A framework for uncertainty propagation in 3D shape measurement using laser triangulation

Abstract

The analysis of measurement uncertainty is necessary in every measurement process. In this paper, we suggest an approach to categorize and model the dominant sources of uncertainty and study the probabilistic propagation of the uncertainties in a 3D inspection using laser line scanners. To each point of the measurement point cloud, we associate a covariance matrix describing the corresponding dispersion ellipsoid in the 3D space. The uncertainties can be analyzed for each desired laser and camera constellation and thus, the method can be applied in designing and optimizing laser scanner setups, reducing the effort of manually evaluating the setup in a trial and error approach. As a demonstration, the inspection of a cylinder head has been simulated using computer graphics and the estimated uncertainty metrics are visualized on the measured surface

Stereovision‐based initial pose estimation relative to non‐cooperative space target

“…The measurement error based on the binocular vision system has a direct effect on the relative parameters’ estimation. So, some effective guidance and theoretical analysis have been proposed to improve measurement accuracy [15–24]. However, these works mainly focus on investigating the factors about how to affect the precision of 3D coordinate accuracy and methods on how to improve the calculation precision.…”

Performance Characterization in Automated Optical Inspection using CAD Models and Graphical Simulations

“…The 3D measurement is achieved by solving a system of linear equations, in which two of the constraints are determined by the 2D camera projection and the third constraint is provided by the laser plane equation. A detailed mathematical derivation of the 3D measurement is discussed in our previous work [9] . Figure 1 illustrates the schematic of the setup and the main geometrical degrees of freedom that we have considered for the simulation and setup evaluation.…”

“…The measurement uncertainty metric indicates the dispersion of the measurement value around the nominal value due to the limited precision of the measurement. The estimation of the measurement uncertainty is primarily based on applying our previous work [9] on the simulated point cloud, where we have proposed an uncertainty propagation framework to model different sources of uncertainty in the measurement process with appropriate random variables, estimate the standard deviation of the random variables in the setup, and propose a probabilistic method to propagate them through the measurement. The uncertainties that are modeled belong to three different groups: laser detection uncertainties on the image, geometrical positioning uncertainties of the camera and the laser, and the camera optical calibration uncertainties.…”

“…For modeling the sources of uncertainty, we have considered a 0.2 𝑝𝑥 standard deviation for the laser peak detection on the image, a 0.5 𝑚𝑚 standard deviation for the positioning of the laser and the camera which is a typical value for the repeatability of industrial robots (neglecting rotational uncertainties), 1 𝑝𝑥 standard deviation for the focal length (pixel unit based on the ratio of the sensor size and pixel numbers), and a 0.5 𝑝𝑥 standard deviation in estimating the projection center of the camera based on a pinhole camera model [12]. The uncertainties are then analytically propagated based on a second order approximation, as described in [9], and each point is associated with a 3×3 covariance matrix which corresponds to an ellipsoid in the 3D space. We have further analyzed the ellipsoids and computed the variance along the direction with the largest spread, which indicates the direction with the largest uncertainty.…”

“…Cajal et al [8] follow a similar intention to simulate a laser triangulation setup where they also account for some sources of uncertainty and propagate them using a Monte-Carlo numerical sampling. Such a method for uncertainty propagation is not suitable for the current application since the sampling procedure needs to be repeated for each 3D measured point and in each setup configuration [9]. In this paper, we apply an analytical second-order uncertainty propagation which is computationally very efficient.…”