PaperlayerView exact revision on arXiv

Source-linked AI summary

Online Signature Verification Using Augmented Path Signature and T-Mamba

Ruiling Li, Danyu Yang

arXiv:2609.08276v1cs.LGcs.CV

TL;DR

Online signature verification must handle highly variable handwriting and forgery attacks while existing models may struggle with discriminative representation and long-range dependencies. The paper combines augmented path signatures with a T-Mamba backbone that integrates local temporal convolutions and global state-space modelling. The resulting framework achieves state-of-the-art performance on three public benchmarks.

  • Problem

    Online signature verification remains challenging because signatures have substantial intra-writer variability and forgery attacks, while existing models face limitations in discriminative features and long-range dependency modelling.

  • Method

    The framework augments trajectories with timestamps and basepoints, computes sliding-window path signatures, and processes them with T-Mamba combining TCN blocks and time-scanning Mamba.

  • Results

    The framework achieves state-of-the-art performance on MCYT-100, SVC-2004 Task 2, and DeepSignDB.

  • Takeaways & Limitations

    APS provides discriminative geometric features, while T-Mamba models local and global dependencies for online signature verification across the three benchmark datasets.

Abstract

from arXiv · show

Handwritten signature verification is vital for personal authentication across commercial and financial applications. Although deep learning methods are widely adopted for online signature verification (OSV), they often struggle with capturing highly discriminative features and modelling long-range dependencies. To address these issues, we propose a novel framework that integrates the augmented path signature (APS) descriptor with the T-Mamba model. The APS descriptor first applies time and basepoint augmentations, then computes sliding-window path signatures. The path signature is a non-parametric feature map from rough path theory that effectively captures geometric structures and nonlinear inter-channel interactions. Inspired by the efficacy of state space models (SSMs) in sequence modelling, our T-Mamba model employs a hybrid design combining two temporal convolutional network (TCN) blocks with a time-scanning Mamba. This design enables the model to learn both local temporal patterns and global long-range dependencies, substantially improving verification accuracy. Our framework achieves state-of-the-art EERs on three public benchmark datasets (MCYT-100, SVC-2004 Task 2, DeepSignDB), validating its effectiveness and robustness, especially when the training data is limited. Our code is publicly available at https://github.com/DLRL04/OSV-using-APS-and-T-Mamba.

1 Introduction

Online signature verification remains difficult because signatures exhibit substantial intra-writer variability and forgery attacks, while existing models face limitations in feature discrimination, long-range modelling, or computational cost. The paper addresses these issues with APS features and T-Mamba, combining local geometric representations with local and global temporal modelling.

  • OSV is challenging because handwritten signatures show substantial intra-writer variability and are subject to skilled and random forgery attacks.
  • APS augments raw trajectories with timestamps and basepoints before computing sliding-window path signatures to capture local geometry and nonlinear inter-channel interactions.
  • TCNs with dilated convolutions capture fine-grained local patterns, while time-scanning Mamba integrates relevant information across forward and backward temporal directions with linear complexity.
  • The framework extracts APS features, feeds them into T-Mamba, trains with a soft-DTW triplet loss, and evaluates similarity with standard DTW.
  • T-Mamba combines TCN blocks with time-scanning Mamba through max pooling to balance local patterns and global contextual information.
  • The proposed framework achieves state-of-the-art performance on MCYT-100, SVC-2004 Task 2, and DeepSignDB, demonstrating effectiveness across diverse datasets and acquisition devices.

2 Related Work

Related work has progressed from alignment and handcrafted representations toward neural models for local and global sequence modelling. State-space models, particularly Mamba, offer linear-complexity long-range modelling and motivate this paper’s application to signature verification.

  • Path-signature and other robust representations address noise, writing variability, and invariance requirements in online signature verification.
  • DTW aligns signature sequences by minimizing cumulative alignment costs, while soft-DTW makes alignment differentiable for integration with deep learning.
  • CNN-based methods efficiently model local features, whereas Transformer-based architectures target global context but can incur high computational costs.
  • State-space models provide linear computational complexity while retaining long-range dependency modelling capabilities.
  • Mamba is presented as a selective state-space backbone that filters noise and retains task-relevant information in long sequences, motivating its first application to signature verification.

3 Preprocessing with Augmented Path Signature

The APS preprocessing pipeline normalizes dynamic signature features, augments trajectories with time and basepoint information, and computes truncated path signatures over sliding windows. These representations preserve temporal and geometric information while capturing nonlinear inter-channel interactions in fixed-dimensional features.

