Technical Summary: Unifying Watermarking via Dimension-Aware Mapping

1. Problem Statement

Deep watermarking methods have largely converged on similar encoder–decoder architectures, yet they exhibit substantial functional differences based on their specific task designs. Current approaches are typically fragmented:

• Copyright Verification: Most methods focus on embedding and extracting one-dimensional (1D) binary messages to verify ownership.
• Tamper Localization: Other methods introduce fragile signals or reformulate extraction as spatial prediction problems to detect manipulated regions.
• Video Limitations: Existing video watermarking methods predominantly model watermarks as global 1D messages. They lack explicit modeling of spatial locality and, critically, fail to encode or recover temporal structures (e.g., frame order) when videos are reordered or shuffled.

The core problem addressed is the lack of a unified modeling perspective. Different watermarking functionalities are realized through ad-hoc, task-specific designs without a shared theoretical framework, raising the question of whether these disparate designs can be interpreted under a single paradigm.

2. Methodology: The DiM Framework

The authors propose DiM (Dimension-aware Mapping), a unified framework that formulates watermarking as a dimension-aware mapping problem. Instead of fixing the watermark form, DiM models watermark information as payloads of varying dimensionalities ($d$) and defines the embedding-extraction process based on the relationship between the embedding dimension ($d_e$) and the extraction dimension ($d_d$).

2.1 Multi-dimensional Payload Space

The framework defines three payload spaces:

• 1D Binary Payload ($P^{(1)}$): Global, permutation-invariant binary information (e.g., ownership IDs).
• 2D Spatial Payload ($P^{(2)}$): Spatially localized structural information (e.g., masks for region-level constraints).
• 3D Spatiotemporal Payload ($P^{(3)}$): Structural information defined over space-time volumes (e.g., spatiotemporal masks).

2.2 Dimension-Aware Mappings

The framework categorizes watermarking behaviors based on the mapping $\mathcal{M}\{d_e, d_d\}$:

• Same-Dimensional Mapping ($d_e = d_d$): Preserves the payload structure, enabling fine-grained control (e.g., copyright verification).
• Cross-Dimensional Mapping ($d_e \neq d_d$):
  • Low-to-High ($d_e < d_d$): Embeds low-dimensional data and extracts high-dimensional representations. This induces structure-expanding projections, enabling spatial or spatiotemporal localization (e.g., detecting tampered regions from a global ID).
  • High-to-Low ($d_e > d_d$): Embeds high-dimensional data and extracts low-dimensional representations. This acts as a structure-decoupling projection, useful for reducing decoding complexity or recovering information when cross-dimensional coherence is weak.

2.3 Instantiation: DiM-V (Video Watermarking)

To explore general dimensional configurations, the authors instantiate DiM in the video domain as DiM-V.

• Payload Instantiation:
  • 1D: Random binary messages.
  • 2D: Spatial masks (full, rectangular, irregular, segmented) sampled per frame.
  • 3D: Spatiotemporal mask tensors. Crucially, DiM-V introduces a multi-channel mask encoding mechanism where each frame is assigned a distinct, permutation-invariant binary code along the channel dimension. This allows the system to explicitly encode frame identity and recover temporal order even under arbitrary frame permutations.
• Unified Pipeline: DiM-V employs a single network architecture (adapted from MaskWM) with a shared noise layer. The input tensor is constructed by concatenating the host video with feature representations of the 1D message and optional 2D/3D masks. By varying only the dimensional configuration of the embedding and extraction heads, the system switches between different functional capabilities without architectural changes.

3. Key Contributions

1. Unified Modeling Perspective: The paper proposes DiM, which interprets existing image and video watermarking methods as specific instances of dimension-aware mappings rather than isolated task-driven designs.
2. Dimensional Configuration as a Control Mechanism: It demonstrates that the functional behavior of a watermark (e.g., robustness vs. localization vs. temporal recovery) is largely determined by the dimensional relationship between embedding and extraction, not just the network architecture.
3. Spatiotemporal Modeling in Video: DiM-V addresses the limitations of current video watermarking by explicitly modeling temporal structures. It introduces a mechanism to encode frame identity, enabling the recovery of temporal sequences even when frames are shuffled.
4. Flexibility without Redesign: The framework shows that diverse capabilities (global copyright verification, local embedding control, spatiotemporal tamper localization, and temporal order recovery) can be achieved by adjusting dimensional settings within a single unified model.

4. Experimental Results

Experiments were conducted on the SA-V dataset (12,000+ videos) with a resolution of 256×256 and 8 frames.

• Robustness and Imperceptibility: In same-dimensional mappings ($\mathcal{M}\{3,3\}$), DiM-V demonstrated superior robustness against value-metric, geometric, and frame-level distortions compared to baselines like VideoSeal, RivaGAN, and REVMark, while maintaining competitive PSNR and SSIM scores.
• Localization Capabilities:
  • Local Extraction: Cross-dimensional mappings (e.g., $\mathcal{M}\{1,3\}$ and $\mathcal{M}\{2,3\}$) enabled the system to perform local extraction and tamper localization, outperforming baselines like WAM and MaskWM-D in Intersection-over-Union (IoU) metrics.
  • Temporal Recovery: The multi-channel encoding in DiM-V successfully recovered the original temporal order of videos even when frames were reordered or shuffled, a capability absent in prior video watermarking methods.
• Efficiency: The framework achieved these diverse capabilities without modifying the underlying network architecture, relying solely on dimensional configuration changes.

5. Significance and Claims

The paper claims that DiM provides a unified modeling perspective that bridges the gap between disparate watermarking tasks. By treating watermarking as a dimension-aware mapping problem, the authors argue that:

• The functional diversity of watermarking (from simple copyright checks to complex spatiotemporal localization) can be systematically understood and controlled through dimensional configurations.
• Current video watermarking designs are limited by their reliance on 1D global messages; explicitly modeling spatial and temporal dimensions (as done in DiM-V) fills critical gaps in content authentication and integrity verification.
• The ability to recover temporal order under frame disruptions represents a significant advancement for video integrity, moving beyond simple robustness to structural recovery.

The authors position DiM not as a new task-specific architecture, but as a framework that reveals how existing methods can be unified and how new capabilities can be derived by manipulating the dimensionality of the payload space.