Camera Calibration Method Research Articles

Calibration of Industrial Cameras for Aerial Photogrammetric Mapping

This paper details the development of a camera calibration method purpose-built for use in photogrammetric survey production. The calibration test field was established in a hangar, where marker coordinates were measured using a high-precision survey methodology guaranteeing very high accuracy. An analytical model for bundle adjustment was developed that does not directly use the coordinates of field calibration markers but integrates bundle adjustment and survey observations into a single process. This solution, as well as a classical calibration method, were implemented in a custom software, for which the C++ source code repository is provided. The method was tested using three industrial cameras. The comparison was drawn towards a baseline method, OpenCV implementation. The results point to the advantages of using the proposed approach utilizing extended bundle adjustment.

In situ calibration of an uncooled thermal camera for the accurate quantification of flower and stem surface temperatures

This paper presents an in situ calibration method for an uncooled thermal camera to reduce bias and root mean square error (RMSE) for the observed surface temperatures of Gerbera jamesonii plants. Surface temperature bias and RMSE were quantified for the calibrated camera constants and compared with respect to the default constant statistics. The averaged calibrated camera constant bias and RMSE values decreased by at least 89.1% relative to the averaged default camera constant bias and RMSE values for individual plant stems and flowers. This calibration approach has the potential to be suitable for other uncooled thermal cameras in fields beyond horticultural applications.

Evaluation of the Pose Tracking Performance of the Azure Kinect and Kinect v2 for Gait Analysis in Comparison with a Gold Standard: A Pilot Study.

Gait analysis is an important tool for the early detection of neurological diseases and for the assessment of risk of falling in elderly people. The availability of low-cost camera hardware on the market today and recent advances in Machine Learning enable a wide range of clinical and health-related applications, such as patient monitoring or exercise recognition at home. In this study, we evaluated the motion tracking performance of the latest generation of the Microsoft Kinect camera, Azure Kinect, compared to its predecessor Kinect v2 in terms of treadmill walking using a gold standard Vicon multi-camera motion capturing system and the 39 marker Plug-in Gait model. Five young and healthy subjects walked on a treadmill at three different velocities while data were recorded simultaneously with all three camera systems. An easy-to-administer camera calibration method developed here was used to spatially align the 3D skeleton data from both Kinect cameras and the Vicon system. With this calibration, the spatial agreement of joint positions between the two Kinect cameras and the reference system was evaluated. In addition, we compared the accuracy of certain spatio-temporal gait parameters, i.e., step length, step time, step width, and stride time calculated from the Kinect data, with the gold standard system. Our results showed that the improved hardware and the motion tracking algorithm of the Azure Kinect camera led to a significantly higher accuracy of the spatial gait parameters than the predecessor Kinect v2, while no significant differences were found between the temporal parameters. Furthermore, we explain in detail how this experimental setup could be used to continuously monitor the progress during gait rehabilitation in older people.

High-accuracy calibration of cameras without depth of field and target size limitations.

During camera calibration, targets need to be placed in the depth of field of the lens to ensure clear imaging, and they should take up proper proportions in the image. These requirements cause difficulty in many calibration scenarios, such as those involving large-field-of-view, shallow-depth-of-field, or online operation cameras. In view of the above-mentioned problems, this study proposes a high-accuracy camera calibration method, which can overcome the influence of image blur and noise and is not limited by depth of field and target size. First, a high-accuracy light-spot small target is placed closely in front of the camera, so that the target image can take up a large proportion in the whole image. In case of defocus blur, the adaptive multi-scale method is used to extract feature point coordinates at first to ensure accuracy, and the location variance of each feature point is estimated concurrently. Finally, the high-accuracy intrinsic and extrinsic parameters of the camera under test are obtained by nonlinear optimization where re-projection errors are normalized by location variances according to the Gauss-Markov theorem. Simulation and physical experiments validate the effectiveness of the proposed method.

STUDY OF DIGITAL CAMERA CALIBRATION ON A FLAT TEST OBJECT

Abstract. The paper presents a method for calibration of digital cameras based on the use of a flat test object. The main distinctive feature of this method is that the camera is fixed and does not change its position in space. A series of images of a flat test object (for example, a chessboard) is taken at various distances and inclination of the test object. One should tilt the test object relative to the image plane in order to avoid ambiguity in solving the problem. All these images are measured separately, and processing is performed together, counting them as one image with common exterior orientation elements. Experimental studies have shown sufficient efficiency of such calibration, which is easily implemented and gives positive results in comparison with the classical calibration of the camera on a spatial test object. The results of experimental studies on real images have shown that proposed calibration method gives the comparable with conventional method accuracy. Thus, it is possible to use simple and cheap flat calibration test object instead of spatial one. To achieve the maximum result in camera calibration accuracy, use this method to tilt the chessboard at angles in the range of 30–40 degrees to the optical axis of the camera being calibrated.

