Kinematic projection in modern technologies

The trajectories and coordinates of unmanned aircrafts spatial location determination is researched with the help of kinematic projection means. The methodology offered below considers the formation of two mobile and independent kinematic projection centers raised into the air by drones. The electromagnetic radio waves emitted by them, penetrating an unknown aircraft object, form two independent projecting rays intersecting at the searched aircraft location point. In this case, the searched object spatial location instantaneous (at a certain point in time) point will be placed on an imaginary “picture plane” on a line connecting the points projections generated by drones interceptors projecting rays. As far as all of the projection objects in this case are movable, all the moving trajectory projection of the searched aircraft will be displayed on the monitor. The introduction of another “picture plane”, perpendicular to the main one, will help to build an axonometric mapping not only for projections, but also for the aircraft spatial movement trajectory itself. Each point of this trajectory gives an information about the “instantaneous” coordinates of the aircraft spatial location. The method of application of kinematic projection for display of a trajectory of movement and search of coordinates of moving objects is described. In kinematic projection, all its key components, namely the object, the center of projection, the image plane and the projecting rays, are in continuous motion with certain speeds and accelerations. Kinematic projection deepens the field of practical application of descriptive geometry. This is confirmed by the example of practical application of kinematic projection presented in the article for improvement of remote control of tillage equipment in automated land treatment complexes. The main technical support for the practical application of kinematic projection are stationary radio towers or unmanned aerial vehicles (BPLA), such as drones. They are equipped with video cameras and electromagnetic radiation devices. This equipment serves as a center of kinematic projection. The projecting rays generated by the projection center will be received by a stationary command post (center). It is equipped with a radar system (radar) and modern computer equipment with appropriate software. This equipment, in this case, performs the function of a “picture plane”, which will reflect the trajectory of agricultural machinery. Actuators and controls of the movement of tillage equipment are equipped with receivers of control radio waves and means of automated control. The use of kinematic projection helps to improve the quality of tillage. This is ensured by the fact that its use is carried out automatically and eliminates possible errors of operators. Kinematic projection can also be used in military affairs to detect enemy drones in the airspace. In this case, use a kind of kinematic projection with its two centers of generation of projecting rays. This is an example of the solution of the so-called “inverse problem” of kinematic projection, which provides the ability to search for the coordinates of the motion of the projected object at a known trajectory of its motion. The main advantage of kinematic projection is the ability to identify and display an object on a computer screen not only in a flat view, but also taking into account its spatial coordinates.

Impacts of Phantom Off-Center Positioning on CT Numbers and Dose Index CTDIv: An Evaluation of Two CT Scanners from GE

The purpose of this work is to evaluate the impacts of body off-center positioning on CT numbers and dose index CTDIv of two scanners from GE. HD750 and APEX scanners were used to acquire a PBU60 phantom of Kagaku and a 062M phantom of CIRS respectively. CT images were acquired at various off-center positions under automatic tube current modulation using various peak voltages. CTDIv were recorded for each of the acquisitions. An abdomen section of the PBU60 phantom was used for CT number analysis and tissue inserts of the 062M phantom were filled with water balloons to mimic the human abdomen. CT numbers of central regions of interests were averaged using the Fiji software. As phantoms were lifted above the iso-center, both CTDIv and CT numbers were increased for the HD750 scanner whilst they were approximately constant for the APEX scanner. The measured sizes of anterior-posterior projection images were also increased for both scanners whilst the sizes of lateral projection images were increased for the HD750 scanner but decreased for the APEX scanner. Off-center correction algorithms were implemented in the APEX scanner. Matching the X-ray projection center with the system’s iso-center could improve the accuracy of CT imaging.

Common self-polar triangle of separate circles for light field camera calibration

Due to the trade-off between spatial resolution and angular resolution of the light field, it is difficult to extract high precision corner points and line features from light fields for calibration. A novel calibration pattern of separate circles is designed, and a light field camera calibration method based on common self-polar triangle with respect to separate circles is proposed in this paper. First, we explore the uniquity and reconstruction of common self-polar triangle with respect to sperate circles. Then, based on projections of the multi-projection-center model on the plane and conic, the common self-polar triangle on the sub-aperture image is reconstructed and used to estimate planar homography. Finally, a light field camera calibration algorithm is then proposed, including linear initialization and non-linear optimization. Experimental results on both synthetic and real data have verified the effectiveness and robustness of the method and algorithm proposed.

