High-precision camera calibration via perspective distortion correction using a hybrid chessboard-circle target.

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.

Camera calibration is a prerequisite for spatial position measurement. The fish-eye camera can increase the field of view, but at the same time, the distortion it brings is more serious. It is difficult to obtain high accuracy when using traditional methods to calibrate the fish-eye camera. Therefore, this paper proposes a fast calibration method for fisheye cameras, which makes the calibration process convenient and fast, and improves the calibration accuracy. The camera is fixed on a high-precision two-dimensional turntable, and the turntable rotates according to the set law through a fully automatic program. At the same time, the camera captures the bright spots in the collimator and extracts the pixel coordinates of its centroid. Collect several sets of data, use the bicubic interpolation method to expand the data, find the relationship between the pixel coordinates of the centroid of the bright spot and the rotation angle of the turntable. Finally, the three-dimensional space coordinates can be obtained by binocular vision triangulation to verify the calibration accuracy. The above method bypasses the traditional camera optical imaging model and distortion model, but uses traversal and interpolation. Experiments show that the accuracy of this method can reach the centimeter level in long-distance, large field of view, and severely distorted scenes.

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

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.

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 plays a crucial role in 3D measurement tasks of machine vision. In typical calibration processes, camera parameters are iteratively optimized in the forward imaging process (FIP). However, the results can only guarantee the minimum of 2D projection errors on the image plane, but not the minimum of 3D reconstruction errors. In this paper, we propose a universal method for camera calibration, which uses the back projection process (BPP). In our method, a forward projection model is used to obtain initial intrinsic and extrinsic parameters with a popular planar checkerboard pattern. Then, the extracted image points are projected back into 3D space and compared with the ideal point coordinates. Finally, the estimation of the camera parameters is refined by a non-linear function minimization process. The proposed method can obtain a more accurate calibration result, which is more physically useful. Simulation and practical data are given to demonstrate the accuracy of the proposed method.

We present a simple cue-based method for camera calibration aimed at 3-D shape measurement with a single domestic camera. This method performs both camera calibration and measurement of the 3-D shape simultaneously by projecting objects of measurement along with a cue object having feature points onto one image plane while moving the single camera by hand. Our proposed method requires only four coplanar points, and hence the use of a simple geometrical structure such as A4 size paper as the cue object allows us to perform measurement of the 3-D shape easily without special equipment. Furthermore, the method modifies the observed feature points' coordinates with the optimization method which formulates the orthogonality constraint between coordinate axes given by the camera calibration.

In mathematical terms, a camera maps all points on a 3D target object surface to a collection of 2D points on the image plane; a <i>camera model</i> thus relates the image coordinates to the physical locations of the object points in the FOV. Camera calibration refers to the process of deriving the internal (<i>intrinsic</i>) and external (<i>extrinsic</i>) parameters of the camera model and image-capture hardware. Intrinsic parameters embody the characteristics of the optical system and its geometric relationship with the image sensor, while extrinsic parameters relate the location and orientation of the camera with respect to the 3D object (Euclidean) space. The 3D object space is used for measuring the collection of object point coordinates [R{(<i>x_o</i>, <i>y_o</i>, <i>z_o</i>)}] in physical units that make up the target scene in the FOV. Extrinsic parameters are derived as a set of rigid body transformation matrices: three rotations about the <i>x</i>, <i>y</i>, and <i>z</i> axes, and three translations along these axes (block 1 in Fig. 8.1). The two sets of output from the extrinsic calibration process are fed into the intrinsic calibration process to make up the complete camera calibration model. In cinematography, rotations about the <i>x</i>, <i>y</i>, and <i>z</i> axes are called <i>pan</i>, <i>tilt</i>, and <i>roll</i>, respectively, and the movement along the <i>z</i> axis is called <i>zooming</i>.

Image coordinates measurement is one of key links in close-range photogrammetry, such as in camera calibration in control fields or in a surveying procedure of artificial targets pasted on surface of lacking texture object. An automatic measurement algorithm about image coordinates of circular artificial targets is researched in this paper. An automatic measurement strategy of artificial targets is put forward, and the main content includes rough positioning of targets in image by direct linear transformation, adaptive image window determination according to the actual size of artificial target and window movement to measure image coordinates of target. Experiments prove that the method is able to complete the automatic measurement of image coordinates of artificial targets with high efficiency.

