Non-linear rotation of signature patterns is one of the major difficulties to solve in off-line signature verification. This paper presents two models utilizing rotation invariant structure features to tackle the problem. In principle, the elaborately extracted ring-peripheral features are able to describe internal and external structure changes of signatures periodically. In order to evaluate match score quantitatively, discrete fast fourier transform is employed to eliminate phase shift and verification is conducted based on a distance model. In addition, the ring-hidden Markov model (HMM) is constructed to directly evaluate similar between test signature and training samples. With respect to the side effect of outlier training samples for stable statistical model and threshold estimation, we propose a selection strategy to improve the performance of system. Experimental results demonstrated that the proposed methods were effective to improve verification accuracy. © 2008 Elsevier Ltd. All rights reserved.