In this paper we present a new physically motivated curve/region descriptor based on the solution of Helmholtz's equation. The descriptor we propose satisfies the six principles set by MPEG-7: it has a good retrieval accuracy, it is compact, it can be applied in general contests, it has a reasonable computational complexity, it is rotation and scale invariant and provides an hierarchical representation of the curve from coarse to fine. In addition to these properties, the descriptor can be generalized in order to take into account also the intensity content of the image region defined by the curve. The construction of the descriptor can be coupled with a preprocessing step that enables us to describe a curve in an affine invariant fashion. The performance of our approach has been tested in the contest of affine invariant curve and region matching, both within a controlled experimental setup and also using real images. The experiments show that the proposed approach compares favorably to the state of the art curve/region descriptors.