Report Number: CSL-TR-91-484
Institution: Stanford University, Computer Systems Laboratory
Title: Self-Consistency and Transitivity in Self-Calibration Procedures
Author: Raugh, Michael
Date: July 1991
Abstract: Self-calibration refers to the use of an uncalibrated measuring instrument and an uncalibrated object called an artifact, such as a rigid marked plate, to simultaneously measure the artifact and calibrate the instrument. Typically, the artifact is measured in more than one position, and the required information is derived from comparisons of the various measurements. The problems of self-calibration are surprisingly subtle. This paper develops concepts and vocabulary for dealing with such problems in one and two dimensions and uses simple (non-optimal) measurement procedures to reveal the underlying principles. The approach in two dimensions is mathematically constructive: procedures are described for measuring an uncalibrated artifact in several stages, involving progressive transformations of the instrument's uncalibrated coordinate system, until correct coordinates for the artifact are obtained and calibration of the instrument is achieved. Self-consistency and transitivity, as defined within, emerge as key concepts. It is shown that self-consistency and transitivity are necessary conditions for self-calibration. Consequently, in general, it is impossible to calibrate a two dimenstional measuring instrument by simply rotating and measureing a calibration plate about a fixed center.