Model fitting with sufficient random sample coverage

It has been observed previously that the number of iterations required to derive good model parameter values used by RANSAC-like model estimators is too optimistic. We present the derivation of an analytical formula that allows the calculation of the sufficient limit of iterations needed to obtain good parameter values with the prescribed probability for any number of model parameters. It explains the values that had been found experimentally for certain numbers of model parameters by others very well. Furthermore, the improvement that our approach of SUfficient Random SAmple Coverage (SURSAC) offers, in comparison to the original RANSAC algorithm as well as to its adaptive modification by Hartley and Zisserman, is demonstrated with synthetic data for the case of a non-linear model function over a wide range of outlier fractions and different ratios of inlier and outlier densities.