A flexible calibration method based on small planar target for defocused cameras

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.

In this study, we propose a rapid method for obtaining camera intrinsic parameters based on a stereo calibration target. First, we selected a texture-rich 3D calibration target and performed sparse reconstruction to establish the correspondence between 3D points resulting from the sparse reconstruction and 2D points in a specific position image, known as the base image. Based on this result, for any camera awaiting calibration, the camera intrinsic parameters and lens distortion coefficients can be determined by capturing only one image. Experimental results show that, compared to Zhang's method, our method not only obtains a greater number of feature points with a more uniform distribution, addressing the issue of sparse corner points at image edges, but also achieves lower reprojection errors and higher calibration accuracy. Furthermore, this method requires only a single image captured from the uncalibrated camera, greatly enhancing the calibration efficiency, and making it suitable for batch calibration of cameras on industrial pipelines.

This paper focuses on the study of 2D calibration method, involving a new planar pattern based on equilateral triangles, and a new camera calibration algorithm using the new pattern. Firstly, three triangles with same size and same color on the same plane, which side length can be any size, are spliced together to form a large equilateral triangle. Secondly, more than three pattern images are captured from different orientation. Thirdly, sub-pixel coordinates of six corners are extracted from each pattern image. Then, using perspective geometry theory and the geometric characteristics of triangle template, more than ten vanishing points are calculated out, vanishing line is fitted out according to them, and the image coordinates of circular points are deduced. Finally, all the five intrinsic parameters can be determined linearly according the coordinates of circular points. Experiments with simulated data as well as with real images show that the new algorithm is robust and accurate. The integral calibration precision of this method can reach about 2% comparing with Zhang's method. Equilateral triangle pattern the method used is easy to access, and easy to build in the industrial field, and its measurement also need not know in the calibration process. So this method with higher precision has a good practical value.

Camera calibration is a critical prerequisite for precision optical measurement systems. Traditional methods predominantly rely on either chessboard or circular calibration targets, each exhibiting inherent limitations. Chessboard targets facilitate straightforward corner detection but suffer from relatively low localization accuracy. Circular targets enable high-precision center extraction but are susceptible to systematic errors induced by perspective distortion, which causes the projected ellipse center to deviate from the true physical circle center (eccentricity error). To overcome these limitations, this paper introduces a high-precision camera calibration method that leverages a novel, to our knowledge, hybrid calibration board embedding circular markers within a chessboard pattern. The proposed approach first detects readily detectable chessboard corners to compute a homography matrix, which rectifies local image regions parallel to the imaging plane, thereby transforming the elliptical marker projections into approximately circular shapes. The centers of these corrected markers are accurately extracted using image moments. Subsequently, an inverse perspective transformation projects the centers back to the original image plane to obtain their precise pixel coordinates, effectively mitigating the perspective-induced eccentricity error. Camera calibration is then performed using Zhang's method with the refined coordinates. Extensive experiments demonstrate that the proposed method achieves an average reprojection error of 0.0365 pixels, representing a significant improvement of 51.13% compared to the traditional chessboard pattern and 35.05% compared to the circle pattern.

The challenging problem of the camera calibration with wide field-view is hard to make large scale target with high precision, while using target of small scale cannot satisfy the required accuracy. According to this problem, the calibrating camera method based on the flexible spliced two-dimensional target is proposed. The spliced two-dimensional target consists of many small targets (called sub-target). Each sub-target includes matching area and extending area. Those sub-targets are combined into virtual large scale planar target (called mother-target) by encode in matching area. The camera parameters can be calibrated by the mother-target. Simulation and real experiment shows that the accuracy of the proposed calibration method is almost the same as Zhang's calibration method using a large planar target which point number is similar to that of the flexible spliced two-dimensional target. The relative error of the calibration result of them is less than 3%. The advantages of this method are that the target is convenience, and the area of target can be extended infinitely.

Design of multi-parameter target used in calibration of high precision CCD camera

For line structured light vision sensor in robotic eye-in-hand system, the calibration of camera parameters, robot hand eye parameters and structured light plane parameters is an indispensable procedure before conducting 3-D measurement. Traditionally, these three sets of parameters are calibrated separately, making the calibration process complicated and inefficient. To address this, an efficient calibration method is proposed in this paper. By changing the poses of robot and calibration target, a set of images of the calibration target is captured, upon which the camera calibration is conducted. The extrinsic parameters obtained from camera calibration are utilized in the calibration of the structured light plane parameters and hand eye parameters, using the same set of images. Therefore, the three sets of parameters can be simultaneously calibrated with simple on-site operations. Moreover, the calibration target used in this method is only a planar checkerboard, which can be easily acquired at low cost. It is verified in the experiment that the proposed method is efficient and accurate, with the calibration duration within 10 minutes and the measurement accuracy within 0.40mm. Additionally, object pose measurement experiment is conducted to validate the effectiveness of the proposed method in practical application.

For traditional camera calibration methods, the calibration accuracy of camera parameters is highly dependent on the feature extraction of the control points of the calibration target. However, due to problems such as perspective and lens distortion, the commonly used checkerboards, circular dots, and other calibration patterns will inevitably undergo large deformation, resulting in a serious impact on the accuracy of the extraction of control points. To solve this problem, a camera calibration method based on active phase calibration targets is proposed. The method uses the MI Pad that can automatically display the structured light patterns as the calibration target. Compared with the method of using a checkerboard calibration target, this method does not require pattern detection and avoids the process of manual marking. Also, based on the phase information of the structured light gratings, a large number of dense, high-precision control point coordinates can be obtained even in areas where the image edge distortion is severe. Not only is it highly automated, but it is also suitable for defocused cameras. Experimental results show that the reprojection error of our method is only onetenth of the comparison method, and it has better robustness and accuracy.

