1 Ă 1 Wavelet–based Off–line Signature Verification Peter Shaohua Deng , Hong–Yuan Mark Liao , Chin Wen Ho , and Hsiao–Rong Tyan Institute of Computer Science and Information Engineering, National Central University , Chung–Li, Taoyuan, Taiwan Institute of Computer Science and Information Engineering, Chung Y uan Christian University , Chung–Li, Taoyuan, Taiwan Institute of Information Science, Academia, Sinica, Nankang, Taipei, Taiwan Ă : [ Ă ]Ą2 [ Ă [ Ă ] Ă : In this paper, a wavelet–based off–line signature verification system is proposed. The proposed sys - tem can automatically identify useful and common features which consistently exist within different sig- natures of the same person and, based on these features, verify whether a signature is a for gery or not. The system starts with a closed–contour tracing algorithm. The curvature data of the traced closed contours are decomposed into multiresolutional signals using wavelet transforms. Then the zero–crossings correspond - ing to the curvature data are extracted as features for matching. Moreover , a statistical measurement is de- vised to decide systematically which closed contours and their associated frequency data of a writer are most stable and discriminating. Based on these data, the optimal threshold value which controls the accura- cy of the feature extraction process is calculated. The proposed approach can be applied to both on–line and off–line signature verification systems. Experimental results show that the average success rates for En - glish signatures and Chinese signatures are 91.71% and 93%, respectively. Ă 2 To whom correspondence should be addressed. E–mail: liao@iis.sinica.edu.tw This work was partially supported by the National Science Council of Taiwan under grant NSC86–2745–E–001–004. Ă 1