Rethinking Domain Generalization for Face Anti-spoofing: Separability and Alignment

Yiyou SunYaojie LiuXiaoming LiuYixuan LiWen-Sheng Chu

article2023CVPR97 citations

Proposes a face anti-spoofing framework that preserves domain-specific signals while aligning live-to-spoof transition directions through invariant risk minimization, outperforming conventional domain-invariant feature learning approaches on cross-domain benchmarks.

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Face recognition systems are critical infrastructure for mobile authentication, payment security, and identity verification. However, these systems remain vulnerable to presentation attacks using printed photos or digital replays. While conventional face anti-spoofing models perform well under controlled conditions, they frequently fail when deployed across new environments, varied camera sensors, and fluctuating image resolutions. Most current solutions attempt to remove these domain-specific differences to create a single, domain-invariant feature space. The article demonstrates that this standard strategy is flawed: attempting to eliminate domain signals often forces models to rely on misleading correlations—such as confusing image blur with spoofing patterns—which degrades detection reliability on unseen test systems.

The article's main objective is to establish a new face anti-spoofing framework that maintains domain-specific variations while learning a domain-invariant decision boundary across all deployment scenarios. To achieve this, the article evaluates a strategy termed separability and alignment, implemented on a standard ResNet-18 architecture and tested across four widely recognized public face anti-spoofing benchmark datasets.

The approach combines two complementary mechanisms. First, it uses supervised contrastive learning to enforce separability, ensuring that samples from distinct environments and attack classes occupy well-defined, distinct clusters rather than being blended together. Second, it aligns the live-to-spoof transition trajectory across all domains using an optimization algorithm called projected gradient invariant risk minimization. Instead of attempting to optimize a single, rigid boundary that frequently leads to convergence failures, the algorithm iteratively updates separate boundaries for each training domain and projects them toward a unified global classifier.

The findings show that this approach substantially outperforms existing state-of-the-art methods. In standard benchmark evaluations, the proposed method lowered the error rate across cross-domain testing protocols, achieving an error reduction of over 25% relative to the best baseline on one challenging test split. Furthermore, when evaluated under a realistic convergence protocol using the final ten training epochs rather than an artificially selected best-performing snapshot, the framework sustained low error rates and high detection stability. Existing baseline methods experienced severe performance drops under stable convergence testing, confirming that prior benchmark conventions overestimated real-world robustness.

These results demonstrate that maintaining environment-specific characteristics in feature representations, rather than attempting to eliminate them, enables more dependable and transferable biometric security. For operational systems, this reduces vulnerability to presentation attacks and avoids the cost of continuously retraining models for new camera hardware. Organizations deploying facial verification should transition away from adversarial domain-invariance approaches toward separability and alignment frameworks. Future work should expand validation to 3D mask attacks and broader edge devices, as current evaluations focus primarily on print and digital replay datasets.

Google Michigan State University University of Wisconsin Madison facial images image resolution sensors face anti-spoofing domain generalization domain-adversarial training

arXiv: 2303.13662 sunyiyou/SAFAS

Paper: Domain Generalization: A Survey, Kaiyang Zhou et al. (2021). Provides a comprehensive survey and theoretical foundation of domain generalization paradigms and statistical alignment approaches that the source analyzes and rethinks.
Paper: PatchNet: A Simple Face Anti-Spoofing Framework via Fine-Grained Patch Recognition, Chien-Yi Wang et al. (2022). Presents a foundational baseline framework for cross-dataset face anti-spoofing using ResNet-18 and margin-based representation learning across the standard presentation attack benchmarks.
Paper: Simultaneous Deep Transfer Across Domains and Tasks, Eric Tzeng et al. (2015). Establishes classic domain alignment and domain-invariant representation learning principles that the source paper directly critiques and seeks to replace.

