Estimation of the geometrical measurement error at the stage of stereoscopic system design

Abstract

The article is dedicated to the error estimation method for stereoscopic systems measuring three-dimensional coordinates and geometric parameters of objects. This method is required for stereoscopic system design to optimize the parameters of the image acquisition system and the data processing algorithms. The technique should be suitable for different mathematical models of image acquisition systems and allow to access the measurement uncertainty with a known uncertainty in determining the coordinates of the corresponding points on the images and the uncertainty of the calibration parameters. We analyzed known methods by comparing their results with the Monte Carlo simulation for the pinhole and the ray tracing models. It is shown that the method using the unscented transformation provides better accuracy and versatility than the linearization method. Using the example of measuring the length of a segment, it is demonstrated that the use of a symmetric confidence interval constructed from the mean and variance can lead to an inaccurate estimation of the error in measuring geometric parameters. We propose a method for calculating confidence intervals based on a combination of unscented transformation and interval analysis and confirm its effectiveness by the computer simulation. The analysis is applicable to the design of both passive stereoscopic devices and active triangulation systems as well as improving their software.