用黎曼几何生成签名数据，提升跨作者验证效果

Offline handwritten signature verification remains a challenging task, particularly in writer-independent settings where models must generalize across unseen individuals. Recent developments have highlighted the advantage of geometrically inspired representations, such as covariance descriptors on Riemannian manifolds. However, past or present, handcrafted or data-driven methods usually depend on real-world signature datasets for classifier training. We introduce a quasi-synthetic data generation framework leveraging the Riemannian geometry of Symmetric Positive Definite matrices (SPD). A small set of genuine samples in the SPD space is the seed to a Riemannian Gaussian Mixture which identifies Riemannian centers as synthetic writers and variances as their properties. Riemannian Gaussian sampling on each center generates positive as well as negative synthetic SPD populations. A metric learning framework utilizes pairs of similar and dissimilar SPD points, subsequently testing it over on real-world datasets. Experiments conducted on two popular signature datasets, encompassing Western and Asian writing styles, demonstrate the efficacy of the proposed approach under both intra- and cross- dataset evaluation protocols. The results indicate that our quasi-synthetic approach achieves low error rates, highlighting the potential of generating synthetic data in Riemannian spaces for writer-independent signature verification systems.