High precision and fast calibration method of fish-eye camera based on two-dimensional turntable

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.

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.

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.

This paper proposes a method to perform accurate camera calibration under poor lighting condition of factories or industrial fields. Preprocessing of camera calibration required for measuring object dimensions has to be able to extract calibration points from patterns of the calibration scale, for example, the calibration from plane pattern scale needs at least seven points of the known dimension marked on the scale. However, industrial fields hardly provide proper lighting condition for camera calibration of the measurement system. The data points for calibration are automatically selected from a probabilistic assumption for size variation of the calibration point when the threshold level changes for image binarization. The system requires user to provide at least four points that are incomplete, these points are used to predict position of exact calibration points and extract accurate calibration parameters in an iterative procedure using nonlinear optimization of the parameters. From real images, we prove the method can be applied to camera calibration of poor quality images obtained under lens distortion and bad illumination.

The accuracy of optical plane calibration is key to achieving high-precision three-dimensional measurement. This paper proposes a high-precision and robust optical plane calibration method (HRPC method) in response to the issues that the accuracy and efficiency of existing optical plane calibration methods are susceptible to errors in homography matrix transformation and laser center point extraction. The method introduces two important innovations: First, by calculating the centroid of calibration points, performing decentralization, applying Gaussian weighting, the scale factor of the matrix can be calibrated, and then the camera extrinsic matrix is optimized based on the partial least squares fitting method. Second, a quadratic denoising-based line laser center point extraction method is proposed. This method uses an adaptive dynamic neighborhood weighting expression to perform initial denoising on the line laser center points. Based on the camera perspective principle and the homography matrix, combined with the optimized camera extrinsic parameters, a quadratic denoising equation is established to carry out secondary denoising on the line laser center points, followed by optical plane fitting. Through experiments conducted on a self-built robotic 3D measurement system, the HRPC method is compared with existing methods. The results show that the accuracy, stability, and adaptability of the proposed method are superior to those of traditional algorithms. For a stepped gauge block with a step height of 5 mm, the average measurement error is 0.0102 mm after multiple measurements.

Camera calibration using one-dimensional information and its applications in both controlled and uncontrolled environments

Abstract. Unmanned Aerial Vehicle (UAV) with adequate sensors enable new applications in the scope between expensive, large-scale, aircraftcarried remote sensing and time-consuming, small-scale, terrestrial surveyings. To perform these applications, cameras and laserscanners are a good sensor combination, due to their complementary properties. To exploit this sensor combination the intrinsics and relative poses of the individual cameras and the relative poses of the cameras and the laserscanners have to be known. In this manuscript, we present a calibration methodology for the Unified Intrinsic and Extrinsic Calibration of a Multi-Camera-System and a Laserscanner (UCalMiCeL). The innovation of this methodology, which is an extension to the calibration of a single camera to a line laserscanner, is an unifying bundle adjustment step to ensure an optimal calibration of the entire sensor system. We use generic camera models, including pinhole, omnidirectional and fisheye cameras. For our approach, the laserscanner and each camera have to share a joint field of view, whereas the fields of view of the individual cameras may be disjoint. The calibration approach is tested with a sensor system consisting of two fisheye cameras and a line laserscanner with a range measuring accuracy of 30 mm. We evaluate the estimated relative poses between the cameras quantitatively by using an additional calibration approach for Multi-Camera-Systems based on control points which are accurately measured by a motion capture system. In the experiments, our novel calibration method achieves a relative pose estimation with a deviation below 1.8° and 6.4 mm.

This paper conducted some experiments to analyze three effect factors on camera calibration, which includes light intensity variation, chessboard planarity and image number. Firstly, three factors are discussed to quantify their effect on calibration accuracy. For convenience of analysis, camera calibration process and methods are explained in detail. Then, error model is constructed by deriving from perspective equation. Finally, some related experiments are conducted under different conditions. Experiments show that light intensity has less effect on feature extraction of chessboard corner. Therefore, its effect could be neglected on calculation accuracy. On the contrary, the world coordinate of chessboard corner is one of main effect factors on camera calibration. In other words, more attentions should be paid to chessboard planarity for improving calibration accuracy. Furthermore, it can be found that position of main point inevitably varies with the increasing of image number and effective focal length. Experiment results point out that the calculation accuracy and efficiency of inner parameters will become more ideal under condition of image number of 17~24.

Multiple cameras are increasingly prevalent for autonomous driving, and the increase need to have 360 degree perception of world space has led to the combination of various cameras in the varieties of narrow-angle and wide-angle field of view. This has led to issues regarding the quality of these optics as a result of bad and cheap designs. Intrinsic calibration is indispensable for accurate perception of the environment in order for it to make accurate decisions such as camera pose estimation and 3-D reconstruction. In this work, we propose a lens distortion model that has been motivated by unintentional tilt in the optical lens system. The proposed distortion model has been added to current state of art generic method of Kannala to form an extended model. To our knowledge, this is the first time that the idea of tilt distortion has been introduced for wide-angle view and fish-eye cameras. We show improved result of 4 to 13% from experiments.