In this paper we design a novel planar 2D fiducial marker and develop fast detection algorithm aiming easy camera calibration and precise 3D reconstruction at the marker locations via the bundle adjustment. Even though an abundance of planar fiducial markers have been made and used in various tasks, none of them has properties necessary to solve the aforementioned tasks. Our marker, X-tag, enjoys a novel design, coupled with very efficient and robust detection scheme, resulting in a reduced number of false positives. This is achieved by constructing markers with random circular features in the image domain and encoding them using two true perspective invariants: cross-ratios and intersection preservation constraints. To detect the markers, we developed an effective search scheme, similar to Geometric Hashing and Hough Voting, in which the marker decoding is cast as a retrieval problem. We apply our system to the task of camera calibration and bundle adjustment. With qualitative and quantitative experiments, we demonstrate the robustness and accuracy of X-tag in spite of blur, noise, perspective and radial distortions, and showcase camera calibration, bundle adjustment and 3d fusion of depth data from precise extrinsic camera poses.

The increased resolution and reduced cost of commercially-available digital cameras have led to their use in close range and low-altitude airborne photogrammetric operations. In addition, the widespread adoption of Mobile Mapping and Unmanned Aerial Vehicle systems in various applications increased the demand for 3D reconstruction using Medium-Format Digital Cameras (MFDCs). The interest of professionals who might lack photogrammetric expertise mandates the development of automated procedures, especially camera calibration, for the manipulation of digital imaging systems. This paper deals with an investigation of the type of signalized targets that can be economically prepared while lending themselves to reliable detection and precise localization in the captured imagery. More specifically, checkerboard and circular targets are evaluated. Efficient techniques are introduced for their automated detection and localization as well as semi-automated identification. The impact of the proposed approaches on the quality of derived IOPs is quantified using similarity measures, which evaluate the degree of similarity of the reconstructed bundles from these IOPs. The experimental results show that automated localization of checkerboard and circular targets yield consistent IOPs. However, the detection and localization of checkerboard targets are easier and more robust to the quality of the involved imagery. Therefore, checkerboard targets are recommended as the target of choice for digital camera calibration.

Circular features are very common in geometric camera calibration. The projection of a circular feature is generally a deformed ellipse, not a true ellipse, due to the presence of lens distortion. The center of the deformed ellipse, obtained by fitting the boundary points with an ellipse, does not necessarily coincide with the distorted point corresponding to the center of the undistorted projection of the circular feature. An eccentricity error will be introduced if the two points are considered to be coincident. In this study three main factors that affect the amount of the eccentricity error are discussed, including the form and amount of lens distortion, the size of the circular feature and the tilt of the supporting plane. Then, an effective geometric camera calibration method is proposed where the eccentricity error is compensated by establishing the correspondence between the estimated model position and the real position of the fitted center of the deformed ellipse. Both simulation and measurement data verify the existence of the eccentricity error and the effectiveness of the proposed method.

Calibration of the transformation between two planes, the image plane and the 2D platform, is important for applications where 2D metric information on the image plane is used to compute the 3D information in a world coordinate system. Efforts have been taken in computer vision literature to perform a full-scale camera calibration, including intrinsic and extrinsic parameters. For some applications, calibration of intrinsic parameters is not required as often as that of the extrinsic parameters. This paper addresses the problem of calibrating a camera's extrinsic parameters with respect to a 2D platform to which a camera is observing. A rational approximation method is proposed. Simulation and experimental results show that the proposed rational approximation method achieves comparable accuracy with the well-known homography-based approach. This work is motivated by our mobile sensor network project. Other relevant applications include vision-based metrology.

With the significant growth in the number of photovoltaic (PV) installations and their size, regular PV system inspection has become a challenge. Aerial drone imaging, based on visual, thermographic, and more recently luminescence, can be viable solutions for PV inspection. However, to achieve effective detection and quantification of failure based on images acquired form Unmanned Aerial Vehicle, there is need for image quality enhancement and correction of distortions, inherent to the drone measurement process. In this work we propose methods to automatically correct the perspective distortion in electroluminescent (EL) images of PV panels. We identified two main cases of perspective distortion: when the imaging plane is parallel to the panel plane or not, and propose methods to correct both. For both cases, theproposed method yields good results, as assessed by visual evaluation.

The external parameter calibration of LiDAR and camera is the core link of multimodal perception fusion technology, and its accuracy directly determines the effectiveness of cross modal information fusion. This article proposes a method for high-precision calibration of laser radar and camera extrinsic parameters using a checkerboard calibration board based on spatial registration theory. In response to the difficulty of feature extraction caused by the sparsity of LiDAR point clouds, this method enhances feature information by accumulating multi view point clouds and combines filtering algorithms to improve feature saliency; A standardized experimental platform was built based on ROS and Matlab, utilizing the reflection intensity distribution pattern of the checkerboard point cloud to achieve accurate extraction of its three-dimensional corner coordinates. At the same time, the corresponding two-dimensional checkerboard corner points are detected in the camera image, and the relative pose transformation matrix between the LiDAR and the camera is solved by establishing an accurate matching relationship between the two-dimensional and three-dimensional corner points. The experimental results show that this method has high-precision calibration results and good repeatability, which can provide a reliable extrinsic basis for multi-sensor fusion perception systems.