Paper: Decompose, Adjust, Compose: Effective Normalization by Playing with Frequency for Domain Generalization, Sangrok Lee et al. (2023). Builds upon domain generalization concepts by tackling feature content distortion in normalization layers to preserve intrinsic domain-invariant signals.
Paper: Frequency-Aware Deepfake Detection: Improving Generalizability through Frequency Space Domain Learning, Chuangchuang Tan et al. (2024). Extends generalization in facial forgery detection by leveraging frequency-space learning across unseen generative models.
Paper: Rethinking the Up-Sampling Operations in CNN-Based Generative Network for Generalizable Deepfake Detection, Chuangchuang Tan et al. (2024). Advances generalizable facial forensic detection across novel generators by isolating universal spatial artifact patterns from generative up-sampling operations.

Cover for Rethinking Domain Generalization for Face Anti-spoofing: Separability and Alignment

Abstract

This work studies the generalization issue of face anti-spoofing (FAS) models on domain gaps, such as image resolution, blurriness and sensor variations. Most prior works regard domain-specific signals as a negative impact, and apply metric learning or adversarial losses to remove them from feature representation. Though learning a domain-invariant feature space is viable for the training data, we show that the feature shift still exists in an unseen test domain, which backfires on the generalizability of the classifier. In this work, instead of constructing a domain-invariant feature space, we encourage domain separability while aligning the live-to-spoof transition (i.e., the trajectory from live to spoof) to be the same for all domains. We formulate this FAS strategy of separability and alignment (SA-FAS) as a problem of invariant risk minimization (IRM), and learn domain-variant feature representation but domain-invariant classifier. We demonstrate the effectiveness of SA-FAS on challenging cross-domain FAS datasets and establish state-of-the-art performance. Code is available at https://github.com/sunyiyou/SAFAS.

Topics

facial images image resolution sensors svm high-dimensional feature space local binary patterns

Keywords

face anti-spoofing domain generalization domain-adversarial training domain-invariant feature space spoof detection domain adaptation metric learning adversarial loss

1. Introduction
2. Related Work
3. Method
3.1. Problem Setup
3.2. Separability
3.3. Alignment
3.4. Training and inference
4. Experiments
4.1. Experimental setups
4.2. Cross-domain performance
5. Ablation and Discussion
5.1. Effectiveness of loss components
5.2. Separability and alignment analysis
5.3. UMAP visualization
6. Conclusion
References

Knowls

Knowl 1 — SA-FAS Framework for Cross-Domain Face Anti-Spoofing
model/method
The Separability and Alignment for Face Anti-Spoofing (SA-FAS) framework addresses cross-domain generalization in face presentation attack detection (PAD). While conventional methods aim to learn domain-invariant representations by eliminating domain discrepancy, SA-FAS retains domain-specific signals and constructs a domain-variant feature space coupled with a domain-invariant decision boundary.

The framework consists of two core principles:
1. Separability: Features belonging to different source domains $\mathcal{E} = \{e^{(1)}, e^{(2)}, \dots, e^{(E)}\}$ and binary classes $\mathcal{Y} = \{0\text{ (live)}, 1\text{ (spoof)}\}$ are encouraged to occupy distinct, compact clusters in the feature space via Supervised Contrastive Learning ( $L_{\text{sep}}$ ).
2. Alignment: The live-to-spoof transitions across domains are aligned along the same directional trajectory by formulating the classifier learning as Invariant Risk Minimization (IRM) optimized via Projected Gradient optimization (PG-IRM).
The complete model comprises a feature encoder $\phi: \mathcal{X} \to \mathbb{R}^m$ producing $l_2$ -normalized feature representations $z = \phi(x)$ , and domain-specific linear classifiers (hyperplanes) $\beta_e: \mathbb{R}^m \to \mathbb{R}$ for each training domain $e \in \mathcal{E}$ . The combined training objective is:

$\min_{\phi, \beta_{e^{(1)}}, \dots, \beta_{e^{(E)}}} L_{\text{align}} + \lambda L_{\text{sep}}$

$\text{s.t. } \forall e \in \mathcal{E}, \; \exists \beta_e \in \Omega_e(\phi), \; \beta_e \in \Upsilon_\alpha(\beta_e)$

where $\lambda$ is a balancing hyperparameter, $\Omega_e(\phi)$ represents the set of domain-optimal classifiers, and $\Upsilon_\alpha(\beta_e)$ is the $\alpha$ -adjacency set enforcing consistency across domains. At inference time on an unseen target domain sample $x \in \mathcal{X}$ , the prediction score is given by ensembling across the domain classifiers:

$f(x) = \mathbb{E}_{e \in \mathcal{E}} [\beta_e^T \phi(x)]$
Knowl 2 — Equivalence of Invariant Risk Minimization and the Projected Gradient IRM Objective
theoretical result
In cross-domain generalization, standard Invariant Risk Minimization (IRM) seeks an encoder $\phi: \mathcal{X} \to \mathbb{R}^m$ and a single classifier $\beta^*: \mathbb{R}^m \to \mathbb{R}$ that minimizes the empirical risk across training domains $\mathcal{E}$ while remaining simultaneously optimal for every domain $e \in \mathcal{E}$ :

$\min_{\phi, \beta^*} \frac{1}{|\mathcal{E}|} \sum_{e \in \mathcal{E}} R^e(\phi, \beta^*) \quad \text{s.t.} \quad \beta^* \in \arg\min_\beta R^e(\phi, \beta), \; \forall e \in \mathcal{E}$

where $R^e(\phi, \beta) = \mathbb{E}_{(x, y, e) \sim \mathcal{D}} [\ell(f(x; \phi, \beta), y)]$ .

Theorem (PG-IRM Objective Equivalence): For all $\alpha \in (0, 1)$ , the bi-level IRM objective is equivalent to optimizing individual domain-wise hyperplanes $\beta_e$ via the projected gradient objective:

$\min_{\phi, \beta_{e^{(1)}}, \dots, \beta_{e^{(E)}}} \frac{1}{|\mathcal{E}|} \sum_{e \in \mathcal{E}} R^e(\phi, \beta_e)$

$\text{s.t.} \quad \forall e \in \mathcal{E}, \; \exists \beta_e \in \Omega_e(\phi), \; \beta_e \in \Upsilon_\alpha(\beta_e)$

where the parametric constrained set for environment $e$ is defined as $\Omega_e(\phi) = \arg\min_\beta R^e(\phi, \beta)$ , and the $\alpha$ -adjacency set $\Upsilon_\alpha(\beta_e)$ is defined as:

$\Upsilon_\alpha(\beta_e) = \left\{ \beta \;\middle|\; \max_{e' \in \mathcal{E} \setminus \{e\}} \min_{\beta_{e'} \in \Omega_{e'}(\phi)} \|\beta - \beta_{e'}\|_2 \le \alpha \max_{e' \in \mathcal{E} \setminus \{e\}} \min_{\beta_{e'} \in \Omega_{e'}(\phi)} \|\beta_e - \beta_{e'}\|_2 \right\}$

This reformulation replaces the potentially empty single-hyperplane constraint set with a non-empty, projectable domain-wise constraint set.
Knowl 3 — Supervised Contrastive Loss for Domain-Class Separability
equation
To achieve feature separability across both domain identities and live/spoof classes, Supervised Contrastive Learning (SupCon) is formulated over mini-batches augmented to size $2b$ , denoted as $\{(\tilde{x}_i, \tilde{y}_i, \tilde{e}_i)\}_{i=1}^{2b}$ with corresponding $l_2$ -normalized feature embeddings $z_i = \phi(\tilde{x}_i) \in \mathbb{R}^m$ .

The per-batch separability loss $L_{\text{sep}}$ is defined as:

$L_{\text{sep}} = \sum_{i=1}^{2b} \frac{-1}{|S(i)|} \sum_{j \in S(i)} \log \frac{\exp(z_i \cdot z_j / \tau)}{\sum_{t=1, t \neq i}^{2b} \exp(z_i \cdot z_t / \tau)}$