Abstract. The recent advances in the field of computer-vision have opened the doors of many opportunities for taking advantage of these techniques and technologies in many fields and applications. Having a high demand for these systems in today and future vehicles implies a high production volume of video cameras. The above criterions imply that it is critical to design test systems which deliver fast and accurate calibration and optical-testing capabilities. In this paper we introduce new generation of test-stands delivering high calibration quality in single-shot calibration of fisheye surround-view cameras. This incorporates important geometric features from bundle-block calibration, delivers very high (sub-pixel) calibration accuracy, makes possible a very fast calibration procedure (few seconds), and realizes autonomous calibration via machines. We have used the geometrical shape of a Spherical Helix (Type: 3D Spherical Spiral) with special geometrical characteristics, having a uniform radius which corresponds to the uniform motion. This geometrical feature was mechanically realized using three dimensional truncated icosahedrons which practically allow the implementation of a spherical helix on multiple surfaces. Furthermore the test-stand enables us to perform many other important optical tests such as stray-light testing, enabling us to evaluate the certain qualities of the camera optical module.

Oblique-viewing endoscopes (oblique scopes) are widely used in medical practice. They are essential for certain procedures such as laparoscopy, arthroscopy and sinus endoscopy. In an oblique scope the viewing directions are changeable by rotating the scope cylinder. Although a camera calibration method is necessary to apply augmented reality technologies to oblique endoscopic procedures, no method for oblique scope calibration has yet been developed. In the present paper, we formulate a camera model and a calibration procedure for oblique scopes. In the calibration procedure, Tsai's calibration is performed at zero rotation of the scope cylinder, then the variation of the external camera parameters corresponding to the rotation of the scope cylinder is modeled and estimated as a function of the rotation angle. Accurate estimation of the rotational axis is included in the procedure. The accuracy of this estimation was demonstrated to have a significant effect on overall calibration accuracy in the experimental evaluation, especially with large rotation angles. The projection error in the image plane was approximately two pixels. The proposed method was shown to be clinically applicable.

Oblique-viewing endoscopes (oblique scopes) are widely used in medical practice. They are essential for certain procedures such as laparoscopy, arthroscopy and sinus endoscopy. In an oblique scope the viewing directions are changeable by rotating the scope cylinder. Although a camera calibration method is necessary to apply augmented reality technologies to oblique endoscopic procedures, no method for oblique scope calibration has yet been developed. In the present paper, we formulate a camera model and a calibration procedure for oblique scopes. In the calibration procedure, Tsai's calibration is performed at zero rotation of the scope cylinder, then the variation of the external camera parameters corresponding to the rotation of the scope cylinder is modeled and estimated as a function of the rotation angle. Accurate estimation of the rotational axis is included in the procedure. The accuracy of this estimation was demonstrated to have a significant effect on overall calibration accuracy in the experimental evaluation, especially with large rotation angles. The projection error in the image plane was approximately two pixels. The proposed method was shown to be clinically applicable.

There exist some problems in the fiber optic gyro inertial measurement unit(FOG-IMU) calibration, such as dependence on high-precision turntable, low precision, rigorous calibration condition and so on. Aiming at these problems, we propose a high-precision grading calibration method. Firstly, system parameters are calibrated by the discrete calibration method, in which the effects of the lever-arm are considered. Secondly, sensors' parameters are compensated effectively. Afterwards, the residual components of the IMU parameters are used as estimated objects and a 27-dimension Kalman filter is established by using velocity errors as observed quantities. The residual errors of coarse calibration will be estimated and compensated as well. Finally, results are validated through turntable experiments.

It is difficult to realize large field of view (FOV) and high-resolution at the same time. How to achieve high-resolution measurement under the premise of large FOV imaging is an important research issue. Aiming at the problem of single point target recognition, especially the angle measurement of single light source, this paper proposes a high-resolution measurement method with array FOV and coded apertures. A mask is added in front of the image sensor. The coded apertures on the mask divide the large FOV into several sub fields of view (sub-FOV). Different sub-FOV are time-sharing multiplexed on the image sensor. Apertures encoded by position information are arranged on the sub-FOV. When a single light source irradiates the apertures, the diffraction spot is imaged on the image sensor. The centroid method can accurately determine the centroid of light spot to submicron scale or even nanoscale. Analyzing the coded information contained in the imaging can realize the recognition of sub-FOV, and then calculate the incident angle of light to realize the target recognition. A mask is designed to realize the method. Through experiments, this mask can achieve a large FOV of 1200×120° with an angle measurement accuracy of 0.003°(3 σ).

As an essential step of 3D reconstruction, research on the camera calibration methods has great important significance of theoretical study and practical value. In this paper, a new simply, flexible and more accurate coplanar camera calibration method is proposed based on neural network. This method only requires a coplanar target and without camera motion. The neural network is used to learn the relationships between the image information and the 3D information to emend aberrance of camera, and it neither requires the inner and outer parameters of the camera and any prior knowledge of the parameters. The experimental results of image simulation show that the proposed method is correct and effective.