A geometry-based error estimation for cross-ratios

For choosing specific cross-ratios as 2D projective coordinates in various computer vision applications, a reasonable error analysis model is usually required. This investigation adopts the assumption of normal distribution for positioning errors of point features in an image to formulate the error variances of cross-ratios. Based on a geometry-based error analysis, a straightforward way of identifying the cross-ratios with minimum error variances is proposed. Simulation results show that the proposed approach, as well as a further simplified alternative, yield much better estimations of minimum error variances in terms of accuracy, cost, and stability compared with some other methods, e.g., the one based on the rule given by Georis et al. (IEEE Trans. Pattern Anal. Mach. Intell. 20 (4) (1998) 366). Some causes of the performance differences in the estimations are explained using a special configuration of point features.