Analyse de la qualité des signatures manuscrites en-ligne par la mesure d'entropie
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Source: PhD Thesis, Telecom SudParis, January 2011
Authors: Nesma HOUMANI
Abstract: This thesis is focused on the quality assessment of online signatures and its application to online signature verification systems. Our work aims at introducing new quality measures quantifying the quality of online signatures and thus establishing automatic reliability criteria for verification systems.
We proposed three quality measures involving the concept of entropy, widely used in Information Theory. We proposed a novel quality measure per person, called "Personal Entropy" calculated on a set of genuine signatures of such a person. The originality of the approach lies in the fact that the entropy of the genuine signature is computed locally, on portions of such a signature, based on local density estimation by a Hidden Markov Model. We show that our new measure includes the usual criteria of the literature, namely: signature complexity, signature variability and signature legibility. Moreover, this measure allows generating, by an unsupervised classification, 3 coherent writer categories in terms of signature variability and complexity. Confronting this measure to the performance of two widely used verification systems (HMM, DTW) on each Entropy-based category, we show that the performance degrade significantly (by a factor 2 at least) between persons of "high Entropy-based category", containing the most variable and the least complex signatures and those of "low Entropy-based category", containing the most stable and the most complex signatures.
We then proposed a novel quality measure based on the concept of relative entropy (also called Kullback-Leibler distance), denoted « Personal Relative Entropy » for quantifying person's vulnerability to attacks (good forgeries). This is an original concept and few studies in the literature are dedicated to this issue. This new measure computes, for a given writer, the Kullback-Leibler distance between the local probability distributions of his/her genuine signatures and those of his/her skilled forgeries: the higher the distance, the better the writer is protected from attacks. We show that such a measure simultaneously incorporates in a single quantity the usual criteria proposed in the literature for writer categorization, namely signature complexity, signature variability, as our Personal Entropy, but also the vulnerability criterion to skilled forgeries. This measure is more appropriate to biometric systems, because it makes a good compromise between the resulting improvement of the FAR and the corresponding degradation of FRR.
We also proposed a novel quality measure aiming at quantifying the quality of skilled forgeries, which is totally new in the literature. Such a measure is based on the extension of our former Personal Entropy measure to the framework of skilled forgeries: we exploit the statistical information of the target writer for measuring to what extent an impostor’s hand-draw sticks to the target probability density function. In this framework, the quality of a skilled forgery is quantified as the dissimilarity existing between the target writer’s own Personal Entropy and the entropy of the skilled forgery sample. Our experiments show that this measure allows an assessment of the quality of skilled forgeries of the main online signature databases available to the scientific community, and thus provides information about systems’ resistance to attacks.
Finally, we also demonstrated the interest of using our Personal Entropy measure for improving performance of online signature verification systems in real applications. We show that Personal Entropy measure can be used to: improve the enrolment process, quantify the quality degradation of signatures due to the change of platforms, select the best reference signatures, identify the outlier signatures, and quantify the relevance of times functions parameters in the context of temporal variability.