THE DEVELOPMENT AND COMPARISON OF ROBUST METHODS FOR ESTIMATING THE FUNDAMENTAL MATRIX

This paper has two goals. The first is to develop a variety of robust methods for the computation of the Fundamental Matrix, the calibration -free representation of camera motion. The methods are drawn from the principal categories of robust estimators, viz. case deletion diagnost ics, M-estimators and random sampling, and the paper develops the theo ry required to apply them to non-linear orthogonal regression problems . Although a considerable amount of interest has focussed on the appli cation of robust estimation in computer vision, the relative merits of the many individual methods are unknown, leaving the potential practi tioner to guess at their value. The second goal is therefore to compar e and judge the methods. Comparative tests are carried out using corre spondences generated both synthetically in a statistically controlled fashion and from feature matching in real imagery. In contrast with pr eviously reported methods the goodness of fit to the synthetic observa tions is judged not in terms of the fit to the observations per se but in terms of fit to the found truth. A variety of error measures are e xamined. The experiments allow a statistically satisfying and quasi-op timal method to be synthesized, which is shown to be stable with up to 50 percent outlier contamination, and may still be used if there are more than 50 percent outliers. Performance bounds are established for the method, and a variety of robust methods to estimate the standard d eviation of the error and covariance matrix of the parameters are exam ined. The results of the comparison have broad applicability to vision algorithms where the input data are corrupted not only by noise but a lso by gross outliers.