A cooperative camera surveillance method based on the principle of coarse-fine coupling boresight adjustment

Visual surveillance systems play a vital role in smart manufacturing scenes. In this paper, a cooperative camera surveillance method is proposed based on the coarse-fine coupling boresight adjustment principle. A master-slave camera cooperative monitoring model is established by combining a high-resolution camera with a large-field camera, the former of which is embedded with a Risley prism pair to perform high-precision boresight pointing for monitoring a local target, while the latter can observe a wide scene and guide the former to catch a region of interest. An effective boresight adjustment strategy is put forward with a method of combining fast convergence and iterative refinement. A calibration method of the master-slave camera is proposed with the combination of binocular vision and equivalent motion plane. The error distribution, adjustment efficiency and tracking accuracy of the dual field monitoring are analyzed in detail to reveal the mapping mechanism between imaging feedback and boresight adjustment. In the surveillance experiment, the root-mean-square tracking error of the fine tracking camera can achieve better than 7.04 pixels, while the adjustment steps only need about 10 times, which validates the feasibility and effectiveness of the proposed method in industrial operation surveillance.

A Calibration Method for Mobile Omnidirectional Vision Based on Structured Light

Mobile omnidirectional structured light vision is increasingly used in scene perception and robot navigation. A wide range of information is obtained by means of the vision system by only one image and laser image features are detected and extracted easily and quickly. In this paper a novel calibration method for mobile omnidirectional camera based on structured light is presented. Firstly, a set of parallel laser planes is emitted on the walls of corridor as auxiliary targets by structured light and intersects with wall orthogonally. Secondly, the constraint relationship is analyzed between the vanishing points in fisheye images and intrinsic parameters of imaging model. Finally, effects of the laser stripes' interval and the angle between the wall which contains laser stripes and ground on calibration results are evaluated. Compared to Scaramuzza method, the calibration method shows its superiority in terms of both feasibility and efficiency. The method with the characteristic of self-calibration since the planar target is replaced by actively projected laser stripes. The result illustrates that our method has the advantages of simple and feasible operation, but result is effective and accurate. The calibration parameters are independent of the laser stripes' interval and the angle between the wall and ground. Therefore, the method of the mobile omnidirectional structured light vision presented in this paper can be applied to many areas.

Studies on deformation measurement with non-fixed camera using digital image correlation method

A digital image correlation technique with non-fixed camera is developed for deformation measurement in the field since it is difficult to fix cameras when the deformations of a large number of areas need to be measured. Multiple reference and target images of the specimen surface and a feature template are captured from different orientations and corrected before the correlation calculation. The relative positions of the specimen surface and the camera are obtained by the camera calibration method. The specimen surface is divided to several meshes to reconstruct the speckle patterns. The technique is more flexible and convenient than traditional digital image correlation method in measuring the deformation of high altitude facilities such as bridges. In order to test the accuracy of this method, the deformations of an aluminum plate under different loading forces are measured and compared to the values recorded by the tensile tester.

Geometric calibration method of plane array camera with 60 degrees two-dimensional pointing mirror

Geometric calibration method of plane array camera with 60 degrees two-dimensional pointing mirror

Camera Rapid Calibration Method for Mobile Road Measurement System

Abstract In recent years, a variety of mobile road measurement equipment has emerged and become an important means of collecting spatial information. As an important part of the mobile road measurement system, a camera’s function implementation and data accuracy largely depend on its internal parameters and the rotation and translation parameters corresponding to the world coordinate system. Based on this and on the traditional camera calibration method, radial and tangential distortion for monocular camera calibration is introduced in this article to establish a calibration model, and the nonlinear least-squares Levenberg‐Marquardt optimization algorithm is used in iterative calculation. The parameters provide a solution to the problem of rapid calibration of camera modules in mobile road measurement systems. The camera parameters obtained by the calibration algorithm in this study are used for visual reconstruction. Compared with two Zhang Zhengyou calibration methods optimized by the Gauss‐Newton method, the former has an average pixel offset of 0.28 pixel and the latter has deviations of 0.66 and 0.38 pixel. Using a monocular camera to collect data on geometric targets on a road, the average relative error does not exceed 2.16%. Experiments show that this method can obtain calibration results quickly and accurately.

