In this study, a scale-invariant representation for closed planar curves (silhouettes) is proposed. The orientations of all points within the Gaussian scale-space of the curve are extracted. This orientation scale-space is used to create the silhouette orientation image in which the positions of each pixel indicate the curve's pixel positions and scales, whereas the colour represents orientation. The representation is extracted for multiple levels of the morphological scale-space of the silhouette. The proposed representation is invariant to scale and transformable under planar rotation. Using linear and non-linear distance learning methods, experiments on the MPEG7, ETH80 and Kimia shape datasets were conducted, with results indicating an advanced recognition capability.