Subscripto multiplex: A Riemannian symmetric positive definite strategy for offline signature verification

Abstract

The human handwritten signature is considered to be a significant biometric trait. In the case of offline signatures, the problem is addressed as an image recognition task. On the other hand, the visual representation of symmetric positive definitive matrices, usually by means of the covariance descriptor of the image feature maps, forms a specific Riemannian manifold with a widespread usage and a favorable performance in a plethora of applications. Surprisingly, no records of offline-signature-verification-oriented research in the space of symmetric positive definitive matrix have been found up to now. In this work, we propose, for the first time in offline signature-verification literature, mapping of handwritten signature images in points of the tangent space of a connected symmetric positive definitive manifold for verification purposes. Furthermore, based on the principles of differential geometry, we address the notorious limited training problem of offline signature verification in this manifold by proposing two different feature augmentation methods. The efficiency of the proposed method is evaluated using three popular datasets of Western and Asian origin. Error rates against skilled and random forgery in both baselines as well augmentation scenarios are strong indicators of the informative and highly discriminative nature of symmetric positive definitive manifold oriented representation.