Invariance Of Cross-ratio Research Articles

Methodology and accuracy evaluation of global calibration for Multi-Line-Scan camera system in rail transit tunnel

Vision-based inspection techniques have improved the efficiency of tunnel inspection. This paper presents a rail transit tunnel multi-line-scan camera inspection system that requires global calibration to obtain the spatial relationships among all line-scan cameras, which is crucial for tunnel panoramic image mosaicking and 3D reconstruction. A flexible global calibration method is proposed, a hybrid calibration target is designed that includes triangular patterns based on the cross-ratio(CR) invariance principle and target holes. Establishing a virtual target field and using coplanarity as a constraint to refit a new view plane and globally optimizing the initial coordinates, which would ensure the calibration accuracy. In addition, an accuracy evaluation method based on CR triangles is proposed to assess the calibration results. The experimental results demonstrate the feasibility and reliability of the proposed calibration method and that the developed accuracy evaluation method is feasible compared with the traditional reprojection error method.

Iterative Camera Calibration Method Based on Concentric Circle Grids

A concentric circle target is commonly used in the vision measurement system for its detection accuracy and robustness. To enhance the camera calibration accuracy, this paper proposes an improved calibration method that utilizes concentric circle grids as the calibration target. The method involves accurately locating the imaged center and optimizing camera parameters. The imaged concentric circle center obtained by cross-ratio invariance is not affected by perspective projection, which ensures the location accuracy of the feature point. Subsequently, the impact of lens distortion on camera calibration is comprehensively investigated. The sub-pixel coordinates of imaged centers are taken into the iterative calibration method, and camera parameters are updated. Through simulations and real experiments, the proposed method effectively reduces the residual error and improves the accuracy of camera parameters.

Polarized light vision pose measurement method by fusing the constraints provided between control points for hand-eye calibration

The accuracy of hand-eye calibration is determined by the pose measurement accuracy of the calibration target. In the hand-eye calibration of industrial robots, the pose measurement can be performed based on the polarization information to filter out high-brightness areas of the image, optimize image processing, and increase effective control points. However, it is hard to decide on an adequate polarization angle. An inadequate polarization angle will affect the image contrast and ultimately affect the extraction accuracy of the 2D projections of the control points. In addition, the existing non-iterative pose measurement methods only consider the constraints provided by the single control points. The constraints provided between the control points are not in consideration. This results in reduced pose measurement accuracy in noisy environments. Aiming at the above problems, a polarized light vision pose measurement method by fusing the constraints provided between control points for hand-eye calibration is proposed: the adequate polarization angle was determined based on the cross-ratio invariance, and the target image collected under the adequate polarization angle was used for subsequent pose measurement to reduce the high-brightness areas on the premise of ensuring the image contrast. We introduced the plane created by two control points and the optical center to represent the constraints provided between these two control points. In this way, the constraints provided by any two control points can be fused with the constraints provided by the single control points to solve the pose non-iteratively. Compared to other current methods, there are more significant increases in our method's pose measurement accuracy and stability. The experimental results show that the angle measurement error is less than 0.052° over the measuring range of -60°-+60°, and the displacement measurement error is less than 0.01 mm over the measuring range of 0-20 mm.

Binocular visual dimension measurement method for rectangular workpiece with a precise stereoscopic matching algorithm

Binocular vision measurement benefits from high prediction robustness and low structural complexity. However, there are still significant flaws in its accuracy. In this paper, binocular vision measurement of a rectangular workpiece is investigated. A new precise measurement method based on binocular vision is designed to achieve precise measurement of rectangular workpiece dimensions. Firstly, an algorithm for workpiece location based on Zernike moments and corner matching is proposed and employed to precisely locate the workpiece and extract the sub-pixel coordinates of discrete points on an image’s edge. Then, a novel stereoscopic matching algorithm combined with epipolar-geometry and cross-ratio invariance (CMEC) is proposed to improve the accuracy of binocular vision stereoscopic matching. Finally, a projection plane is introduced after the 3D reconstruction of discrete points in the workpiece contours by fitting the plane with least squares. The projection plane limits the coordinate fluctuations of discrete points. Furthermore, the data screening is used to further improve the accuracy of size calculation. The experimental results of the standard checkerboard and actual workpiece show that CMEC’s matching accuracy reached 99%, and the proposed method’s measurement accuracy reached 0.018 mm. This work presents a novel algorithm for stereoscopic matching in binocular vision and machine vision measurement.

