# A Brief, In-Depth Survey of Deep Learning-Based Image Watermarking
## 3 Comprehensive Survey of Deep Learning-Based Image Watermarking
### Embedder-Extractor Joint Training Methods  
As depicted in Figure 2, methods within this category fundamentally involve the training of two core components: an embedder network, responsible for watermark integration into a cover image, and an extractor network, tasked with retrieving the embedded watermark from the marked image. Variations in design are present, with some iterations incorporating separate feature extraction networks within the embedder for the preliminary processing of the watermark and cover image. To enhance robustness, a noise module is typically positioned subsequent to the marked image. This module is instrumental in introducing and amalgamating noise into the marked image during training, equipping the extractor network with an augmented capacity to counteract disturbances. Typically, all components are jointly trained within a unified deep neural network framework, employing gradient descent as the optimization technique. The objective is to optimize a loss function, aiming to uphold imperceptibility while ensuring the effective extraction of the embedded watermark. Mathematically, a representative loss function for such joint training can be defined as follows:  
\[l=f_{1}(c,m)+f_{2}(w,w^{\prime}), \tag{3}\]  
where \(c,m,w,w^{\prime}\) represent the cover image, marked image, watermark, and extracted watermark, respectively. The function \(f_{1}\) quantifies the visual disparity between \(c\) and \(m\), aligning with the traditional criterion of achieving a high \(PSNR\). Concurrently, \(f_{2}\) assesses \begin{table}
\begin{tabular}{l p{142.3 pt}} \hline \hline
**Methodology** & **Key Features/Requirements/Potential Drawbacks** \\ \hline Deep network as a feature transformation & **Key features:** Employment of deep networks for feature transformation, leveraging pre-trained models for adept feature extraction. \\  & **Requirements:** Pre-training of deep networks on tasks related to robustness within the domain, alongside a separate design of embedding and extraction in this feature space. \\  & **Potential drawbacks:** Robustness may be compromised if the feature transformation efficacy is subpar, and pre-trained networks might not adequately prioritize robustness. \\ \hline Hybrid Methods & **Key features:** Fusion of classical watermarking with deep learning, harnessing strengths from both realms for enhanced watermarking. \\  & **Requirements:** Rigorous design and fine-tuning of both traditional watermarking schemes and deep learning models to ensure harmonious operation. \\  & **Potential drawbacks:** Increased design complexity and potential amplification of limitations inherited from both classical and deep learning-based techniques, necessitating a sagacious design strategy. \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._  
Figure 2: General process of the embedder–extraction joint training. the variance between \(w\) and \(w^{\prime}\), fulfilling the conventional benchmarks of elevated BER or \(NC\). The elements within \(l\) present a trade-off: minimizing \(f_{1}(c,m)\) to zero implies an exact resemblance between the marked and cover images. However, this may constrain the space available for watermark embedding, potentially leading to extraction inefficacy. To orchestrate a network capable of harmonizing this trade-off, a prevalent approach involves utilizing the gradients engendered by \(f_{2}(w,w^{\prime})\) to refine the weights of all components, effectuating back-propagation extending to both \(c\) and \(m\). Conversely, gradients emanating from \(f_{1}(c,m)\) are exclusively employed to optimize the embedder network's weights. Subsequent sections will unfold the intricate designs and distinct characteristics embodied by representative state-of-the-art methods within this joint training category. The concept of joint training was first introduced in the HiDDeN (hiding data with deep networks) paper by [PERSON] et al. [7].