Handwritten Online Signature Verification and Forgery Detection Using Hybrid Wavelet Transform-2 with HMM Classifier

Abstract

Online signature verification stands out as a distinctive biometric feature, offering both static and dynamic attributes within 2D signature images. A Hybrid Wavelet Transform-2 (HWT-2) with a size of 256 is constructed by employing the Kronecker product of two orthogonal transforms: DCT, DHT, Haar, Hadamard, and Kekre, each with sizes of 4 and 64. The HWT enables the analysis of signals at both global and local levels, akin to wavelet transforms. HWT-2 is applied to 256 samples of online handwritten signatures, and the first 128 samples of the output are utilized as feature vectors for the verification and forgery detection of online handwritten signatures. These feature vectors are inputted into Left-Right and Ergodic Hidden Markov Model (HMM) classifiers for analysis. The HMMs are trained using 10 randomly selected genuine signature samples, and subsequently tested on the remaining 10 genuine signatures and 20 forged signatures from 40 users of the SVC 2004 signature database. This process is repeated 20 times, and the average values are computed. Among all possible combinations of HWT-2 using DCT, DHT, Haar, Hadamard, and Kekre transforms for the Left-Right HMM model, the combination of DCT 4 and DHT 64 demonstrates the best performance, with False Rejection Rate (FRR) and False Acceptance Rate (FAR) values of 3.96% and 1.48%, respectively, for state 5. Similarly, for the Ergodic HMM model, the combination of DCT 4 and DHT 64 exhibits the best performance, with FRR and FAR values of 1.10% and 2.88%, respectively, for state 5. These results indicate that combinations of HWT-2 outperform individual orthogonal transforms, and further, that HWT-2 combinations within the Ergodic HMM model offer superior performance compared to the Left-Right HMM model.