This paper presents a novel approach to representing 2-d shapes that adaptively models different portions of the shape at different resolutions, having higher resolution where it improves the quality of the representation and lower resolution elsewhere. The proposed representation is invariant to scale, translation and rotation. The representation is amenable to indexing using existing multidimensional index structures and can thus support efficient similarity retrieval. Our experiments show that the adaptive resolution technique performs significantly better compared to the fixed resolution approach previously proposed in the literature.