# Face Anti-Spoofing Based on Deep Learning: A Comprehensive Survey
## 3 Face Anti-Spoofing
### Domain Adaptation  
The purpose of domain adaptation (DA) is to train the model on the source domain to perform as well as possible on the target domain by using the given target domain's knowledge [114]. Given a labeled source domain \(\mathrm{D_{s}}=\{\mathrm{x_{i}},\mathrm{y_{i}}\}\) and a target domain \(\mathrm{D_{t}}=\{\mathrm{x_{i}},\mathrm{y_{i}}\}\), we assume that their feature space and class space are the same, but their joint distribution is different, that is, \(\mathrm{X_{s}}=\mathrm{X_{t}}\), \(\mathrm{Y_{s}}=\mathrm{Y_{t}}\), \(\mathrm{P_{s}(x,y)}\
eq\mathrm{P_{t}(x,y)}\). The task of domain adaptation is to use source domain data to learn the prediction function \(\mathrm{f:x_{t}\to y_{t}}\) so that \(\mathrm{f}\) has the smallest prediction error in the target domain. In unsupervised domain adaptation, where the labels are not available in the target domain, that is, \(\mathrm{Y}\) is unknown. The schematic diagram of the model is shown in Figure 10a. \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline
**Ref. ** & **Main Ideas** & **Backbone** & **Datasets** & **2D-F** & **2D-R** & **3D-M** & **OA** & **Understanding** & **DUnderstanding** \\ \hline \multirow{4}{*}{ \begin{tabular}{} \end{tabular}  } & Utilizing noise modeling to \\  & domain-specific modeling, and using \\  & for transformation \\  & & & & &  
Domain distribution discrepancy: [PERSON] et al. [115] proposed minimizing the maximum mean discrepancy (MMD) between the latent features in source and target domains was to learn a more generalized classifier. [PERSON] et al. [116] further proposed a novel optimization function for network distillation by combining cross-entropy loss, the MMD, and paired sample similarity embedding to effectively capture spoofing information. However, merely reducing the MMD distance between domains may not sufficiently exploit useful information from the source domain. This is why adversarial transfer learning has recently become a research hotspot. Adversarial training: [PERSON] et al. [117] proposed a disentangled representation learning net (DR-Net), which enabled the transfer of domain-independent knowledge to distinguish live and spoof faces in unlabeled target domains, with extensive evaluations on public datasets. [PERSON] et al. [118] introduced a unified unsupervised and semi-supervised domain adaptation network (USDAN). It employed a marginal and conditional distribution alignment module for adversarial learning to minimize domain discrepancies and improve generalization. A Conditional Distribution Alignment (CDA) module could be flexibly used for semi-supervised or unsupervised settings. [PERSON] et al. [119] combined adversarial training with deep clustering to generate pseudo-labels for auxiliary training, addressing domain and device differences. [PERSON] et al. [120] utilized GANs to stylize target data to match source domain style, aligning features and reducing domain discrepancies to improve generalization and accuracy. Other methods: [PERSON] et al. [121] proposed a total pairwise confusion loss (TPC) and a fast DA module to improve generalization in live face detection and recognition, mitigating the negative impact of domain changes on prosthetic attack representation. [PERSON] et al. [122] introduced a self-domain adaptation framework that utilizesd meta-learning to learn discriminative features across multiple source domains and adapt to target domain data during inference. [PERSON] et al. [123] developed an adaptive transfer mechanism to reduce domain bias by gradually increasing the contribution of unlabeled target domain data during training. DA typically assume access to source and target data, but this is often unrealistic. To reduce reliance on source data source-free domain adaptation (SFDA) [124] was proposed. [PERSON] et al. [125] introduced a SFDA framework for FAS (SDA-FAS), which utilized source-oriented regularization and contrastive domain alignment to reduce domain discrepancies.