Camera calibration method with focus-related intrinsic parameters based on the thin-lens model.

In this paper, a calibration method for a camera with focus-related intrinsic parameters based on the thin-lens model is proposed to realize highly accurate measurement for small objects with extended depth of field (DOF). It mainly solves inaccurate calibration and small DOF problems at high magnification of vision systems. The mathematical camera model, initial camera calibration based on the iterative radial alignment constraint (IRAC) and optimization strategy are presented. The effectiveness, accuracy and practicality of the proposed calibration method are verified by both simulations and experiments. The root mean square errors of measured points in the 3D world coordinates with the proposed calibration method decrease from 22.02 μm to 1.66 μm when the magnification of the vision system increases from 0.12× to 0.66×. With the proposed calibration method based on the thin-lens model, accurate measurement, extended DOF and low calibration workload can be achieved.

Calibrating stereo-digital image correlation system using synthetic speckle-pattern calibration target

We describe an alternative stereo calibration method for stereo-digital image correlation (stereo-DIC) using computer-simulated speckle-pattern calibration targets and a DIC-based control points matching technique. The present work refines and extends the recently proposed camera calibration method to stereo calibration, which is an essential part of stereo-DIC measurement. In the proposed calibration method, the calibration target is generated by displaying a synthetic speckle pattern on a commercial tablet. On the simulated speckle pattern, a group of control points is specified with flexible location and number, which is further precisely matched to the captured calibration images using the well-developed subset-based DIC algorithm. These precisely matched control points are subsequently used to calibrate the intrinsic and extrinsic parameters of the stereo-DIC system with stereo calibration algorithm. For better accuracy, the error in the manufacture of the calibration target is also considered and compensated. As a flexible number of control point matches are registered with high accuracy and strong robustness, the presented stereo calibration method using synthetic speckle pattern calibration target offers higher calibration accuracy than that based on a calibration target with a limited number of designated features, such as checkerboard target and circular point target. After being demonstrated by a set of simulated calibration tests, the proposed stereo calibration method was applied to calibrate a real stereo-DIC system, which was then used to measure 3D full-field shapes and displacements. The results confirm the effectiveness and accuracy of the proposed stereo calibration method for stereo-DIC applications.

A flexible targetless LiDAR–GNSS/INS–camera calibration method for UAV platforms

There is a growing need for 3D colored maps acquired from multi-sensor moving platforms. Accurate multi-sensor data alignment is an important prerequisite for the construction of 3D colored maps derived from simultaneously acquired camera and Light Detection and Ranging (LiDAR) data. However, current alignment methods are hampered by low automation, heavy computational costs or tedious system calibration set-ups. In this paper, we consider a LiDAR–global navigation satellite system (GNSS)/inertial navigation system (INS)–camera system mounted on an Unmanned Aerial Vehicle (UAV) platform. We present a detailed literature review of existing calibration methods for such systems. We propose a new versatile automatic and targetless calibration method of this system. This method involves estimating the calibration parameters by optimizing the correspondence between pairs of conjugate image points extracted from overlapping images and the projection of these points onto the georeferenced LiDAR point cloud. Experiments on actual data show the suitability of this method for the construction of 3D colored point clouds. Quantitative calibration results using checkpoints indicate that the obtained calibration accuracy is compatible with the accuracy of the georeferenced LiDAR point cloud, i.e. 5 cm. Further experiments on simulated data show the robustness of this approach to initial calibration parameters and low sensitivity to LiDAR point cloud density and noise. As this method is quite flexible, we believe it is more suitable for 3D color map generation than other methods proposed in the literature.

A Hough-Space-Based Automatic Online Calibration Method for a Side-Rear-View Monitoring System.

We propose an automatic camera calibration method for a side-rear-view monitoring system in natural driving environments. The proposed method assumes that the camera is always located near the surface of the vehicle so that it always shoots a part of the vehicle. This method utilizes photographed vehicle information because the captured vehicle always appears stationary in the image, regardless of the surrounding environment. The proposed algorithm detects the vehicle from the image and computes the similarity score between the detected vehicle and the previously stored vehicle model. Conventional online calibration methods use additional equipment or operate only in specific driving environments. On the contrary, the proposed method is advantageous because it can automatically calibrate camera-based monitoring systems in any driving environment without using additional equipment. The calibration range of the automatic calibration method was verified through simulations and evaluated both quantitatively and qualitatively through actual driving experiments.

