Résumé : For automatic registration of medical images, we must search for geometric features that are invariant both with respect to rigid transformations and to smooth changes of resolution. Beginning with Witkin's seminal paper, scale space theory provides an elegant framework for studying the multiscale behavior of these characteristics. However, a natural scale-space representation of features, useful for practical applications, is still missing. We address here the problem of multiscale extraction and representation of characteristic points based on iso-surface techniques. Our main concern is with $2D$ images: we analyze corner points at increasing scales using the Marching Lines algorithm. Since we can exploit the intrinsic nature of intensity of medical images, segmentation of components or parameterization of curves is not needed, in contrast with other methods. Due to the direct use of the coordinates of points, we get a representation of orbits, which is very convenient both for detection at coarse scale and for localization at fine scale. We find that the significance of \corner\ depends not only on their scale-space lifetime but also on their relationship with curvature inflexion points.