A Unified Linear Camera Calibration Method Using Two Parallel Calibration Planes

Abstract

In this paper, we examine the two plane camera calibration model in terms of perspective mapping, and present a new effective camera calibration method by taking the advantage of the conventional method and modifying it based on the exact perspective imaging.It also takes the advantage that each of intrinsic and extrinsic camera parameters can be obtained by solving linear equations only. So that the solutions will be provided uniquely and stably under some conditions, and which can be definitely specified.In our method a priori knowledge on camera intrinsic parameters is only physical pixel sizes. Exact focal length of the lens, the position of image center or optical center, and the camera pose are unknown and to be calibrated. This is a practical assumption for common commercial TV camera systems.For the cases where non-linear lens distortions must be taken into account, our method can be extended and their parameters are calibrated also using only linear solutions. It is shown that higher performance and accurate calibration can be achieved by this method theoretically and experimentally.

A polynomial model with line-of-sight constraints for Lagrangian particle tracking under interface refraction

“…By combining the abovementioned strategies of polynomial function calibration, reprojection based on LOS interpolation, 3D shaking, and LOSC, we realize an LPT framework as LOSC-LPT based on the original STB, and then the performance evaluation is conducted using synthetic images and an experimental dataset in the presence of refractive interfaces. The determination of LOSs between two planes for the 3D position reconstruction is referred to the works [28,29], and the stereo matching with two planes and LOS constraints are built upon the particle triangulation procedure by Dracos [34] and Mann and Ott [35], the track linking and STB parts of particle tracking are based on the methods proposed by Ouellette et al [9], Schanz et al [1], and Tan et al [13], and track initialization is based on IPR [5] and 4BE-ETI [36], or particle-space correlation [37]. This framework has been parallelized based on open multi-processing with the CPU [38] and will be further improved using the compute unified device architecture (CUDA) [39] with graphics processing unit (GPU) devices in the future.…”

“…This multi-plane polynomial camera model [26] has been applied in 3D tomographic reconstruction of Tomo-PIV [7,8] to enhance accuracy, assuming that the LOSs between two planes are linear, its mapping functions between points on calibration planes and images can be accurately represented using only 10 parameters in a 3rd-order model. In addition, the determination of LOSs between two planes for the 3D position reconstruction can be found in works [28,29], while the projection of the 3D particle positions onto camera images using multi-plane polynomials model is not easy and challenging, a common projection idea is to find the point where the LOS intersects the image plane, which is difficult to achieve in the presence of refractive interfaces. The projection of particles onto the images by Z-interpolation according to particle position between multi Z-plane might be non-physical due to the LOSs of pixels are not parallel [6], causing reprojection error of several pixels (px) and huge triangulation error for PTV (will be discussed in section 2.3 in details).…”

Automated 3-D optic disk reconstruction and feature extraction for glaucoma analysis

“…Deguchi and Morishita [32] presented a linear camera calibration method using two parallel planes (2-D object-based calibration). The main idea of this technique is to determine the spatial lines-of-sight corresponding to every image points, instead of directly identifying the intrinsic parameters.…”