A. Criminisi, I. Reid, A. Zisserman
Department of Engineering Science, University of Oxford,
Parks Road, Oxford, UK
E-mail: criminis@robots.ox.ac.uk
A visual measurement device for planes requires that both measurements and their uncertainties can be determined. This paper develops an uncertainty analysis which includes both the errors in image localisation and the uncertainty in the imaging transformation.
The matrix representing the imaging transformation is estimated from image to world point correspondences. A general expression is derived for the covariance of this matrix. The covariance expression is valid if the matrix is over determined and also if the minimum number of correspondences are used. A bound on the errors of the first order approximations involved is also derived.
Armed with this covariance result the uncertainty of any measurement can be predicted, and furthermore the distribution of correspondences can be chosen to achieve a particular bound on the uncertainty.
Examples are given of measurements such as distance and parallelism for several applications. These include indoor scenes and architectural measurements.
Keywords: Video Metrology, Error Analysis, Projective Geometry.
Antonio Criminisi