where:
- $\tau > 0$ is a scalar temperature parameter;
- $i$ is the anchor index;
- $S(i) = \{j \in \{1, \dots, 2b\} : j \neq i, \tilde{y}_j = \tilde{y}_i, \tilde{e}_j = \tilde{e}_i\}$ is the set of positive indices containing samples that have both the identical class label (live vs. spoof) and the identical domain origin as anchor $i$ ;
- $|S(i)|$ is the cardinality of $S(i)$ .
All samples in the batch with either a different domain or a different class label act as negative pairs, forcing the feature space to retain domain-specific characteristics in separated clusters.
Knowl 4 — Projected Gradient Training Algorithm for SA-FAS
algorithm
The training pipeline optimizes the shared feature encoder $\phi$ alongside domain-specific hyperplanes $\{\beta_e\}_{e \in \mathcal{E}}$ by alternating between stochastic gradient descent and Euclidean projection via linear interpolation onto the $\alpha$ -adjacency set.
Input: Training dataset $D = \{(x_i, y_i, e_i)\}_{i=1}^N$ , network encoder $\phi$ , classifiers $\{\beta_e\}_{e \in \mathcal{E}}$ , learning rate $\gamma$ , alignment parameter $\alpha$ , alignment starting epoch $T_a$ , total epochs $T$ .
Output: Optimized encoder $\phi$ and aligned classifiers $\{\beta_e\}_{e \in \mathcal{E}}$ .
for $t = 0, 1, \dots, T$ do
    Sample and augment mini-batch to obtain pairs $\{(\tilde{x}_i, \tilde{y}_i, \tilde{e}_i)\}_{i=1}^{2b}$
    Calculate total loss $L_{\text{all}} = L_{\text{align}} + \lambda L_{\text{sep}}$
    for $e \in \mathcal{E}$ do
         $\tilde{\beta}_e^{t+1} = \beta_e^t - \gamma \nabla_{\beta_e^t} L_{\text{all}}$
        Select farthest domain classifier $\bar{e} = \arg\max_{e' \in \mathcal{E} \setminus \{e\}} \|\tilde{\beta}_e^{t+1} - \beta_{e'}^t\|_2$
         $\alpha' = 1 - \mathbf{1}_{t > T_a} (1 - \alpha)$
         $\beta_e^{t+1} = \alpha' \tilde{\beta}_e^{t+1} + (1 - \alpha') \beta_{\bar{e}}^t$
    end for
     $\phi^{t+1} = \phi^t - \gamma \nabla_{\phi^t} L_{\text{all}}$
end for
Key execution parameters in the framework are set to $\alpha = 0.995$ , $\lambda = 0.1$ , $T_a = 20$ , with base learning rate $\gamma = 5\times 10^{-3}$ and weight decay $5\times 10^{-4}$ .
Knowl 5 — Separability and Alignment Quantitative Metrics
definition
To evaluate the geometric properties of the learned feature space and its decision boundaries on an unseen test domain without relying solely on classification error, two quantitative metrics are defined:
1. Separability Score ( $S_{\text{sep}}$ ): Measures the angular separation between the live and spoof feature representations in the test domain:
$S_{\text{sep}} = 1 - \cos\left(\mathbb{E}_{\text{spoof}}[z], \; \mathbb{E}_{\text{live}}[z]\right)$

where $z = \phi(x) \in \mathbb{R}^m$ is the $l_2$ -normalized feature embedding, and $\mathbb{E}_{\text{spoof}}[z]$ and $\mathbb{E}_{\text{live}}[z]$ denote the mean feature vectors of spoof and live test samples, respectively. A higher $S_{\text{sep}}$ indicates greater class separation.
1. Alignment Score ( $S_{\text{align}}$ ): Measures the cosine similarity between the learned domain hyperplane normal vectors $\beta_e$ and the oracle transition vector from live to spoof in the test domain:
$S_{\text{align}} = \mathbb{E}_{e \in \mathcal{E}} \left[ \cos\left(\beta_e, \; \mathbb{E}_{\text{spoof}}[z] - \mathbb{E}_{\text{live}}[z]\right) \right]$

where $\mathbb{E}_{\text{spoof}}[z] - \mathbb{E}_{\text{live}}[z]$ serves as the oracle live-to-spoof transition direction in the embedding space. A higher $S_{\text{align}}$ indicates that the classifiers are aligned with the true attack transition trajectory.
Knowl 6 — Cross-Domain Face Anti-Spoofing Benchmark Protocols and Evaluation Setup
experimental setup
Cross-domain performance is evaluated across four standard public datasets: CASIA-FASD (C), Idiap Replay-Attack (I), MSU-MFSD (M), and Oulu-NPU (O). A leave-one-out cross-validation protocol evaluates generalization to unseen domains: $\text{OCI}\to\text{M}$ , $\text{OMI}\to\text{C}$ , $\text{OCM}\to\text{I}$ , and $\text{ICM}\to\text{O}$ (where letters denote training sets and the arrow indicates the held-out test set).