A static and fast calibration method for line scan camera based on cross-ratio invariance

This paper presents a new calibration method of line scan camera model based on cross-ratio invariance using a calibration pattern on the top of the gauge block. Instead of using the 3D pattern, planner pattern with precise motion platform, or pre-calibrated matrix camera, only a planner pattern with gauge blocks is used in this new method. A group of data on the line scan camera projection plane is obtained by placing the planner pattern at a different height. Line scan camera parameters were calibrated through a derived mathematical model. This method is simple, inexpensive and easy to use. The experimental results demonstrated that the average reprojection error of this method is 0.0431, which is 62.2% lower than the traditional method, which proves the feasibility and effectiveness of this method.

A ball-shaped target development and pose estimation strategy for a tracking-based scanning system

This paper describes a pose measurement and tracking strategy for an automatic tracking-based scanning system through developing a ball-shaped target. The target structure is introduced. Then, to determine the target pose, a coded marker and accurate center extraction method is proposed using subpixel and cross-ratio invariance principle. Furthermore, the target coordinate system is established by vision-based target calibration. A confidence-based tracker is proposed, enabling higher tracking confidence and accuracy, and keeping a high tracking speed. The stereo vision estimates the 3D position and orientation of the moving target in real-time. The trajectory is smoothed dynamically based on the Kalman filter. Experiments are implemented to verify the tracking speed, accuracy, and spatial accessibility in robot tracking applications. Additionally, the proposed target and strategy have good performance in full-space and fall-orientation tracking.

A novel cooling hole inspection method for turbine blade using 3D reconstruction of stereo vision

Cooling holes (number 100 ∼ 200, diameter 0.3 ∼ 1.2 mm) are important heat dissipation structures of a turbine blade in aero-engine. Due to the small sizes and similar contours of cooling holes, it is difficult to extract and match their features by traditional stereo reconstruction methods. This paper proposes a novel cooling hole inspection method for turbine blades utilizing 3D reconstruction technique of stereo vision, which combines the stereo vision principle with the invariance of cross-ratio. The feature points of contours are extracted and matched by calculating two intersection points of circular contours and a line through the center points of adjacent cooling holes. Additionally, the 3D points corresponding to the feature points are reconstructed, by which, the diameters of cooling holes can be calculated successfully. Moreover, measurement experiments verify the effectiveness and accuracy of the proposed method. The experimental results show that the average errors of the standard circle ruler and tiny hole sample are within 0.05 mm, which satisfies the inspection requirement of cooling holes.

Measurement of Apparent Building Damage by Using a Single Image

In the proposed detection method, a single image was used for the rapid quantitative measurement of the damage area of a building. By using cross-ratio invariability between real and image coordinates, the damage area and the side lengths of the selected region were measured using the vanishing point, the vanishing line, and a line segment with a known length. Perspective transformation and image binarisation were performed on the selected frame to convert the length into area information. The damage area was obtained rapidly from the proportion of pixels in the damage region to pixels in the selected region. Corner detection and subpixel methods were combined to determine measurement errors because of the selection of measurement points. The experimental results from the example test revealed that quantitative area measurement of surface damage on buildings could be realised using the proposed method.

Distortion correction based on off-axis Schwarzschild two-mirror hyperspectral imager.

A new method of distortion correction based on the off-axis Schwarzschild two-mirror hyperspectral imager is proposed in this paper. The polynomial model is used to indicate the distortion in the pushbroom direction and the correction method is based on linear feature. The radial distortion model is used to indicate the vertical pushbroom direction of distortion and the correction method is based on the cross ratio invariance. Compared with the common precision angle measurement method, this method is simple and efficient. This method can be applied to the distortion correction of the non-mapping pushbroom hyperspectral imager.

Application of a Vision-Based Single Target on Robot Positioning System.

In this paper, we propose a Circular-ring visual location marker based on a global image-matching model to improve the positioning ability in the fiducial marker system of a single-target mobile robot. The unique coding information is designed according to the cross-ratio invariance of the projective theorem. To verify the accuracy of full 6D pose estimation using the Circular-ring marker, a 6 degree of freedom (DoF) robotic arm platform is used to design a visual location experiment. The experimental result shows in terms of small resolution images, different size markers, and long-distance tests that our proposed robot positioning method significantly outperforms AprilTag, ArUco, and Checkerboard. Furthermore, through a repeatable robot positioning experiment, the results indicated that the proposed Circular-ring marker is twice as accurate as the fiducial marker at 2–4 m. In terms of recognition speed, the Circular-ring marker processes a frame within 0.077 s. When the Circular-ring marker is used for robot positioning at 2–4 m, the maximum average translation error of the Circular-ring marker is 2.19, 3.04, and 9.44 mm. The maximum average rotation error is also 1.703°, 1.468°, and 0.782°.