Confidence-based camera calibration with modified census transform

Most camera calibration methods assume that the camera is nearly in-focus for precisely estimating the intrinsic and extrinsic camera parameters. However, the camera is generally out-of-focus in real calibration applications. This paper presents a method that is capable of accurately calibrating an out-of-focus camera. A confidence-based camera calibration with modified census transform (MCT) is proposed for a checkerboard calibration pattern. No additional devices or special calibration targets are required. First, the MCT utilizes the intensity information and local image structure to construct a descriptor. Then, the dissimilarity between the control point on the real image and the one on the sharp image is evaluated using the Hamming distance. This similarity metric is treated as the confidence of each control point. Finally, the confidence of each control point is added to the calibration energy minimization procedure to enhance the calibration performance. The experimental results on real images demonstrate that the proposed method achieves a more accurate calibration result than conventional methods.

A Novel Camera Calibration Method Based on Multilevel-Edge-Fitting Ellipse-Shaped Analytical Model

In this paper, a novel camera calibration method based on a multilevel-edge-fitting ellipse-shaped analytical model (CCM-MEF-ESAM) is proposed. First, an ellipse-shaped analytical model (ESAM) is derived which considers distortion error of the spherical image. Second, multilevel-edge-fitting (MEF) is presented to select the edge points to fit the ellipse. Then the actual projection of the sphere is calculated by CCM-MEF-ESAM, which can be utilized to obtain the accurate external parameters of the camera. Finally, the robustness and accuracy of CCM-MEF-ESAM are validated by simulations and experiments. Within the environments of incomplete edges and complex illumination, CCM-MEF-ESAM can realize an improvement of calibration accuracy of 74% compared to the traditional method, which indicates that CCM-MEF-ESAM holds great potential in the field of vision navigation.

Simple and precise multi-view camera calibration for 3D reconstruction

A precise calibration in multi-view camera environments allows to perform accurate 3D object reconstruction, precise tracking of objects and accurate pose estimation. Those techniques are of high value in the industry today in fields as quality control or automation. In the present work, an improvement of a simple existing multi-view camera calibration method is presented. The improved method employs a specially developed reference token to overcome some issues in the original algorithm. We prove that the new method overcomes those problems thus attaining a higher accuracy while keeping the process simple and the implementation costs low. This last aspects makes the method interesting for the industry but specially suitable for SMEs typical in traditional sectors.

Camera calibration method for solid spheres based on triangular primitives

A new camera calibration method based on triangular primitives for solid grid sphere objects are proposed in this work to address the contradiction among the number of cameras, calibration accuracy, and algorithm stability in the current camera calibration process. In the proposed method, a sphere is used as the base, and the surface coverage curve of the sphere forms a calibration object as the grid based on triangular primitives. We use the absolute quadratic curve and vanishing point to calculate the intrinsic and extrinsic parameters of the camera, respectively. The proposed method can simplify the element correspondence in the calibration and calibrate multiple cameras in different positions simultaneously. Experimental results show that the new 3D calibrator exceeds the calibration accuracy and stability of traditional algorithms. Moreover, the comprehensive evaluation of the algorithm is improved significantly.

Fourier-transform-based two-stage camera calibration method with simple periodical pattern

Clear and focused pattern images are essential prerequisites for accurate feature detection in traditional camera calibration methods, which introduce numerous limitations in various areas, such as long-distance photogrammetry. A feature detection method robust against defocusing is proposed for extracting the centers or corners of a planar square periodic target. A Fourier transform is employed to calculate two wrapped phase maps from the periodic target images, which are then used to accurately extract the feature points. The calibration procedure is divided into two stages to obtain more accurate results. A rough calibration is performed to calculate the rotation angles between the target and the camera. If the tilt angle is larger than 12°, the corresponding images are removed. Subsequently, the remaining images are used for precise calibration. The simulations and the experiments demonstrate that the proposed method can accurately calibrate a camera with a planar square periodic pattern, even in the case of severe defocusing.

Camera calibration by using weighted differential evolution algorithm: a comparative study with ABC, PSO, COBIDE, DE, CS, GWO, TLBO, MVMO, FOA, LSHADE, ZHANG and BOUGUET

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.