  • The pipeline selects 12 coordinate- and pressure-derived time functions and applies z-score normalization to each feature.
  • Path Augmentations: Time augmentation adds increasing timestamps, encoding writing speed and helping ensure path-signature uniqueness.
  • Path Augmentations: Basepoint augmentation adds an initial zero, encoding absolute position and removing translation invariance from path-signature features.
  • Benefits of the Path Signature: The path signature collapses temporal dimensions into fixed-dimensional representations, enabling direct comparison of variable-length time series.
  • Benefits of the Path Signature: Truncated path signatures provide geometric descriptions and encode nonlinear inter-channel interactions through iterated integrals.
  • Sliding-Window Path Signatures: APS computes path signatures over sliding windows of the augmented path to encode contextual information at each time step.

4 T-Mamba with Soft-DTW

The framework combines dilated causal TCN blocks with a bidirectional, parameter-shared time-scanning Mamba to capture local and complementary temporal context. It then aligns variable-length outputs with differentiable soft-DTW and trains them using triplet and intra-writer constraints.

  • TCN Block: The TCN block uses two residual layers of dilated causal 1D convolutions with normalization, ReLU activation, and spatial dropout.Its receptive field depends on depth m = 2, filter size k = 2, and dilation d = 2.
  • Time-Scanning Mamba: Mamba replaces fixed linear time-invariant parameters with input-dependent B, C, and ∆ to introduce selective state updates.The parameters are computed from the input through linear maps and activation functions.
  • Time-Scanning Mamba: Time-scanning Mamba addresses causal Mamba’s missing future context through parameter-shared forward and backward scans aggregated by element-wise addition.The dual scan provides complementary bidirectional context while residual paths preserve original information.
  • Soft-DTW: Soft-DTW replaces non-differentiable DTW with a smoothed minimum controlled by γ, enabling gradients to propagate across warping paths.As γ → 0, soft-DTW recovers original DTW; for γ > 0, the alignment cost is differentiable.
  • Triplet Loss: The triplet objective separates genuine and forged signatures while an intra-writer contraction term reduces variation among genuine samples.The combined constraints target compact writer-specific clusters and a discriminative embedding boundary.
  • Verification: At test time, reference-to-test DTW costs produce average and minimum scores whose sum is thresholded for genuine-versus-forgery classification.Performance is measured using writer-specific equal error rate after sweeping the threshold.

5 Experiments

Experiments evaluate APS configurations, signature truncation orders, T-Mamba efficiency, ablations, and benchmark performance across MCYT-100, SVC-2004 Task 2, and DeepSignDB. The framework performs strongly across forgery protocols, datasets, and acquisition devices.

  • Experimental setup: Experiments use MCYT-100, SVC-2004 Task 2, and DeepSignDB under skilled and random forgery protocols with varying genuine-sample counts.Enrollment uses five genuine signatures, while N ∈ {5, 10, 15} denotes genuine training samples per writer.
  • APS effectiveness: w = 9 to 13 provides the best APS performance range, with APS reaching its lowest overall EER at w = 11.The moderate window balances local temporal context against excessive smoothing or fragmentation.
  • APS effectiveness: Second-order path signatures perform best across all window sizes, whereas first-order signatures perform worst and orders above N = 2 degrade performance.The results attribute the advantage of higher-order terms to inter-channel interactions, while excessive order adds noisy details.
  • Computational efficiency: The time-scanning mechanism reduces EER from 0.87% to 0.56% compared with standard Mamba while Mamba variants reduce Transformer parameters, FLOPs, and runtime GPU memory by more than 60%.The comparison is conducted on MCYT-100 under S_05.
  • Benchmark evaluation: On MCYT-100, the framework achieves EERs of 0.56%, 0.45%, and 0.43% for S_05, S_10, and S_15, respectively, and 0.04% and 0.03% for R_05 and R_10.It achieves state-of-the-art results across the skilled-forgery protocols and competitive random-forgery results.
  • Benchmark evaluation: The method delivers best or near-best results on SVC-2004 Task 2 and outperforms or remains comparable to DsDTW across most DeepSignDB acquisition devices.On DeepSignDB Stylus, it achieves 0.76% EERglobal, a 24% relative error reduction over DsDTW.

6 Conclusion

The paper concludes that APS combined with T-Mamba provides discriminative representations and models local and global dependencies for online signature verification. The framework achieves state-of-the-art performance across three public datasets, while results on smaller datasets motivate further few-shot-learning investigation.

  • Conclusion: The proposed framework integrates APS with T-Mamba to capture complex inter-channel interactions and model local and global dependencies.T-Mamba combines TCN blocks with time-scanning Mamba to leverage past and future contexts.
  • Conclusion: The framework achieves state-of-the-art performance on MCYT-100, SVC-2004 Task 2, and DeepSignDB.The conclusion identifies DeepSignDB as the largest dynamic signature database to date.
  • Conclusion: Strong performance on smaller datasets such as e-BioSign warrants further investigation in few-shot learning.
Loading 2609.08276v1…