Quasi-Synthetic Riemannian Data Generation for Writer-Independent Offline Signature Verification

2025-09-24

AI Summary

Offline handwritten signature verification faces dual challenges in writer-independent scenarios: poor cross-subject generalization and scarcity of authentic labeled data. To address these, we propose the first Riemannian geometry-based quasi-synthetic data generation framework. Specifically, we construct a Riemannian Gaussian mixture model on the symmetric positive-definite (SPD) matrix manifold to explicitly capture the intrinsic geometric distribution of genuine signatures, and perform Riemannian sampling to generate semantically plausible, class-controllable (genuine/forgery) synthetic signature samples. Our method requires minimal authentic signature annotations and—uniquely—enables discriminative synthetic data generation directly within the Riemannian space. Experiments across diverse Eastern and Western multi-source signature datasets demonstrate substantially improved cross-domain generalization: our approach achieves consistently low error rates and high stability under cross-dataset evaluation, validating its effectiveness and broad applicability.

Technology Category

• Machine Learning: Learning with Manifolds
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Computer Vision: Computational Photography, Image & Video Synthesis

Application Category

• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Web Mining and Content Analysis: Web data provenance, reliability, and authenticity
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs

Abstract

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.

Problem

• Addressing writer-independent offline signature verification generalization challenges
• Generating quasi-synthetic data using Riemannian geometry for SPD matrices
• Reducing dependency on real-world datasets through synthetic population creation

Innovation

• Quasi-synthetic data generation using Riemannian Gaussian Mixture
• Leveraging SPD matrix geometry for synthetic writer creation
• Metric learning framework with synthetic positive and negative pairs