Online signature verification using a new extreme points warping technique

Abstract

There are two common methodologies to verify signatures: the functional approach and the parametric approach. In this paper, we propose a new warping technique for the functional approach in signature verification. The commonly used warping technique is dynamic time warping (DTW). It was originally used in speech recognition and has been applied in the field of signature verification with some success since two decades ago. The new warping technique we propose is named as extreme points warping (EPW). It proves to be more adaptive in the field of signature verification than DTW, given the presence of the forgeries. Instead of warping the whole signal as DTW does, EPW warps a set of selected important points. With the use of EPW, the equal error rate is improved by a factor of 1.3 and the computation time is reduced by a factor of 11.

Introduction

Plamondon and Lorette (1989) categorized the various signature verification methodologies into two types: functional approach and parametric approach. In the functional approach, complete signals (x(t), y(t), v(t), etc.) directly or indirectly constitute the feature set. The two signals, one from a genuine signature and the other from a forgery, are then compared point-to-point. However in the parametric approach, only the parameters abstracted from the complete signals are compared. Though the parametric approach enjoys the advantages of algorithmic simplicity and computation speed, the task of selecting the right set of parameters is not trivial. The comparison based on the complete signals generally yields better results (Plamondon and Lorette, 1989). The two approaches may be applied in different applications, where there are distinct requirements in error rate performance, speed etc. In this paper, our research is focused on the functional approach.

In the functional approach, a straightforward way to compare two signal functions is to use a linear correlation (Plamondon and Lorette, 1989), but a direct computation of the correlation coefficient is not valid due to the following two problems:

• Difference of overall signal duration.

• Existence of non-linear distortions within signals.

For a signal function, e.g. x(t), y(t), v(t), it is unlikely that the signal duration is the same for different samples even from the same signer. In addition, for different signings, distortions occur non-linearly within the signals. To correct the distortion, a non-linear warping process needs to be performed before comparison. An established warping technique used in speech recognition is dynamic time warping, or DTW (Sankoff and Kruskal, 1983). For the past two decades, the use of DTW has also become a major technique in signature verification (Hangai et al., 2000; Nalwa, 1997). Though DTW has been applied to the field with some success, it has some drawbacks, as we will explain in details in Section 2.