Implementation Details:
- Face images are cropped via MTCNN and resized to $256 \times 256$ .
- Backbone architecture is ResNet-18 producing $l_2$ -normalized penultimate embeddings.
- Optimization uses SGD with an initial learning rate of $5\times 10^{-3}$ (decayed by a factor of 2 at epochs 40 and 80 for 100 total epochs; $\text{ICM}\to\text{O}$ runs for 300 epochs, decaying at 120 and 240).
- Weight decay is $5\times 10^{-4}$ and per-domain batch size is 96.
- SA-FAS hyperparameters: $\alpha = 0.995$ , $\lambda = 0.1$ , and alignment start epoch $T_a = 20$ .
Evaluation Metrics:
- Half Total Error Rate ( $\text{HTER} = \frac{\text{FAR} + \text{FRR}}{2}$ , lower is better);
- Area Under the Receiver Operating Characteristic Curve ( $\text{AUC}$ , higher is better);
- True Positive Rate at a False Positive Rate of 5% ( $\text{TPR95}$ , higher is better).

Knowl 7 — Cross-Domain FAS Performance under Converged Evaluation Protocol

data/table

Reporting cross-domain PAD metrics using the best-performing test snapshot introduces selection bias and high variance. The converged evaluation protocol reports the mean and standard deviation over the last 10 training epochs upon convergence (where the binary loss drops below $10^{-3}$ for 10 consecutive epochs or maximum epochs are reached).

Method (%)	OCI $\to$ M	OMI $\to$ C	OCM $\to$ I	ICM $\to$ O
	HTER $\downarrow$ / AUC $\uparrow$ / TPR95 $\uparrow$	HTER $\downarrow$ / AUC $\uparrow$ / TPR95 $\uparrow$	HTER $\downarrow$ / AUC $\uparrow$ / TPR95 $\uparrow$	HTER $\downarrow$ / AUC $\uparrow$ / TPR95 $\uparrow$
SSDG-R	14.65 $^{1.21}$ / 91.93 $^{1.35}$ / 53.68 $^{2.56}$	28.76 $^{0.89}$ / 80.91 $^{1.10}$ / 41.47 $^{2.68}$	22.84 $^{1.14}$ / 78.67 $^{1.31}$ / 50.80 $^{5.95}$	15.83 $^{1.29}$ / 92.13 $^{0.96}$ / 66.54 $^{4.00}$
SSAN-R	21.79 $^{3.68}$ / 84.06 $^{3.78}$ / 51.91 $^{4.28}$	26.44 $^{2.91}$ / 78.84 $^{2.83}$ / 45.36 $^{4.29}$	35.39 $^{8.04}$ / 70.13 $^{9.03}$ / 64.00 $^{2.70}$	25.72 $^{3.74}$ / 79.37 $^{4.69}$ / 36.75 $^{5.19}$
PatchNet	25.92 $^{1.13}$ / 83.43 $^{0.87}$ / 38.75 $^{8.31}$	36.26 $^{1.98}$ / 71.38 $^{1.89}$ / 19.22 $^{3.85}$	29.75 $^{2.76}$ / 80.53 $^{1.35}$ / 54.25 $^{2.18}$	23.49 $^{1.80}$ / 84.62 $^{1.92}$ / 39.39 $^{6.83}$
SA-FAS (Ours)	14.36 $^{1.10}$ / 92.06 $^{0.53}$ / 55.71 $^{4.82}$	19.40 $^{0.66}$ / 88.69 $^{0.67}$ / 50.53 $^{3.60}$	11.48 $^{1.10}$ / 95.74 $^{0.55}$ / 77.05 $^{3.26}$	11.29 $^{0.32}$ / 95.23 $^{0.24}$ / 73.38 $^{1.64}$

