Perspective Projection Matrix Research Articles

Improving Measurement Accuracy of Deep Hole Measurement Instruments through Perspective Transformation.

Deep hole measurement is a crucial step in both deep hole machining and deep hole maintenance. Single-camera vision presents promising prospects in deep hole measurement due to its simple structure and low-cost advantages. However, the measurement error caused by the heating of the imaging sensor makes it difficult to achieve the ideal measurement accuracy. To compensate for measurement errors induced by imaging sensor heating, this study proposes an error compensation method for laser and vision-based deep hole measurement instruments. This method predicts the pixel displacement of the entire field of view using the pixel displacement of fixed targets within the camera's field of view and compensates for measurement errors through a perspective transformation. Theoretical analysis indicates that the perspective projection matrix changes due to the heating of the imaging sensor, which causes the thermally induced measurement error of the camera. By analyzing the displacement of the fixed target point, it is possible to monitor changes in the perspective projection matrix and thus compensate for camera measurement errors. In compensation experiments, using target displacement effectively predicts pixel drift in the pixel coordinate system. After compensation, the pixel error was suppressed from 1.99 pixels to 0.393 pixels. Repetitive measurement tests of the deep hole measurement instrument validate the practicality and reliability of compensating for thermal-induced errors using perspective transformation.

Applied Mathematics of Ray Tracing and Perspective Projection in Fiducial-Based Registration of X-Ray Images.

Ray tracing (RT) and perspective projection (PP) using fiducial-based registration can be used to determine points of interest in biplanar X-ray imaging. We sought to investigate the implementation of these techniques as they pertain to X-ray imaging geometry. The mathematical solutions are presented and then implemented in a phantom and actual case with numerical tables and imaging. The X-ray imaging is treated like a Cartesian system in millimeters (mm) with a standard frame-based stereotactic system. In this space, the point source is the X-ray emitter (focal spot), the plane is the X-ray detector, and fiducials are in between the source and plane. In a phantom case, RT was able to predict locations of fiducials after moving the point source. Also, a scaled PP matrix could be used to determine imaging geometry, which could then be used in RT. Automated identification of spherical fiducials in 3D was possible using a center of mass computation with average Euclidean error relative to manual measurement of 0.23 mm. For PP, RT projection or a combinatorial approach could be used to facilitate matching 3D to 2D points. Despite being used herein for deep brain stimulation (DBS), utilization of this kind of imaging analysis has wide medical and non-medical applications.

Charuco Board-Based Omnidirectional Camera Calibration Method

In this paper, we propose a Charuco board-based omnidirectional camera calibration method to solve the problem of conventional methods requiring overly complicated calibration procedures. Specifically, the proposed method can easily and precisely provide two-dimensional and three-dimensional coordinates of patterned feature points by arranging the omnidirectional camera in the Charuco board-based cube structure. Then, using the coordinate information of the feature points, an intrinsic calibration of each camera constituting the omnidirectional camera can be performed by estimating the perspective projection matrix. Furthermore, without an additional calibration structure, an extrinsic calibration of each camera can be performed, even though only part of the calibration structure is included in the captured image. Compared to conventional methods, the proposed method exhibits increased reliability, because it does not require additional adjustments to the mirror angle or the positions of several pattern boards. Moreover, the proposed method calibrates independently, regardless of the number of cameras comprising the omnidirectional camera or the camera rig structure. In the experimental results, for the intrinsic parameters, the proposed method yielded an average reprojection error of 0.37 pixels, which was better than that of conventional methods. For the extrinsic parameters, the proposed method had a mean absolute error of 0.90° for rotation displacement and a mean absolute error of 1.32 mm for translation displacement.

Obstacle detection system based on colour segmentation using monocular vision for an unmanned ground vehicle

An obstacle detection algorithm is introduced for aiding the navigation of unmanned ground vehicles (UGV). Coloured obstacles are placed randomly in an indoor environment. The coloured obstacles are detected, analysed and processed using a proposed monocular vision algorithm. A camera calibration is conducted to determine the relative position and orientation of the UGV with respect to the obstacles based on intrinsic and extrinsic matrices to form a perspective projection matrix. The field geometry is used to obtain a mapped environment in the world coordinates. Our obstacle detection algorithm is proposed to identify the existence of the obstacles in the field. Using bounding boxes around the detected obstacle allows the determination of the obstacles locations in a pixel coordinate frame. Thus, the depth perception is determined by using the pixel coordinates and the camera projection matrix. Real-time experiments are carried out to demonstrate the validity and efficiency of the proposed algorithm.

