Legendre polynomials based feature extraction for online signature verification. Consistency analysis of feature combinations

• A feature extraction approach based on Legendre series representation of the time functions associated with the signatures is proposed.
• A consistency factor is proposed to quantify the discriminative power of different combinations of the time functions.
• The correlation between the proposed consistency factor and the verification performance of a feature combination is analyzed.
• A recent signature database, containing Western and Chinese signatures is used. The verification performance is quantified based on log-likelihood ratios.

In this paper, feature combinations associated with the most commonly used time functions related to the signing process are analyzed, in order to provide some insight on their actual discriminative power for online signature verification. A consistency factor is defined to quantify the discriminative power of these different feature combinations. A fixed-length representation of the time functions associated with the signatures, based on Legendre polynomials series expansions, is proposed. The expansion coefficients in these series are used as features to model the signatures. Two different signature styles, namely, Western and Chinese, from a publicly available Signature Database are considered to evaluate the performance of the verification system. Two state-of-the-art classifiers, namely, Support Vector Machines and Random Forests are used in the verification experiments. Error rates comparable to the ones reported over the same signature datasets in a recent Signature Verification Competition, show the potential of the proposed approach. The experimental results, also show that there is a good correlation between the consistency factor and the verification errors, suggesting that consistency values could be used to select the optimal feature combination.