Characterizing the uncertainty of the fundamental matrix

This paper deals with the analysis of the uncertainty of the fundamental matrix. The basic idea is to compute the fundamental matrix and its uncertainty at the same time. We give two different methods. The first one is a statistical approach. As in all statistical methods the precision of the results depends on the number of analyzed samples. This means that we can always improve our results if we increase the number of samples but this process is very time consuming. Alternatively, we propose a much simpler method which gives analytical results which are close to the results of the statistical method. Experiments with synthetic and real data have been conducted to validate the proposed methods. At the end of the paper, we provide three applications of the estimated uncertainty of the fundamental matrix: definition of the epipolar band for stereo matching, projective reconstruction, and self-calibration. (C) 1997 Academic Press.