Calibration of Bi-prism Stereo Systems: A Model Free Approach

A simple stereo system can be constructed from a single camera using a prism in the optical path to provide the required two views of a system. The simplicity of these systems has several advantages, particularly if the target is an underwater robot, where compact size and ability to seal the optical components are key factors. However, dispersion by the prism, in addition to the lens distortion, makes calibration challenging. By using a model-free approach, we were able to calibrate a prism-based stereo system effectively. We also aimed to use readily available 45° prisms, which present significant dispersion in the system, but retain simplicity and reduce cost, compared to custom low angle prisms. Modern LEDs provide high intensity, low bandwidth light sources and we used a set of three sources, roughly centered on the RGB channels of a readily available commercial camera. Our system used a circular target pattern covering the binocularly visible region in the scene and collected sets of images at known distances, using three separate light sources. From these images, we generated two look-up tables, one for each pixel in the image and a disparity derived by matching corresponding points, Cp(u,v,du), which has three dimensions, and another look-up table, which has a single dimension, Cz(z), so are not quite large, and not beyond the memory capability of even small modern camera systems, but provide fast, O(1), lookup times, suitable for real-time systems. Our calibration strategy enables a simple stereo system built from a single camera to measure depths in a scene: the single camera requires no electronic synchronization and is built from a single, inexpensive, and readily available optical component – a right-angle prism.