We consider the problem of improving contour detection by filling gaps between collinear contour pieces. A fast algorithm is proposed which takes into account local edge orientation and local curvature. Each edge point is replaced by a curved elongated patch, whose orientation and curvature match the local edge orientation and edge. The proposed contour completion algorithm is integrated in a multiresolution framework for contour detection. Experimental results show the superiority of the proposed method to other well-established approaches.