In this paper we present a method for motion segmentation, in which accurate grouping of pixels undergoing the same motion is targeted. In the presented technique true object edges are first obtained by combining anisotropic diffusion of the original image with edge detection and contour reconstruction in the inherent scale-space. Contours are then matched according to the distance given by a metric defined on their polygonal approximations and the shape of the one-dimensional intensity function along the contour. Masks of objects are obtained by merging image areas inside of edges having the same motion. The performance of the presented technique has been evaluated by computer simulations.