# Review of Image Forensic Techniques Based on Deep Learning
## 4 Robust Image Watermarking Based on Deep Learning
### Robust Image Watermark against Differentiable Attack
#### 4.1.2 Robust Image Watermark against Geometric Attacks  
Geometric attacks mainly include rotation, cropping, and translation that change the spatial position relationship of pixels and affect the spatial synchronization of codecs. According to the method of recovering spatial synchronization, it can be divided into transform domain-based, zero-watermarking, and robust feature-based. For cropping attacks, when the cropping involves the watermark embedding region, the watermark extraction algorithm may not match the watermark features correctly, resulting in the quality of the extracted watermark information being reduced. Multi-location embedding, multi-watermark embedding, and multi-watermark embedding are three main methods to improve the robustness of cropping attacks. [PERSON] and [PERSON] [107] used the sinusoidal function and the wavelength of the sinusoidal function to design the embedding rule, which gives each watermark bit multiple copies spread across different blocks. Therefore, even under cropping attacks, other watermarks can be saved to achieve copyright authentication. **Transform Domain-based:** The transform domain-based watermarking algorithm embeds the watermark into the transform domain coefficients, avoiding geometric attacks from corrupting the synchronization of the codec effectively. [PERSON] [108] implemented watermark embedding and extraction in the transform domain (such as DCT, DWT, Haar, etc. ), and introduced circular convolution in the convolution layer used for feature extraction to make the watermark information diffuse in the transform domain, which effectively improved the robustness against cropping. [PERSON] et al. [109] embedded a watermark in the DCT domain and introduced the attention mechanism to calculate the confidence of each image block. In addition, joint source-channel coding was introduced to make the algorithm maintain good robustness and imperceptibility under the gray image watermarking with the background. **Zero-watermarking:** The idea of the zero-watermarking is to obtain geometrically invariant features from robust features in images and generate zero-watermark through zero-watermark generation by sequence synthesis operation such as dissimilar operation. [PERSON] et al. [110] used pre-trained VGG19 [111] network to extract original image features and selected DFT-transformed low-frequency sub-bands to construct a medical image feature matrix. [PERSON] et al. [112] used neural style transfer (NST) [113] technique combined with a pre-trained VGG19 network to extract the original image style features, fused the original image style with the original watermark content to obtain the style fusion image, and Arnold dislocation [114] to obtain the zero-watermark. [PERSON] et al. [115] used the low-frequency features of the DCT of the original image as labels. Skip connection and loss functions were applied to enhance and extract high-level semantic features. However, none of the authors [110; 112; 115] could resist the robustness of multiple types of attacks effectively. **Robust Feature-based:** Unlike zero-watermarking, the idea of this method is to search for embedded feature coefficients or tensors in the image and embed the watermark in it robustly. [PERSON] et al. [116] embedded the watermark in low-order Zernike moments with rotation and interpolation invariance. [PERSON] et al. [117] proposed a robust image watermarking scheme based on lifting wavelet transform (LWT) and deep neural network (DNN). The DNN was trained to identify the changes caused by attacks in different frequency bands and select the best subbands for embedding. However, it was not robust to speckle noise. [PERSON] et al. [118] combined the multiscale features in GAN and used pyramid filters and multiscale maximum pooling techniques to learn the watermark feature distribution and improve the geometric robustness of watermarking fully.