Using vision to measure world distances requires that both measurements and their uncertainties can be determined and modelled. The work described in this report develops the theory of computing distances using only images and an uncertainty analysis which includes both the errors in image localisation and the uncertainty in the imaging transformation. We present different methods of estimating the geometry of the imaging transformation between world and camera plane using image to world point correspondences. A general expression is then derived for the uncertainties in the measurements. We mainly focus our attention on computing measures and related uncertainties on world planes and then we extend these results to a complete 3D reconstruction of the scene. While the research presented here is of a general nature a particular application is presented showing how to use the results obtained to build a plane measuring device. This device finds its application in several commercial and industrial fields.
|Institution||Department of Engineering Science, University of Oxford|