Efficient on-line signature recognition based on multi-section vector quantization

Abstract

This paper proposes a multi-section vector quantization approach for on-line signature recognition. We have used a database of 330 users which includes 25 skilled forgeries performed by 5 different impostors. This database is larger than those typically used in the literature. Nevertheless, we also provide results from the SVC database. Our proposed system obtains similar results as the state-of-the-art online signature recognition algorithm, Dynamic Time Warping, with a reduced computational requirement, around 47 times lower. In addition, our system improves the database storage requirements due to vector compression, and is more privacy-friendly because it is not possible to recover the original signature using the codebooks. Experimental results reveal that our proposed multi-section vector quantization achieves a 98% identification rate, minimum Detection Cost Function value equal to 2.29% for random forgeries and 7.75% for skilled forgeries.

Appendices

Appendix 1: DTW algorithm

To find the optimal path to (i _k , j _k ) we simply take the minimum over all distance predecessors:

$$D_{{\min }} \left( {i_{k} ,j_{k} } \right) = \begin{array}{l} {\min } \\ {\left( {i_{{k - p}} ,j_{{k - p}} } \right)} \\ \end{array} \left\{ {D_{{\min }} \left[ {\left. {\left( {i_{k} ,j_{k} } \right)} \right|\left( {i_{{k - p}} ,j_{{k - p}} } \right)} \right]} \right\} $$

(1)

The simplest case corresponds to three predecessors.

The distance between a reference signature and a candidate’s signature can be computed using the following algorithm:

Best path has cost:

$$ \tilde{D} = \min \left\{ \begin{gathered} {{D_{{\min }} \left( {I,j} \right)} \mathord{\left/ {\vphantom {{D_{{\min }} \left( {I,j} \right)} {I,\quad j = J - \varepsilon , \ldots ,J}}} \right. \kern-\nulldelimiterspace} {I,\quad j = J - \varepsilon , \ldots ,J}} \hfill \\ {{D_{{\min }} \left( {i,J} \right)} \mathord{\left/ {\vphantom {{D_{{\min }} \left( {i,J} \right)} I}} \right. \kern-\nulldelimiterspace} I},\quad i = I - \varepsilon , \ldots ,I \hfill \\ \end{gathered} \right. $$

This notation is consistent with those provided in (Deller et al. 3). A complete explanation of this dynamic programming technique is beyond the scope of this paper.

Appendix 2: VQ algorithm

Given a distance measure between vectors i and j, such as, for instance, the euclidean distance:

$$ D\left( {i,j} \right) = \left\| {i - j} \right\|_{2} $$

The distance between a codebook and a candidate’s signature can be computed using the following algorithm:

Best match has cost $\tilde{D}$