This paper presents a differential optical flow method which accounts for two typical motion-estimation problems : (1) flow regularization within regions of uniform motion while (2) preserving sharp edges near motion discontinuities i.e., where motion is multimodal by nature. The method proposed is a modified version of the well known Lucas Kanade (LK) algorithm. Based on documented assumptions, our method computes motion with a classical leastsquare fit on a local neighborhood shifted away from where motion is likely to be multimodal. This edge-avoidance procedure is based on the non-parametric mean-shift algorithm which shifts the LK integration window away from local sharp edges. Our method also locally regularizes motion by performing a fusion of local motion estimates. Our method is compared with other edge-preserving methods on image sequences representing different challenges.