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Cost Effective Simulation
Published in Terry M. Peters, Cristian A. Linte, Ziv Yaniv, Jacqueline Williams, Mixed and Augmented Reality in Medicine, 2018
Ziv Yaniv, Özgür Güler, Ren Hui Gong
The fluoroscopy machine is modelled using the standard pinhole camera model (Yaniv and Cleary 2006a) with the following set of parameters: focal length, location of the principle point in the x-ray image, distortion coefficients, and the rigid transformation between the camera and world coordinate systems. In our case, the world coordinate system coincides with the phantom model, and the transformation is denoted as modelT x-ray. To estimate these parameters, we acquire a single x-ray image of a 3D, tracked calibration phantom. which consists of two planes embedded with 36 metal spheres arranged in a regular grid. The sphere configuration defines seven line segments: four on the top plane with 3-mm spheres and three on the bottom plane with 2-mm spheres. The sphere projections are first localized in the x-ray image using a multiscale blob detection algorithm (Lindeberg 1998). They are then classified into two groups based on their size. The lines in each group are detected using the RANSAC algorithm (Fischler and Bolles 1981), and the correspondence between the two-dimensional projections and 3D spheres is established. The camera parameters are then estimated using a least squares formulation that minimizes the reprojection error via the Levenberg-Marquardt algorithm (Hartley and Zisserman 2003).
A static and fast calibration method for line scan camera based on cross-ratio invariance
Published in Journal of Modern Optics, 2022
Shuaipeng Yuan, Dexue Bi, Zexiao Li, Ning Yan, Xiaodong Zhang
In camera calibration, reprojection error is usually used to determine camera calibration accuracy. The reprojection error refers to the deviation between the projection point coordinates and the actual imaging point coordinates, which is obtained using the internal and external parameters of the camera and the distortion coefficient to construct the camera imaging model and re-projecting the three-dimensional points in the space. Generally, the smaller the reprojection error, the higher the camera calibration accuracy. The reprojection errors of this method and the traditional method [12] for each image and the average reprojection errors for all images are shown in Figure 12. It can be seen that compared with the traditional method, the reprojection error of this method is reduced by 43.8%–73.2% and is lower than the traditional method. It can be seen that the average reprojection error of this method is 0.0431, which is 62.2% lower than the traditional method. Figure 12 shows that this method dramatically improves camera calibration accuracy and proves its feasibility and effectiveness.
Application of improved particle swarm optimization algorithm in solving camera extrinsic parameters
Published in Journal of Modern Optics, 2019
In order to simulate the actual experimental conditions, an approximately planar calibration board is constructed. The calibration board contains 24 feature points, and the world coordinate system is established on the calibration board. The intrinsic parameter matrix is as follows: We obtain the extrinsic parameters of the camera by generating 3 rotation angles and 3 translation vectors randomly, and then the ideal image coordinates of the feature points are obtained according to the pinhole camera model. In order to verify the robustness of the algorithm, random Gaussian noise with zero mean and varying standard deviations is added to the image points in the simulations. Define the rotation angle error as: where is the number of repeated experiments at the same level of Gaussian noise. In this paper, , and the translation vector error is as follows: The reprojection error is defined as the mean Euclidean distance between the image coordinates of the projected control points and the image coordinates of the detected control points.