SM-DTW: Stability Modulated Dynamic Time Warping for signature verification

TL;DR

The paper tackles on-line signature verification by exploiting stability within signer motor plans. It defines stability regions via stroke-level segmentation and a multiscale similarity framework to identify long, shape-consistent stroke sequences (LSSS) and their reliability across multiple references. The key contribution is SM-DTW, a weighted DTW variant where pointwise distances are modulated by stroke relevance through a sigmoid-based weight, yielding distance $d^{\text{SM}}(\overline{Q}, \overline{R}_i)$ along a warping path. Empirical results on MCYT-100 and BiosecureID-SONOF show that SM-DTW improves over baseline DTW in most settings and is competitive with state-of-the-art DTW-based methods, supporting the premise that stability regions capture subject-specific signing habits and motor plans.

Abstract

Building upon findings in computational model of handwriting learning and execution, we introduce the concept of stability to explain the difference between the actual movements performed during multiple execution of the subject's signature, and conjecture that the most stable parts of the signature should play a paramount role in evaluating the similarity between a questioned signature and the reference ones during signature verification. We then introduce the Stability Modulated Dynamic Time Warping algorithm for incorporating the stability regions, i.e. the most similar parts between two signatures, into the distance measure between a pair of signatures computed by the Dynamic Time Warping for signature verification. Experiments were conducted on two datasets largely adopted for performance evaluation. Experimental results show that the proposed algorithm improves the performance of the baseline system and compares favourably with other top performing signature verification systems.

Figures (2)

• Figure 1: (a) The search for the stability regions. In the top of the figure a set of reference signatures and a questioned signature are shown. The stability regions found between the reference $R_{3}$ and the questioned signature are coloured in green, magenta and yellow. The questioned signature is segmented in 23 strokes. Segmentation points are depicted in red. (b) The relevance of each stroke of the questioned is shown in the histogram. Two regions of the signature are strongly stable (from stroke 0 to 7 and from stroke 19 to stroke 23), whereas stroke 10 doesn't match with any stroke of the reference set. (c) On the right of the histogram, the classical DTW cost matrix is represented. In the bottom part of the image, (d) the weight matrix and (e) the SM-DTW cost matrix are reported. In the DTW and SM-DTW cost matrices is depicted in red the minimum warping path. The visual comparison between the cost matrix of DTW and SM-DTW shows that the modulation due to the stability regions filters out local similarities between points, thus favouring the emergence of the global one.
• Figure 2: (a) Values of $b$ and $c$ parameters by varying the stroke relevance. (b) Sigmoid functions used for modulating the DTW distance by varying the stroke relevance.