[Paper Review] Hyperbolic Face Anti-Spoofing

Shuangpeng Han, Rizhao Cai+4 more|arXiv (Cornell University)|Aug 17, 2023

Biometric Identification and SecurityComputer Science3 citations

TL;DR

This paper proposes a hyperbolic face anti-spoofing framework that leverages the hierarchical nature of spoofing attacks by projecting features into Poincaré ball space, improving generalization to unseen attack types. It introduces hyperbolic contrastive learning, a novel feature clipping method to stabilize training, and a multimodal fusion strategy using Euclidean decomposition and hyperbolic fusion, achieving state-of-the-art performance across seven benchmark datasets.

ABSTRACT

Learning generalized face anti-spoofing (FAS) models against presentation attacks is essential for the security of face recognition systems. Previous FAS methods usually encourage models to extract discriminative features, of which the distances within the same class (bonafide or attack) are pushed close while those between bonafide and attack are pulled away. However, these methods are designed based on Euclidean distance, which lacks generalization ability for unseen attack detection due to poor hierarchy embedding ability. According to the evidence that different spoofing attacks are intrinsically hierarchical, we propose to learn richer hierarchical and discriminative spoofing cues in hyperbolic space. Specifically, for unimodal FAS learning, the feature embeddings are projected into the Poincaré ball, and then the hyperbolic binary logistic regression layer is cascaded for classification. To further improve generalization, we conduct hyperbolic contrastive learning for the bonafide only while relaxing the constraints on diverse spoofing attacks. To alleviate the vanishing gradient problem in hyperbolic space, a new feature clipping method is proposed to enhance the training stability of hyperbolic models. Besides, we further design a multimodal FAS framework with Euclidean multimodal feature decomposition and hyperbolic multimodal feature fusion & classification. Extensive experiments on three benchmark datasets (i.e., WMCA, PADISI-Face, and SiW-M) with diverse attack types demonstrate that the proposed method can bring significant improvement compared to the Euclidean baselines on unseen attack detection. In addition, the proposed framework is also generalized well on four benchmark datasets (i.e., MSU-MFSD, IDIAP REPLAY-ATTACK, CASIA-FASD, and OULU-NPU) with a limited number of attack types.

Motivation & Objective

• Address the challenge of generalizing face anti-spoofing models to unseen spoofing attack types, especially with diverse and evolving attack forms.
• Overcome the limitations of Euclidean space in modeling hierarchical relationships among spoofing attacks, which are inherently structured across shape, material, and coverage.
• Improve model robustness and generalization in cross-dataset and zero-shot settings by exploiting the intrinsic hierarchical topology of spoofing data.
• Develop a stable and effective training framework for hyperbolic neural networks, particularly addressing the vanishing gradient problem in hyperbolic space.
• Design a multimodal FAS framework that combines Euclidean feature decomposition with hyperbolic fusion and classification for enhanced performance.

Proposed method

• Project unimodal face features into the Poincaré ball using a hyperbolic neural network to exploit hierarchical structure in spoofing attacks.
• Introduce a hyperbolic binary logistic regression layer for classification after hyperbolic feature projection.
• Propose a hyperbolic contrastive learning loss that encourages close clustering of bonafide samples while relaxing constraints on diverse attack types to improve generalization.
• Develop a novel feature clipping method to mitigate vanishing gradients in hyperbolic space, enhancing training stability.
• Design a multimodal FAS framework with Euclidean-based feature decomposition and hyperbolic-based feature fusion and classification, using complex hyperbolic concatenation.
• Integrate multiple loss functions: discriminative loss ($\mathcal{L}^{Dis}$), hyperbolic binary cross-entropy loss ($\mathcal{L}^{Hyp-BCE}_{decom}$), and hyperbolic contrastive loss ($\mathcal{L}^{BF}_{fus}$), to supervise model learning across different aspects.

Experimental results

Research questions

• RQ1 Can hyperbolic space better model the hierarchical structure of spoofing attacks compared to Euclidean space?
• RQ2 Does hyperbolic contrastive learning improve generalization to unseen attack types in face anti-spoofing?
• RQ3 Can a hybrid framework—using Euclidean decomposition and hyperbolic fusion—achieve better performance than fully Euclidean or fully hyperbolic approaches?
• RQ4 How effective is the proposed feature clipping method in stabilizing training of hyperbolic neural networks?
• RQ5 To what extent does the hyperbolic framework improve explainability and attention localization on spoofing cues?

Key findings

• The proposed hyperbolic unimodal FAS framework achieves state-of-the-art performance on WMCA, PADISI-Face, and SiW-M, with significant improvements in unseen attack detection over Euclidean baselines.
• On the MSU-MFSD, IDIAP REPLAY-ATTACK, CASIA-FASD, and OULU-NPU datasets, the model generalizes well even with limited attack types, demonstrating strong zero-shot generalization capability.
• The ablation study confirms that all three additional losses ($\mathcal{L}^{Dis}$, $\mathcal{L}^{BF}_{decom}$, $\mathcal{L}^{BF}_{fus}$) contribute positively to model generalization, with $\mathcal{L}^{BF}_{decom}$ and $\mathcal{L}^{BF}_{fus}$ being most effective in RGB+Depth, and $\mathcal{L}^{Dis}$ in RGB+IR settings.
• Grad-CAM visualization shows that the hyperbolic model focuses on realistic spoofing cues (e.g., unnatural eye regions), while the Euclidean baseline attends to noisy or irrelevant background regions.
• Multimodal feature decomposition in Euclidean space followed by hyperbolic fusion and classification yields the best performance, indicating that hyperbolic fusion is more effective than hyperbolic decomposition.
• The proposed feature clipping method significantly improves training stability in hyperbolic networks, enabling effective optimization despite the curvature-induced gradient vanishing problem.