Data-Driven Laser Plane Optimization for High-Precision Numerical Calibration of Line Structured Light Sensors

Line structured light sensor has been applied in various three dimensional (3D) measurement scenes with the advantages of non-contact, low cost and high speed. Its accuracy, which is directly determined by the calibration method, needs to be further improved to fulfill the measuring tasks of precision parts. Here, we proposed a numerical method that can eliminate the errors of the model based methods through two strategies. One is the establishment of the numerical mapping relationship between stripe pixel coordinates and their world coordinates through piecewise cubic interpolation. Corner points of a checkerboard target are used to obtain sufficient interpolating nodes. This target can be manually aligned with the laser plane and the alignment error would be eliminated via the point projection. The other is the data-driven laser plane optimization. The data set of reference interval distance is computed based on the invariance of cross ratio. The optimization model is to minimize the root mean squared error of measured interval distances by adjusting the laser plane coefficients. After the optimization, a higher numerical mapping relationship can be achieved. It bypasses the camera and the distortion models and reaches a calibration error of only 0.005mm. The comparison studies and the measurement of the steps further validate the proposed method.

Projector calibration based on cross ratio invariance

Projector calibration based on cross ratio invariance

Line structured light calibration method and centerline extraction: A review

Line structured light system has made rapid progress in recent years owing to the improvement of camera resolution and image processing technology. The calibration of line structured light system and centerline extraction affect the imaging quality. Hence, numerous innovations have occurred in both line structured light calibration methods and centerline extraction methods. In this paper, key technologies of line structured light calibration are reviewed. Major calibration methods such as vector cross product, linear equation solution, cross ratio invariance, vanishing points and lines, Plücker matrix are analyzed and compared in detail. Methods of centerline extraction are analyzed furthermore. This review concludes with a discussion of the future development of line structured light system, providing a good reference for researchers.

Line Structured Light 3D Sensing With Synchronous Color Mapping

A line structured light measurement system is proposed which can obtain both the 3D geometrical and color information of objects. The profile sensor of the system is consisted of a black-and-white camera and an infrared laser line projector. A high precision calibration method is presented for the range sensor by use of a planar target. Then, the point coordinates of the measurement profile can be computed according to center coordinates of laser stripe and the calibrated sensor parameters. The wavelength of the laser projector is 850nm which is out of the spectrum response range of the color camera. Thus, the projected laser line would not affect the color acquisition. The transformation matrix between the two camera coordinate systems is determined and then optimized based on the invariance of cross ratio. By use of the transformation matrix, each point on the profile can be projected onto the image plane of the color camera, and the color information can be obtained synchronously. The measurement results show that the mean radius error of a ceramic ball can reach 0.009mm, and the mean mapping error of profile points on color image plane is 0.16pixel. The 3D measurement results of the textured objects further validate the proposed system.

Efficient depth recovering method free from projector errors by use of pixel cross-ratio invariance in fringe projection profilometry.

In fringe projection profilometry, errors related to projectors are not easy to compensate for, as a projector is much more difficult to calibrate than a camera. Immune to projector errors, the depth recovering method based on pixel cross-ratio invariance enables circumventing this issue by calculating the depth of a point from the shift of its camera pixel instead of from its fringe phase. With this existing technique, however, one has to search three reference phase maps along epipolar lines for pixels having the same phases. Doing so increases the measurement time significantly. To improve measurement efficiency, this paper derives, from the pixel cross-ratio invariance, a generic function representing the relationship between the depths and the corresponding pixel shifts and suggests a calibration method for determining its coefficient matrices. Using this function allows us to recover object depths just by searching a single reference phase map, thus reducing the time duration for data processing to about one-third. Besides, different from the previous method, which depends on exactly three reference phase maps, the proposed method calculates the function coefficients from more reference phase maps in the least-squares sense and denoises the benchmark reference phases by use of averaging technique, thus improving measurement accuracy. Experimental results demonstrate this method to be effective in improving measurement accuracy and efficiency.

