Optimization Solution of Laser Plane Generated from Maximum Likelihood Estimation of Projection Plane

Abstract

An enhanced solution method that based on the maximum likelihood estimation (MLE) of the projection plane is proposed. The method utilizes a 2D target and an optimization process to achieve a higher accuracy and noise immunity. The projection plane is parameterized by the laser plane coordinates. The maximum likelihood function is obtained from the stochastic vector of the projection planes in the camera coordinate system. The coordinates of the laser plane are achieved by the optimization process. The MLE method is compared with the original method. The experimental results reveal the relative error reductions of 18.97, 19.81, 21.22, and 21.60% under the test distances of 200, 300, 400, and 500 mm, respectively. Moreover, for the images under noise, the results show the relative error reductions of 20.06, 18.77, 19.64, and 20.35%, respectively. The experimental results suggest that the MLE of the projection plane would be useful to improve the measurement accuracy of active vision in both fundamental research and potential applications.

A Camera Intrinsic Matrix-Free Calibration Method for Laser Triangulation Sensor

“…Hence, the laser plane fitting is less affected by the noise amplitude and number of images. Xu et al [2], the authors estimated the laser plane using maximum likelihood estimation, and their experimental results show that the relative error is reduced by about 20%. Xu et al [6], the laser plane is optimized using the RANSAC algorithm.…”

“…The laser triangulation sensor (LTS) is widely used to acquire depth information in industrial applications such as rail inspection [1], reverse engineering [2], and workpiece inspection [3]. In industrial environments, collisions and impacts can often change the parameters of the LTS setups, compromising the performance and measurements of the sensors.…”

“…Thanks to the well-developed machine vision methods for corner and line detection, the use of a carefully designed pattern is an effective approach for localizing the 2D planar target. The chessboard pattern is widely used to determine the extrinsic parameters of the camera [4], and then the laser plane can be fitted using optimization [2,5,6]. Since the accuracy of the corner detection limits the localization precision for the chessboard pattern, the camera coordinate and pixel coordinate are optimized together to solve the problem [7].…”

“…The designed 1D target has three colinear feature points and the LTS can be calibrated based on the geometry constraint of the target. In contrast to the traditional methods that rely on the precise camera intrinsic matrix [1,2,[4][5][6][7][8][9][10][11][12][13][14][15] or methods that use auxiliary devices [16][17][18][19][20], we formulate the LTS calibration as an optimization problem without the need for either of them. More precisely, many equivalent pairs of the camera intrinsic matrix and the equation of the laser plane can be solved by optimization, simultaneously.…”