Conventional camera calibration that employs calibration targets is a commonly used method to acquire a camera’s intrinsic and/or extrinsic parameters. The calibration targets are usually designed as periodic arrays of simple high-contrast patterns that provide highly accurate world coordinate system points and the corresponding image pixel coordinate system points. The existing pixel coordinate extraction algorithms can reach a sub-pixel level; however, they treat each single pattern in one image as an independent individual, which makes it difficult to further improve extraction accuracy. In this paper, a novel method is proposed by utilizing the periodic arrangement characteristics of the calibration target pattern as a global constraint to improve the calibration accuracy. Based on a camera’s pinhole model, the intersection point of two fitted curves is used as an optimized pixel point to replace the initial one. Following the pixel coordinate optimization procedures, experiments were performed using real data from a 3D laser line scanner and a dynamic precision calibration target. Our results show that the relative errors of camera homography matrix elements obtained by the proposed optimization method were reduced compared with the commonly used method. The average coordinate measurement accuracy can be improved by nearly 0.05 mm. It is shown that the proposed optimization method can enhance the camera calibration accuracy, especially when the extracted pixels are of poorer precision.

According to the characteristics of fish-eye camera, such as large field of view and super short focal length, the traditional camera calibration algorithm based on the small hole imaging model cannot achieve the calibration. This paper proposed a fish-eye camera calibration optimization based on the traditional Kannala model. Firstly, the camera imaging model and distortion type of the fish-eye camera are studied, and on the basis of the traditional Kannala model, the piecewise polynomial approximation model is established to realize the original model optimization. Then, the intrinsic parameters and distortion coefficients of the camera are obtained according to the traditional Kannala model and the optimization model，and the distortion correction images are obtained by intrinsic parameters and distortion coefficients. Finally, the advantages of this algorithm are quantitatively and qualitatively analyzed by using the re-projection error and the multiview stereo vision 3D reconstruction of the distorted correction image. The results indicate that the camera parameters and distortion coefficients were obtained by calibration to correct the original image and to carry out 3D reconstruction of multi-view stereo vision, and the reverse projection error analysis and 3D reconstruction visualization of the camera check are proved to be effective in the calibration of the optimized model camera.

A constrained optimization process is proposed for camera calibration with an imperfect and not-measured calibration target. The proposed method uses the geometry of the calibration target in an optimization process with constraints based on the pattern design statistically. As a result, the camera can be calibrated in the absolute scale without taking any measurement of the imperfect calibration target. It is verified through simulation and experiment that the reprojection errors by using the proposed method are obviously smaller than those of the traditional calibration approach by trusting an imperfect target. The slightly higher measurement precision is also exemplified through an experimental calibration of a stereo vision system.

Camera calibration is a necessity in various tasks including 3D reconstruction, hand-eye coordination for a robotic interaction, autonomous driving, etc. In this work we propose a novel method to predict extrinsic (baseline, pitch, and translation), intrinsic (focal length and principal point offset) parameters using an image pair. Unlike existing methods, instead of designing an end-to-end solution, we proposed a new representation that incorporates camera model equations as a neural network in a multi-task learning framework. We estimate the desired parameters via novel camera projection loss (CPL) that uses the camera model neural network to reconstruct the 3D points and uses the reconstruction loss to estimate the camera parameters. To the best of our knowledge, ours is the first method to jointly estimate both the intrinsic and extrinsic parameters via a multi-task learning methodology that combines analytical equations in learning framework for the estimation of camera parameters. We also proposed a novel CVGL Camera Calibration dataset using CARLA Simulator [1]. Empirically, we demonstrate that our proposed approach achieves better performance with respect to both deep learning-based and traditional methods on 8 out of 10 parameters evaluated using both synthetic and real data. Our code and generated dataset are available at https://github.com/thanif/Camera-Calibration-through-Camera-Projection-Loss.

Experimental study on an FBG strain sensor

In this paper, we propose a genetic algorithm based approach to determine the pose of an object in Automated Visual Inspection having three degrees of freedom. We have investigated the effect of noise at 20 dB SNR and also mismatch resulting from incorrect correspondences between the object space points and the image space points, on the estimation of pose parameters. The maximum error in translation parameters is less than 0.45 cm and rotational error is less than 0.2 degree at 20 dB SNR. The error in parameter estimation is insignificant upto 7 pairs of mismatched points out of 24 points in object space and the results skyrockets when 8 or more pairs of points are mismatched. We have compared our result with that obtained by least square technique and it shows that GA based method outperform the gradient based technique when the number of vertices of the object to be inspected is small. These results have clearly established the robustness of GA in estimating the pose of an object with small number of vertices in automated visual inspection.

The consumer digital stereo camera FinePix REAL 3D W1, which was designed to take a pair of stereo images for stereo viewing, was released in August 2009. The aim of our study is to evaluate camera calibration methods for a low-cost and easy-operation system to measure dimensions of an object on a sub-meter scale only by using a pair of stereo images acquired by the camera without any controls such as control points whose spatial locations are known or a ruler which provides the scale of the object. Three camera calibration methods were evaluated by estimation errors of lengths of line segments measured without any controls. The experiment results indicate that the best calibration method would be the method that ordinary camera calibration is first executed for each imaging unit in order to estimate its image distortion model, and then alignment between two imaging units is estimated by using two sets of the exterior orientation parameters of both imaging units obtained in the ordinary camera calibration executed previously. The experiment results indicate that the suitable calibration method would be able to provide sufficiently accurate measurement results less than 0.4 pixels on an image as well.