use different camera internal parameters depending on the depth of the imaging target, thus enabling highly accurate 3D reconstruction. The experimental results show that the imaging model and calibration method proposed in this paper greatly improve the accuracy and robustness of visual 3D measurement and have a promising future in the field of large-depth 3D reconstruction.

Research on the calibration method of non-source temperature area of multispectral pyrometer based on a new exponential curve model

For the temperature measurement of high temperature targets, the use of multispectral pyrometers has a great advantage. However, with the increase of the measured target temperature, the research on the high-precision calibration method in the non-source temperature area falls far behind. Therefore, in order to break through the bottleneck of the calibration method of the non-source temperature area for high temperature targets, a new non-source temperature area calibration method is proposed in this paper. In this method, a temperature-gray/voltage (T-G/U) model based on the modified exponential function is established by using the close relationship between the change trend of the extrapolated temperature curve and the modified exponential curve model. There will be a large error in the prediction of the high temperature section in the non-source temperature area, so a quadratic polynomial term with error compensation is introduced on the basis of this model. The method of fitting estimation is employed to obtain the estimated temperature value of the predicted point in the high temperature section of the non-source temperature area. For the prediction of the entire non-source temperature area, the genetic algorithm is used to adaptively select the model parameter t, and the high-precision extrapolation calibration of the high temperature target in the entire non-source temperature area is realized. Both theoretical and experimental data verify the effectiveness and feasibility of the new method.

A high-efficiency and high-precision automatic 3D scanning system for industrial parts based on a scanning path planning algorithm

To achieve high-precision and high-efficiency 3D scanning of industrial parts, this research proposes an automated 3D scanning system based on path planning algorithms, in which the 3D scanning sensor is realized based on the principle of raster projection. The proposed automated scanning system is composed of a robotic arm, a 3D scanner, and a turntable to achieve a complete 3D scanning of the object to be measured. More precisely, this paper proposes a virtual 3D scanning principle, which can accurately determine whether a certain point on the CAD model can be scanned by a viewpoint. Further, this paper proposes a path planning algorithm based on the virtual 3D scanning principle, which can calculate the optimal scanning path required to scan the object according to the CAD model of the scanned object. Furthermore, to ensure the accuracy of the system, a high-precision system calibration method is proposed to establish the accurate positional relationship between various parts of the system. Firstly, this research proposes a camera calibration algorithm based on close-range photogrammetry, which can calculate the high-precision interior and exterior orientation parameters of the camera, and apply the method of calculating camera external parameters to the hand-eye calibration, making the accuracy of hand-eye calibration is also improved accordingly. In addition, this research proposes a photogrammetry-based projector calibration algorithm to determine the positional relationship between the projector and the camera in the 3D scanner, and a turntable calibration method to determine the positional relationship between the rotation center of the turntable and the camera. Eventually, according to different usage requirements, two 3D scanning data splicing methods are proposed. One is a high-efficient automatic splicing method based on the results of system calibration without pasting mark points, and the other is a high-precision data splicing method based on photogrammetry. Experimental results demonstrate that this system has higher accuracy and better performance in system calibration, scanning path calculation, and multi-view scanning data splicing.

High-precision and rapid binocular camera calibration method using a single image per camera.

This study proposes a precise and rapid binocular camera calibration (BCC) method based on a stereo target composed of 12 coded planar targets on which each calibration corner has a unique coded number. Unlike Zhang's method which requires numerous pairs of images in a binocular calibration process and fails to realize the matching of homonymous corners in the case of the incomplete target projection, the proposed method can implement an accurate BCC using a single calibration image per camera even in the case of target incompete projection. The proposed method greatly decreases the complexity of the calibration process. An optimization method based on multi-constraint is also presented to improve the accuracy of the BCC. The reprojection error and the 3D measurement errors are combined to evaluate the precision of the BCC more comprehensively. A binocular camera is calibrated by utilizing the proposed method and Zhang's method for comparison. The reprojection error and 3D measurement errors are remarkably reduced by applying the proposed method. The supplementary experiment further verifies the advantage of the proposed optimization method.

An advanced multi-camera system for automatic, high-precision and efficient tube profile measurement

In this paper, an advanced multi-camera system based on stereo vision is developed for automatic, highly accurate and efficient tube three-dimensional profile measurement of tubes, which can be applied to tube pre-assembly or in-process tube profile inspection. Multiple cameras are designed to acquire the tube images from different angles to help avoid image understanding disaster in case of tube overlap of complex tubes. A high precision calibration method based on photography is adopted to provide basic accuracy guarantee of the developed system. Then importantly, a new approach to tube model reconstruction is proposed, including a creative and adaptive tube seed growing method for accurate tube axis reconstruction, and a direct tube end reconstruction method. Furthermore, an automatic method of tube features calculation to help improve the efficiency of tube measurement. Finally, several experiments are performed to verify the reliability, efficiency and high-precision of the developed system. According to the experimental results, the tube measurement process can be finished in about 1.5 s/m. The average deviation of the radial deviation and axial deviation is within 0.062 mm respect to its reference value with the maximum standard deviation of 0.025 mm. For the bending angle and rotate angle, the average deviations from the reference values are within 0.025° and 0.031° with the maximum standard deviation of 0.011° and 0.012°, respectively.

Measured uncertainty analysis of detection efficiency of single photon detectors with correlated photons calibration

Detection efficiency calibration based on correlated photons is a high precision calibration method at the single photon level. During the calibration process, measured time, photon count rate, and channel detection efficiency are important experimental parameters that affect the measured uncertainty of detection efficiency. This paper constructs simulation models of measured uncertainty with experimental parameters by the correlated photons method. Our experiment measures and predicts the uncertainty when parameters change. This research provides a quantitative basis for experimental parameter settings of calibration of single photon detectors using correlated photons technology.

