## 2 Introduction to Digital Watermarking: Trajectory, Techniques, and Applications
### Techniques of Digital Watermarking  
Digital watermarking techniques are classified according to several criteria: visibility, robustness, embedding domain, and extraction process, as shown in Figure 1. Each criterion influences watermark behaviour under different conditions and attacks and affects its overall usability [17, 18, 19].  
Visibility:  
Watermarks exist in multiple visibility states. Visible watermarks appear clearly in media and serve as a branding and copyright assertion in public-facing content [20]. Invisible watermarks remain hidden within the media and support covert use cases, including ownership verification and content authentication [21]. Perceptually tuned watermarks adjust visibility according to content characteristics [22], while layered watermarks combine multiple visibility levels for different recovery scenarios [23].  
Domain of Embedding:  
Watermarks are embedded in various transform domains. Spatial domain techniques directly modify pixel values. This approach offers computational simplicity, but comes with an increased vulnerability to compression attacks [5]. Transform domain methods include Discrete Fourier Transform (DFT), Discrete Cosine Transform (DCT), Discrete Wavelet Transform (DWT), Singular Value Decomposition (SVD), and Contourlet transforms [19; 24; 25]. These methods embed watermarks in transformed coefficients [26] and provide improved robustness against compression and common manipulations. Deep feature space embedding represents recent advancements that utilise neural network feature spaces to enhance resilience [18; 19].  
Robustness:  
Watermarking techniques demonstrate varying resistance to alterations. Robust watermarks withstand manipulation, including compression and geometric changes [18; 19; 27]. In contrast, fragile watermarks degrade or disappear after modification [10; 28] and provide effective mechanisms for content authentication and tamper detection. Semi-fragile watermarks offer intermediate functionality that allows minor modifications and tamper-evident indication [29]. Adaptive watermarks adjust their strength based on content characteristics, while adversarially robust watermarks resist deliberate removal attempts [18; 19]. Task-specific watermarks are optimised for particular applications, and self-healing watermarks can recover from certain types of damage [30; 31].  
Extraction Process:  
Watermark extraction incorporates multiple types of processes. Blind watermarking extracts watermarks without requiring the original content [32]. Non-blind techniques require access to the original content [10]. Semi-blind approaches use partial information from the original image. Zero-knowledge protocols enable verification without revealing the watermark [33]. Self-supervised extraction uses unsupervised learning to improve detection [34]. Adversarial-resilient methods withstand adversarial attacks, while privacy-preserving techniques protect sensitive information during extraction [34; 35].  
Figure 1: Taxonomy of digital watermarking methods by core design criteria.  
Media Type:  
Watermarking applies across diverse media types. Traditional applications include image, audio, video, and text [10]. Modern techniques extend to 3D models, point clouds, AR/VR streams, and synthetic media [36; 37]. Each media type presents unique challenges and opportunities for watermark embedding.