THEORETICAL ADVANCES Bin Li Æ David Zhang Æ Kuanquan Wang Online signature verification based on null component analysis and principal component analysis Received: 31 January 2005 / Accepted: 4 September 2005 / Published online: 24 November 2005 Ó Springer-Verlag London Limited 2005 Abstract This paper describes a method for stroke-based online signature verification using null component analysis (NCA) and principal component analysis (PCA). After the segmentation and flexible matching of the signature, we extract stable segments from each reference signature in order that the segment sequences have the same length. The reference set of feature vectors are transformed and separated into null components (NCs) and principal components (PCs) by K-L trans- form. Online signature verification is a special two-cat- egory classification problem and there is not a single available forgery set in an actual system. Therefore, it is different from the typical application of PCA in pattern recognition that both NCA and PCA are used to respectively analyze stable and unstable components of genuine reference set. Experiments on a data set con- taining a total 1,410 signatures of 94 signers show that the NCA/PCA-based online signature verification method can achieve better results. The best result yields an equal error rate of 1.9%. Keywords NCA Æ PCA Æ K-L transform Æ Signature verification Æ Stable segment extraction 1 Introduction E-transactions involving legal or financial documents require a highly secure, reliable, and legally acceptable way to approve or authenticate contents or authorship. Some personal devices such as pocket PC and tablet PC also require a high secure access authentication which can replace the conventional password to resist the invasion of privacy well. Along with the development of computer science and technology, biometrics is an active topic in the research of secure authentication. Of the many possible biometrics schemes, online signature verification is a strong candidate for technology, since handwriting is a skill that is personal to individuals and a handwritten signature is commonly used to authenti- cate the contents of a document or a financial transac- tion. Especially, online signature verification can provide a new secure access authentication for pocket PC and tablet PC without any additional devices. With many people engaged in research on online signature verifi- cation, the results have been a wide range of reported methods. The methods of online signature verification can be generally classified into two categories: function-based and parameter-based [1]. In the function-based method, a signature is usually taken as some time-dependent function and each original point (or resample point) of the signature is used for verification [1–4]. Many meth- ods of online signature verification in literature are parameter-based [5–12]. In parameter-based method, the enrollment data size and computation is very small; the privacy problems of the users are also considered, since only parameters are enrolled and original signature cannot be constructed [12]. Rhee et al. extract segments by Brault’s method [5], present 11 features to define a segment and use dynamic time warping (DTW) algo- rithm and Euclidean distance for verification [9]. Qu et al. distinguish strokes from a signature by the point which is decreased in pressure or velocity etc. They introduce a definition of the significant stoke into veri- fication to denote the stable component in references [10, 11]. Lee et al. [12] propose an approach for segmenting a signature by geometric extrema. They achieve segment- to-segment correspondence by DTW algorithm and take a BP neural network as the classifier. Online signature verification is a special two-category classification problem. Only genuine signature references B. Li Æ K. Wang Department of Computer Science and Technology, Harbin Institute of Technology, Harbin, China D. Zhang (&) Biometrics Research Centre, Department of Computing, The Hong Kong Polytechnic University, Hung Hum Kowloon, Hong Kong E-mail: csdzhang@comp.polyu.edu.hk Tel.: +852-2766-7271 Fax: +852-2774-0842 Pattern Anal Applic (2006) 8: 345–356 DOI 10.1007/s10044-005-0016-4