Robust and accuracy calibration method for a binocular camera using a coding planar target.

High-accuracy binocular camera calibration is a vital basis of precise binocular vision 3D measurement. In this work, a high-precision and robust binocular camera calibration method based on a coding target is proposed. First, a coding target with the simple patterns is designed. Every corner on the coding target has a unique code number, which can make the identification of homonymous corners easier and more valuable, even if the target is partially occluded. The decoding of the coding target is rapid, robust, and accurate at a complex background. Subsequently, the zenith and azimuth angles are introduced in the proposed calibration method to study the effect of the orientation of the coding target on the stability of calibration results and improve the robustness of the calibration results. Finally, to fully utilize the 3D information of the calibration corners on the coding target, we combine the reprojection and 3D geometric constraints to propose a multi-constraint optimization method for refining the parameters of binocular camera and improving the accuracy of binocular camera calibration. The comparison experiments have been done to verify the performance of the proposed calibration method. The standard deviations of the intrinsic and extrinsic parameters are greatly decreased, compared with Zhang's method. The mean reprojection and 3D geometric errors calculated by the proposed method have a large reduction. And the application experiment furtherly validates the effectiveness of the proposed method.

High-Precision Extrinsic Calibration Method of a Time-of-Flight IMU RGB-Camera With Loop Closure Constraints

Accurate localization is key to realizing an autonomous mobile robot. The fusion of depth data measured by a time-of-flight (TOF) camera with visual-inertial simultaneous localization and mapping (SLAM) can greatly improve depth estimation and mapping. To achieve a robust sensor fusion system, precise calibration of one sensor to another is essential. In this paper, we propose a joint extrinsic calibration method for a TOF- IMU RGB-camera system. Further, we design a pattern that consists of white circles with high reflectivity, and a black background with high absorptivity. Using our calibration method, circular features can be accurately extracted from amplitude images as well as from RGB images. We correct the TOF depth measurement errors, which depend on the pixel location and distance of the pixel away from the object, by establishing an error distribution model with a B-spline function. All sensors are fixed on a platform, and the position of each sensor relative to the other sensors is unchanged, forming loop closure constraints. Based on this prerequisite, we utilize the loop closure constraints between multiple sensors to obtain more accurate extrinsic parameters. By taking the loop closure constraints into account, the stability and robustness of the calibration is increased. The experimental results validate the proposed method and prove its accuracy. Thus, we achieve high precision in multi-sensor extrinsic calibration, which is the necessary foundation of SLAM research.

Precise calibration of dynamic geometric parameters cameras for aerial mapping

Calibration is crucial for mapping cameras. Traditional calibration methods assume the geometric parameters are unchanged during the imaging process. However, aerial mapping cameras perform earth observation during a moving process. Owing to the forward flying of airplane, the exterior orientation parameters are changed during the exposure process. This leads to problems if directly applying the traditional methods to aerial mapping cameras. This paper presents a set of working time sequence and a new high-precision calibration method for aerial mapping cameras. We prove that the aerial mapping on a moving platform can be transformed into a mapping on a stationary platform by using the proposed method. Specifically, three steps are given to perform as follows. First, a proper distance is selected to decide a spot for the detector. We fix the detector at the selected spot and calibrate intrinsic parameters by exploiting traditional calibration methods. Second, the working time sequence of camera imaging is designed. The camera starts to expose an image and the exterior orientation parameters are obtained when the detector is driven to move to the calibrated spot. Third, a distortion model is proposed to correct distortions. We show that the dynamic measurement is identical to static measurement by using the proposed method. Experiments based on both simulated and real data are provided to show the effectiveness of the method.

An intelligent and automated 3D surface defect detection system for quantitative 3D estimation and feature classification of material surface defects

To evaluate defects on the surface of the materials at the 3D level accurately and quantitatively, a 3D surface defect detection system based on stereo vision is presented, which can extract the precise 3D defect features of the detected object. The proposed detection system consists of two image capture modules and a turntable to capture the complete 3D information and color texture information from the object surface. More precisely, each image capture module is a binocular stereo vision system containing two monochrome cameras, a color camera, and a speckle projector which is used to reconstruct the 3D point clouds of the object surface based on stereo digital image correlation (stereo-DIC). Furthermore, a point-image mapping relationship between the reconstructed 3D object points and the color images is established. Eventually, the 3D characteristic parameters of defects are calculated by the corresponding 3D point cloud of the defect area obtained by segmenting the defect area using the image segmentation and point cloud segmentation algorithms according to this point-image mapping relationship. A convolutional neural network named DenseNets is employed to identify defect types intelligently. A high-precision multi-camera calibration method based on close-range photogrammetry is applied to ensure system detection accuracy in the proposed system. The experimental results demonstrate that the system has higher accuracy and better performance in system calibration, 3D reconstruction, and defect feature calculation.

Automatic and rapid calibration method for temperature coefficient of fiber grating temperature sensor

Bare fiber Bragg grating (FBG) is packaged by thermal conductive materials and to be used as a temperature sensor. In the oil bath calibration of the temperature coefficient of the FBG temperature, it is difficult to accurately synchronize the single point temperature measurement and the simultaneously record FBG central wavelength using different devices. An automatic, fast and high precision calibration method for temperature coefficient of FBG temperature sensor is proposed. The experimental results show that the temperature coefficient obtained by the proposed method can accurately measure the temperature, and the calibration process is fast and avoids the error caused by manual recording and formula derivation. The system is suitable for rapid calibration of mass-produced FBG sensors.