Under this evaluation setting:

Error rates for all methods are noticeably higher than single-snapshot best numbers, demonstrating that conventional metrics overestimate generalization.
Adversarial domain-generalization methods (e.g., SSAN-R) exhibit large standard deviations across late epochs.
SA-FAS demonstrates consistent performance across all four cross-domain benchmarks, achieving the lowest HTER and highest AUC and TPR95 with lower variance.

Knowl 8 — Best-Snapshot Cross-Domain FAS Performance Comparison

data/table

Cross-domain face anti-spoofing performance evaluated under the conventional best-test-snapshot protocol across CASIA (C), Idiap Replay (I), MSU-MFSD (M), and Oulu-NPU (O):

Method (%)	OCI $\to$ M		OMI $\to$ C		OCM $\to$ I		ICM $\to$ O
	HTER $\downarrow$	AUC $\uparrow$	HTER $\downarrow$	AUC $\uparrow$	HTER $\downarrow$	AUC $\uparrow$	HTER $\downarrow$	AUC $\uparrow$
MMD-AAE	27.08	83.19	44.59	58.29	31.58	75.18	40.98	63.08
MADDG	17.69	88.06	24.50	84.51	22.19	84.99	27.98	80.02
SSDG-M	16.67	90.47	23.11	85.45	18.21	94.61	25.17	81.83
DR-MD-Net	17.02	90.10	19.68	87.43	20.87	86.72	25.02	81.47
RFMeta	13.89	93.98	20.27	88.16	17.30	90.48	16.45	91.16
NAS-FAS	19.53	88.63	16.54	90.18	14.51	93.84	13.80	93.43
D2AM	12.70	95.66	20.98	85.58	15.43	91.22	15.27	90.87
SDA	15.40	91.80	24.50	84.40	15.60	90.10	23.10	84.30
DRDG	12.43	95.81	19.05	88.79	15.56	91.79	15.63	91.75
ANRL	10.83	96.75	17.83	89.26	16.03	91.04	15.67	91.90
SSAN-M	10.42	94.76	16.47	90.81	14.00	94.58	19.51	88.17
SSDG-R	7.38	97.17	10.44	95.94	11.71	96.59	15.61	91.54
SSAN-R	6.67	98.75	10.00	96.67	8.88	96.79	13.72	93.63
PatchNet	7.10	98.46	11.33	94.58	13.40	95.67	11.82	95.07
SA-FAS (Ours)	5.95	96.55	8.78	95.37	6.58	97.54	10.00	96.23

SA-FAS achieves the lowest HTER across all four leave-one-out protocols, outperforming the previous best baseline SSAN-R on $\text{OCM}\to\text{I}$ by 2.30% in HTER (a relative error reduction exceeding 25%).

Knowl 9 — Ablation Study of Loss Formulations for Separability and Invariant Risk Minimization

data/table

Ablation performance averaged over all four cross-domain FAS benchmarks (OCI $\to$ M, OMI $\to$ C, OCM $\to$ I, ICM $\to$ O) compares various representation learning losses and IRM formulation strategies:

Method	HTER (%) $\downarrow$	AUC (%) $\uparrow$	TPR95 (%) $\uparrow$
SimCLR	22.53 $^{1.31}$	84.42 $^{1.04}$	51.14 $^{3.44}$
SimSiam	18.89 $^{0.97}$	89.93 $^{0.80}$	56.62 $^{2.88}$
Triplet	18.75 $^{2.31}$	88.11 $^{2.30}$	50.53 $^{8.76}$
SupCon (SSDG)	17.91 $^{1.05}$	90.10 $^{0.68}$	61.98 $^{2.87}$
SupCon	17.03 $^{1.73}$	90.68 $^{1.29}$	56.72 $^{5.06}$
ERM	17.22 $^{1.26}$	90.21 $^{1.38}$	58.62 $^{3.77}$
DANN	17.93 $^{1.02}$	90.66 $^{0.56}$	58.66 $^{3.14}$
IRM-v1	17.41 $^{0.77}$	91.16 $^{0.52}$	60.98 $^{2.10}$
VREx	25.02 $^{1.92}$	80.65 $^{2.20}$	45.12 $^{3.78}$
IB-IRM	17.57 $^{0.74}$	91.71 $^{0.51}$	62.16 $^{2.35}$
PG-IRM (Ours)	15.58 $^{0.96}$	92.03 $^{0.62}$	63.31 $^{2.59}$
SA-FAS (Ours)	14.25 $^{0.79}$	92.93 $^{0.49}$	64.16 $^{3.33}$

