Optimal calibration of a prism-based videoendoscopic system for precise 3D measurements

Modern videoendoscopes are capable of performing precise three-dimensional (3D) measurements of hard-to-reach elements. An attachable prism-based stereo adapter allows one to register images from two different viewpoints using a single sensor and apply stereoscopic methods. The key condition for achieving high measurement accuracy is the optimal choice of a mathematical model for calibration and 3D reconstruction procedures. In this paper, the conventional pinhole camera models with polynomial distortion approximation were analyzed and compared to the ray tracing model based on the vector form of Snell’s law. We, first, conducted a series of experiments using an industrial videoendoscope and utilized the criteria based on the measurement error of a segment length to evaluate the mathematical models considered. The experimental results confirmed a theoretical conclusion that the ray tracing model outperforms the pinhole models in a wide range of working distances. The results may be useful for the development of new stereoscopic measurement tools and algorithms for remote visual inspection in industrial and medical applications.