Target-less approach of vibration measurement with virtual points constructed with cross ratios

For structures with distinguished edge features, a target-less approach of vibration measurement method based on stereo vision system is proposed in this paper. The edge is precisely identified through skeleton thinning, and then the virtual points are constructed and tracked. A sub-pixel algorithm to minimize continuous curvature change is used, which is based on the interpolation in the normal direction of the line edge skeleton. Virtual points are constructed according to different cross ratios. Based on the invariance of cross ratio in affine transformation, the image coordinates of the same virtual point can be found accurately. The edge displacement is measured through matching and tracking of these virtual homologous points. A 3 KW wind turbine blade is experimented. The measured frequencies are compared with those from target approach and hammer impact testing. The reliability and efficiency of the proposed target-less approach is verified by the experimental results.

Calibration Method Based on the Image of the Absolute Quadratic Curve

In this paper, a new camera calibration method based on the image of the absolute quadratic curve (IAC) is proposed, and a new target is designed for this method, which is both convenient and flexible. It first extracts the characteristic points and the characteristic lines of the target and finds out the vanishing point and the vanishing line. The radial and tangential distortion coefficients are obtained by using the cross ratio invariance to correct the target image distortion. Then, the four internal parameters of the camera are obtained by IAC. The influence of the skew parameters is ignored. The rotation matrix is then calculated by the orthogonal characteristic of the coordinate system, and the translation vector is calculated by the center coordinates of the camera. In this way, the internal and external parameters of the camera can be obtained. The internal and external parameters are taken as initial values, and the optimal results are obtained by nonlinear optimization using the reprojection method. Finally, the relative position between different target images can be obtained by using the fundamental matrix, namely, the rotation angle. In the process of solving, the normalization method is used to improve the accuracy of data processing. Not requiring any prior information of the camera, the method has a wide range of applications.

Lens distortion correction method based on cross-ratio invariability and compressed sensing

Optical lens distortions will seriously affect the measurement accuracy of the vision system. An independent lens distortion correction method based on cross-ratio invariability and compressed sensing is, thus, proposed to improve the measurement accuracy of the system. A virtual distortion correction template is designed according to the characteristics of the lens distortion. The ideal projection coordinate in the imaging plane of the camera and the distortion correction value of the characteristic points in the virtual correction template can be calculated based on the four-point cross-ratio invariance principle. The ideal projection coordinate of the other pixels in the image can then be reconstructed based on compressed sensing theory and, thus, correcting the distortion of all pixels. The experimental results show that for the same vision measurement system, when the independent distortion correction algorithm is used, its measurement accuracy is significantly improved, and the maximum error is only 0.069 mm. This method can correct the distortion effectively, thus improving the precision of the system.

Depth recovering method immune to projector errors in fringe projection profilometry by use of cross-ratio invariance

In fringe projection profilometry, the projector parameters are difficult to calibrate accurately thus inducing errors in measurement results. To solve this problem, this paper analyzes the epipolar geometry of the fringe projection system, revealing that, on an epipolar plane, the depth variation along an incident ray induces the pixel movement along the epipolar line on the image plane of the camera. The depth variation and the pixel movement can be related to each other by using projective transformations. Under this condition, their cross-ratio keeps invariant. By use of this cross-ratio invariance, we suggest a depth recovering method immune to projector errors. To calibrate the measurement system, we shift a reference board perpendicularly to three positions with known depths and measure its phase maps as the reference phase maps. When measuring an object, we calculate the object depth at each pixel by equating the cross-ratio of the depths to that of the corresponding pixels having the same phase. Experimental results demonstrate that, with this technique, the errors associated with the projector, including its errors in geometry parameters, its lens distortions, and its luminance nonlinearity, do not affect the measurement results.

Cross-ratio–based line scan camera calibration using a planar pattern

A flexible new technique is proposed to calibrate the geometric model of line scan cameras. In this technique, the line scan camera is rigidly coupled to a calibrated frame camera to establish a pair of stereo cameras. The linear displacements and rotation angles between the two cameras are fixed but unknown. This technique only requires the pair of stereo cameras to observe a specially designed planar pattern shown at a few (at least two) different orientations. At each orientation, a stereo pair is obtained including a linear array image and a frame image. Radial distortion of the line scan camera is modeled. The calibration scheme includes two stages. First, point correspondences are established from the pattern geometry and the projective invariance of cross-ratio. Second, with a two-step calibration procedure, the intrinsic parameters of the line scan camera are recovered from several stereo pairs together with the rigid transform parameters between the pair of stereo cameras. Both computer simulation and real data experiments are conducted to test the precision and robustness of the calibration algorithm, and very good calibration results have been obtained. Compared with classical techniques which use three-dimensional calibration objects or controllable moving platforms, our technique is affordable and flexible in close-range photogrammetric applications.