Key takeaways:

Separability losses: Supervised Contrastive Learning (SupCon) outperforms self-supervised (SimCLR, SimSiam) and metric learning (Triplet) alternatives by forming distinct clusters per domain-class pair.
Alignment/Invariance losses: Lagrangian-penalty IRM approximations (IRM-v1, VREx, IB-IRM) yield marginal improvements or instability in deep networks, whereas PG-IRM directly enforces consistency among hyperplanes via projected gradient descent, reducing average HTER to 15.58%.
Combined Framework: Combining SupCon and PG-IRM in SA-FAS yields the best overall performance (14.25% HTER, 92.93% AUC, 64.16% TPR95).

Coverage note — None was omitted; all key contributions including framework formulation, theoretical equivalence, training algorithm, diagnostic metrics, convergence evaluation, benchmark comparisons, and loss ablations are fully covered.

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Citation

MLA

Sun, Y., et al. “Rethinking Domain Generalization for Face Anti-spoofing: Separability and Alignment”. arXiv, 2023, http://arxiv.org/abs/2303.13662v1.

APA

Sun, Y., Liu, Y., Liu, X., Li, Y., & Chu, W.-S. (2023). Rethinking Domain Generalization for Face Anti-spoofing: Separability and Alignment. arXiv. http://arxiv.org/abs/2303.13662v1

Chicago

Sun, Y., Y. Liu, X. Liu, Y. Li, and W.-S. Chu. 2023. “Rethinking Domain Generalization for Face Anti-spoofing: Separability and Alignment”. arXiv. http://arxiv.org/abs/2303.13662v1.

Harvard

Sun, Y. et al. (2023) “Rethinking Domain Generalization for Face Anti-spoofing: Separability and Alignment”, arXiv [Preprint]. Available at: http://arxiv.org/abs/2303.13662v1.

Vancouver

1. Sun Y, Liu Y, Liu X, Li Y, Chu W-S (2023) Rethinking Domain Generalization for Face Anti-spoofing: Separability and Alignment. arXiv

BibTeX

@article{sun2023rethinking,
  title = {Rethinking Domain Generalization for Face Anti-spoofing: Separability and Alignment},
  author = {Sun, Yiyou and Liu, Yaojie and Liu, Xiaoming and Li, Yixuan and Chu, Wen-Sheng},
  year = {2023},
  journal = {arXiv},
  url = {http://arxiv.org/abs/2303.13662v1},
  eprint = {2303.13662}
}

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Rethinking Domain Generalization for Face Anti-spoofing: Separability and Alignment

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Knowls

Knowl 1 — SA-FAS Framework for Cross-Domain Face Anti-Spoofing

Knowl 2 — Equivalence of Invariant Risk Minimization and the Projected Gradient IRM Objective

Knowl 3 — Supervised Contrastive Loss for Domain-Class Separability

Knowl 4 — Projected Gradient Training Algorithm for SA-FAS

Knowl 5 — Separability and Alignment Quantitative Metrics

Knowl 6 — Cross-Domain Face Anti-Spoofing Benchmark Protocols and Evaluation Setup

Knowl 7 — Cross-Domain FAS Performance under Converged Evaluation Protocol

Knowl 8 — Best-Snapshot Cross-Domain FAS Performance Comparison

Knowl 9 — Ablation Study of Loss Formulations for Separability and Invariant Risk Minimization

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