This paper is concerned with the problem of computing normal displacements along contours in image sequences. Our estimation is restricted to the perpendicular-to-the-edge velocity component, since the well-known "aperture problem" restricts any local estimation to this only component. We model moving edges as spatio-temporal surface patches in the image sequence space (x, y, t). A statistical regularization scheme based on Markov random fields allows us to get a homogeneous and relevant normal motion field along contours. It turns out that it can be implemented in an efficient way, mostly leading to convolution-like computations. Subpixel accuracy comes straightforwardly with this modeling, and is handled within the optimization stage itself, not as a post-processing step. Results are presented concerning synthetic experiments and real-world sequences.