Identifying the existence or approval of a human in a number of past, recent and present day activities with the use of a handwritten signature is a captivating biometric challenge. Several engineering branches such as computer vision, pattern recognition and quite recently data-driven machine learning algorithms are combined in a multi-disciplined signature verification framework in order to deliver an equivalent and efficient e-assistance to manually executed duties, which usually demand knowledge and skills. In this work, we propose, for the first time, the use of a learnable Symmetric Positive Definite manifold distance framework in offline signature verification literature in order to build a global writer-independent signature verification classifier. The key building block of the framework relies on the use of regional covariance matrices of handwritten signature images as visual descriptors, which maps them into the Symmetric Positive Definite manifold. The learning and verification protocol explores both blind intra and blind inter transfer learning frameworks with the use of four popular signature datasets of Western and Asian origin. Experiments strongly indicate that the learnable SPD manifold similarity distance can be highly efficient for offline writer independent signature verification.

In spite of the overwhelming high-tech marvels and applications that rule our digital lives, the use of the handwritten signature is still recognized worldwide in government, personal and legal entities to be the most important behavioral biometric trait. A number of notable research approaches provide advanced results up to a certain point which allow us to assert with confidence that the performance attained by signature verification (SV) systems is comparable to those provided by any other biometric modality. Up to now, the mainstream trend for offline SV is shared between standard -or handcrafted- feature extraction methods and popular machine learning techniques, with typical examples ranging from sparse representation to Deep Learning. Recent progress in graph mining algorithms provide us with the prospect to re-evaluate the opportunity of utilizing graph representations by exploring corresponding graph features for offline SV. In this paper, inspired by the recent use of image visibility graphs for mapping images into networks, we introduce for the first time in offline SV literature their use as a parameter free, agnostic representation for exploring global as well as local information. Global properties of the sparsely located content of the shape of the signature image are encoded with topological information of the whole graph. In addition, local pixel patches are encoded by sequential visibility motifs-subgraphs of size four, to a low six dimensional motif profile vector. A number of pooling functions operate on the motif codes in a spatial pyramid context in order to create the final feature vector. The effectiveness of the proposed method is evaluated with the use of two popular datasets. The local visibility graph features are considered to be highly informative for SV; this is sustained by the corresponding results which are at least comparable with other classic state-of-the-art approaches.