Abstract

While handwritten signatures are a staple of biometric authentication, conventional verification models typically rely on Euclidean space assumptions, restricting the capture of complex, intrinsic signature structures. To address this, offline signature verification has increasingly modeled signatures as points on the Symmetric Positive Definite (SPD) manifold. Nevertheless, selecting an appropriate metric on this manifold for a given problem remains a significant challenge, typically relying on heuristic trial-and-error processes. To solve this, our primary contribution is a novel, end-to-end Riemannian framework featuring the Collective Background Knowledge (CBK) mechanism. CBK establishes synthetic writers as Riemannian centers, utilizing a learnable αβ-Log-Determinant divergence to adaptively discover the optimal local geometry from data. Instead of computing the direct distance between two SPD signature representations, we evaluate them relationally by measuring how each signature diverges from the shared CBK reference centers. These individual deviations form unique relational profiles for each signature, which are then compared using the dichotomy transform to create a dissimilarity vector. By jointly optimizing the CBK parameters under an SPD metric-learning approach, our model separates effectively similar and dissimilar pairs of signatures. Evaluated across five datasets under challenging blind intra- and cross-lingual conditions, our geometry-aware framework demonstrates robust generalization and competitive performance.

IPC Classification

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