Obstacle detection system based on colour segmentation using monocular vision for an unmanned ground vehicle

An obstacle detection algorithm is introduced for aiding the navigation of unmanned ground vehicles (UGV). Coloured obstacles are placed randomly in an indoor environment. The coloured obstacles are detected, analysed and processed using a proposed monocular vision algorithm. A camera calibration is conducted to determine the relative position and orientation of the UGV with respect to the obstacles based on intrinsic and extrinsic matrices to form a perspective projection matrix. The field geometry is used to obtain a mapped environment in the world coordinates. Our obstacle detection algorithm is proposed to identify the existence of the obstacles in the field. Using bounding boxes around the detected obstacle allows the determination of the obstacles locations in a pixel coordinate frame. Thus, the depth perception is determined by using the pixel coordinates and the camera projection matrix. Real-time experiments are carried out to demonstrate the validity and efficiency of the proposed algorithm.

Self-calibration of stationary non-rotating zooming cameras

This paper proposes a new method for self-calibrating a set of stationary non-rotating zooming cameras. This is a realistic configuration, usually encountered in surveillance systems, in which each zooming camera is physically attached to a static structure (wall, ceiling, robot, or tripod). In particular, a linear, yet effective method to recover the affine structure of the observed scene from two or more such stationary zooming cameras is presented. The proposed method solely relies on point correspondences across images and no knowledge about the scene is required. Our method exploits the mostly translational displacement of the so-called principal plane of each zooming camera to estimate the location of the plane at infinity. The principal plane of a camera, at any given setting of its zoom, is encoded in its corresponding perspective projection matrix from which it can be easily extracted. As a displacement of the principal plane of a camera under the effect of zooming allows the identification of a pair of parallel planes, each zooming camera can be used to locate a line on the plane at infinity. Hence, two or more such zooming cameras in general positions allow the obtainment of an estimate of the plane at infinity making it possible, under the assumption of zero-skew and/or known aspect ratio, to linearly calculate the camera's parameters. Finally, the parameters of the camera and the coordinates of the plane at infinity are refined through a nonlinear least-squares optimization procedure. The results of our extensive experiments using both simulated and real data are also reported in this paper.

Design of highly realistic virtual environment for excavator simulator

On the basis of an open source engine Delta3D, a PC-based excavator simulator has been developed in this paper for training human operators and evaluating control strategies for heavy-duty hydraulic machines. Real-time Optimally Adapting Mesh (ROAM) algorithm is involved to produce terrain deformation with dynamic resolution and a modified Fundamental Earthmoving Equation model is applied to predict excavation forces. A GPU (graphics processing unit) based terrain-rendering method is adopted to create realistic visual appearance of different operating regions on terrain such as excavated pit and dumped mound during the simulation. In the system, surrounding LCDs (liquid crystal displays) are placed at the corresponding windows’ position in the driving cab instead of using multiple projectors. For irregular screens, the oblique perspective projection matrix is deduced for the seamless conjoining of graphic scenes in different LCDs. Finally, through the feedback of consumers, we proceed the comprehensive evaluation about the simulator.

가상 평면 기법을 이용한 3차원 기하 정보 획득 알고리즘

This paper presents an algorithm to acquire 3D geometric information using a virtual plane method. The method to measure 3D information on the plane is easy, because it's not concerning value on the z-axis. A plane can be made by arbitrary three points in the 3D space, so the algorithm is able to make a number of virtual planes from feature points on the target object. In this case, these geometric relations between the origin of each virtual plane and the origin of the target object coordinates should be expressed as known homogeneous matrices. To include this idea, the algorithm could induce simple matrix formula which is only concerning unknown geometric relation between the origin of target object and the origin of camera coordinates. Therefore, it's more fast and simple than other methods. For achieving the proposed method, a regular pin-hole camera model and a perspective projection matrix which is defined by a geometric relation between each coordinate system is used. In the final part of this paper, we demonstrate the techniques for a variety of applications, including measurements in industrial parts and known patches images.

Calibrating a Structured Light Stripe System: A Novel Approach

The problem associated with calibrating a structured light stripe system is that known world points on the calibration target do not normally fall onto every light stripe plane illuminated from the projector. We present in this paper a novel calibration method that employs the invariance of the cross ratio to overcome this problem. Using 4 known non-coplanar sets of 3 collinear world points and with no prior knowledge of the perspective projection matrix of the camera, we show that world points lying on each light stripe plane can be computed. Furthermore, by incorporating the homography between the light stripe and image planes, the 4 × 3 image-to-world transformation matrix for each stripe plane can also be recovered. The experiments conducted suggest that this novel calibration method is robust, economical, and is applicable to many dense shape reconstruction tasks.