Errors-in-variables modeling in optical flow estimation

Gradient-based optical flow estimation methods typically do not take into a ccount errors in the spatial derivative estimates. The presence of these er rors causes an errors-in-variables (EIV) problem. Moreover, the use of fini te difference methods to calculate these derivatives ensures that the error s are strongly correlated between pixels. Total least squares (TLS) has oft en been used to address this EIV problem. However, its application in this context is flawed as TLS implicitly assumes that the errors between neighbo rhood pixels are independent. In this paper, a new optical flow estimation method (EIVM) is formulated to properly treat the EIV problem in optical no w. EIVM is based on Sprent's procedure which allows the incorporation of a general EIV model in the estimation process. In EIVM, the neighborhood size acts as a smoothing parameter. Due to the we ights in the EIVM objective function, the effect of changing the neighborho od size is more complex than in other local model methods such as Lucas and Kanade (LK). These weights, which are functions of the flow estimate, can alter the effective size and orientation of the neighborhood. In this paper , we also present a data-driven method for choosing the neighborhood size b ased on Stein's unbiased risk estimators (SURE).