Alignment Method of an Axis Based on Camera Calibration in a Rotating Optical Measurement System

The alignment problem of a rotating optical measurement system composed of a charge-coupled device (CCD) camera and a turntable is discussed. The motion trajectory model of the optical center (or projection center in the computer vision) of a camera rotating with the rotating device is established. A method based on camera calibration with a two-dimensional target is proposed to calculate the positions of the optical center when the camera is rotated by the turntable. An auxiliary coordinate system is introduced to adjust the external parameter matrix of the camera to map the optical centers on a special fictitious plane. The center of the turntable and the distance between the optical center and the rotation center can be accurately calculated by the least square planar circle fitting method. Lastly, the coordinates of the rotation center and the optical centers are used to provide guidance for the installation of a camera in a rotation measurement system. Simulations and experiments verify the feasibility of the proposed method.

Refined Calibration Model for Improving the Orientation Precision of Electron Backscatter Diffraction Maps

For the precise determination of orientations in polycrystalline materials, electron backscatter diffraction (EBSD) requires a consistent calibration of the diffraction geometry in the scanning electron microscope (SEM). In the present paper, the variation of the projection center for the Kikuchi diffraction patterns which are measured by EBSD is calibrated using a projective transformation model for the SEM beam scan positions on the sample. Based on a full pattern matching approach between simulated and experimental Kikuchi patterns, individual projection center estimates are determined on a subgrid of the EBSD map, from which least-square fits to affine and projective transformations can be obtained. Reference measurements on single-crystalline silicon are used to quantify the orientation errors which result from different calibration models for the variation of the projection center.

Dimensional and Layout Optimization Design of Multistage Gear Drives Using Genetic Algorithms

In the minimal weight/volume design of multistage gear drives, both the dimensional and layout parameters of gear pairs have a direct effect on the design result. A new optimization model that can carry out both dimensional- and layout-constrained optimization design for any number of stages of cylindrical gear drives simultaneously is proposed. The optimization design of a three-stage cylindrical gear drive is conducted as a design example to test the application of this model. In the attempt to solve this constrained optimization problem using an elitist genetic algorithm (GA), different constraint handling methods have a crucial effect on the optimal results. Thus, the results obtained by applying three typical constraint handling methods in GA one by one are analyzed and compared to figure out which one performs the best and find the optimal solution. Moreover, a more precise projection center distance (PCD) method to calculate the degree of interference constraint violation is proposed and compared with the usually used (0, 1) method. The results show that the proposed PCD method is a better one.

Digital Camera Calibration Study by series of shots with a common projection center

Рассматривается метод калибровки цифровых фотокамер (ЦФК) по маркированному тест-объекту с использованием дополнительных геометрических условий. Представлены результаты исследований калибровки по макетным снимкам.

RESEARCH OF THE CAMERA CALIBRATION USING SERIES OF IMAGES WITH COMMON CENTER OF PROJECTION

The method for calibration of cameras equipped with long focal distance lens is researched in the present work. The basic idea is as follows. The camera to be calibrated is placed on the tripod with panoramic head. The main condition of panorama shooting is that the rotation center of the camera and the front nodal point of the lens should be the same. The camera is calibrated based on a series of images of a test object with a common center of projection. Special software has been created for this purpose. The results of experimental studies on digital simulated data and for a real camera Hasselblad H4D-60 are presented. Results of these experiments show that use of common projection center allow to increase accuracy of the calibration process of the long focal length cameras.

Analysis for center deviation of circular target under perspective projection

Purpose Accurate feature localization is a fundamental problem in computer vision and visual measurement. In a perspective projection model of the camera, the projected center of a spatial circle and the center of the projection ellipse are not identical. This paper aims to show how to locate the real projection center precisely in the perspective projection of a space circle target. Design/methodology/approach By analyzing the center deviation caused by projection transformation, a novel method is presented to precisely locate the real projection center of a space circle using projective geometry. Solution distribution of the center deviation is analyzed, and the quadratic equation for determining the deviation is derived by locating vanishing points. Finally, the actual projected center of the circular target is achieved by solving the deviation quadratic equations. Findings The procedures of the author’s method are simple and easy to implement. Experimental data calculated that maximum deviation occurs at approximately between 3π/10 and 2π/5 of the angle between the projection surface and the space target plane. The absolute reduction in error is about 0.03 pixels; hence, it is very significant for a high-accuracy solution of the position of the space circle target by minimizing systematic measurement error of the perspective projection. Originality/value The center deviation caused by the space circle projection transformation is analyzed, and the detailed algorithm steps to locate the real projection center precisely are described.