The beneficial properties of the Radon transform make it an useful intermediate representation for the extraction of invariant features from pattern images for the purpose of indexing/matching. This paper revisits the problem with a generic view on a popular Radon-based pattern descriptor, the R-signature, bringing in a class of descriptors spatially describing patterns at all the directions and at different levels. The domain of this class and the selection of its representative are also discussed. Theoretical arguments validate the robustness of the generic R-signature to additive noise and experimental results show its effectiveness.