The generalization of the R-transform for invariant pattern representation

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 of Radon image utilization with a generic view on a popular Radon transform-based transform and pattern descriptor, the R-transform and R-signature, bringing in a class of transforms and descriptors spatially describing patterns at all directions and at different levels, while maintaining the beneficial properties of the conventional R-transform and R-signature. The domain of this class, which is delimited due to the existence of singularities and the effect of sampling/quantization and additive noise, is examined. Moreover, the ability of the generic R-transform to encode the dominant directions of pattern is also discussed, adding to the robustness to additive noise of the generic R-signature. The stability of dominant direction encoding by the generic R-transform and the superiority of the generic R-signature over existing invariant pattern descriptors on grayscale and binary noisy datasets have been confirmed by experiments.