Error analysis of robust optical flow estimation by least median of squares methods for the varying illumination model

The apparent pixel motion in an image sequence, called optical flow, is a useful primitive for automatic scene analysis and various other applications of computer vision. In general, however, the optical flow estimation suffers from two significant problems: the problem of illumination that varies with time and the problem of motion discontinuities induced by objects moving with respect to either other objects or with respect to the background. Various integrated approaches for solving these two problems simultaneously have been proposed. Of these, those that are based on the LMedS (least median of squares) appear to be the most robust. The goal of this paper is to carry out an error analysis of two different LMedS-based approaches, one based on the standard LMedS regression and the other using a modification thereof as proposed by us recently. While it is to be expected that the estimation accuracy of any approach would decrease with increasing levels of noise, for LMedS-like methods, it is not always clear as to how much of that decrease in performance can be attributed to the fact that only a small number of randomly selected samples is used for forming temporary solutions. To answer this question, our study here includes a baseline implementation in which all of the image data is used for forming motion estimates. We then compare the estimation errors of the two LMedS-based methods with the baseline implementation. Our error analysis demonstrates that, for the case of Gaussian noise, our modified LMedS approach yields better estimates at moderate levels of noise, but is outperformed by the standard LMedS method as the level of noise increases. For the case of salt-and-pepper noise, the modified LMedS method consistently performs better than the standard LMedS method.