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Unifying Watermarking via Dimension-Aware Mapping

Jiale Meng, Runyi Hu, Jie Zhang, Zheming Lu, Ivor Tsang, Tianwei Zhang

TL;DR

The paper addresses unifying deep watermarking by treating embedding and extraction as dimension-aware mappings between multi-dimensional payloads. It introduces DiM, defining payload spaces $\mathcal{P}^{(d)}$ for $d\in\{1,2,3\}$ and mappings $\mathcal{M}\{d_e,d_d\}$ that connect embedding and extraction across dimensions, including same-dimensional and cross-dimensional configurations. The authors instantiate DiM in video as DiM-V, demonstrating payloads $\mathbf{W}$, $\mathbf{M}^{(2)}$, and $\mathbf{M}^{(3)}$ and a unified pipeline that supports global and local embedding, spatiotemporal localization, and temporal order recovery without architectural changes. Results show that varying $d_e$ and $d_d$ yields capabilities such as spatiotemporal tamper localization, frame-order reconstruction under disruptions, and robust performance under diverse distortions, with a compression-aware fine-tuning strategy further enhancing robustness. Overall, DiM provides a principled, generalized framework for interpreting and designing watermarking systems with clarified trade-offs and richer functionality.

Abstract

Deep watermarking methods often share similar encoder-decoder architectures, yet differ substantially in their functional behaviors. We propose DiM, a new multi-dimensional watermarking framework that formulates watermarking as a dimension-aware mapping problem, thereby unifying existing watermarking methods at the functional level. Under DiM, watermark information is modeled as payloads of different dimensionalities, including one-dimensional binary messages, two-dimensional spatial masks, and three-dimensional spatiotemporal structures. We find that the dimensional configuration of embedding and extraction largely determines the resulting watermarking behavior. Same-dimensional mappings preserve payload structure and support fine-grained control, while cross-dimensional mappings enable spatial or spatiotemporal localization. We instantiate DiM in the video domain, where spatiotemporal representations enable a broader set of dimension mappings. Experiments demonstrate that varying only the embedding and extraction dimensions, without architectural changes, leads to different watermarking capabilities, including spatiotemporal tamper localization, local embedding control, and recovery of temporal order under frame disruptions.

Unifying Watermarking via Dimension-Aware Mapping

TL;DR

The paper addresses unifying deep watermarking by treating embedding and extraction as dimension-aware mappings between multi-dimensional payloads. It introduces DiM, defining payload spaces for and mappings that connect embedding and extraction across dimensions, including same-dimensional and cross-dimensional configurations. The authors instantiate DiM in video as DiM-V, demonstrating payloads , , and and a unified pipeline that supports global and local embedding, spatiotemporal localization, and temporal order recovery without architectural changes. Results show that varying and yields capabilities such as spatiotemporal tamper localization, frame-order reconstruction under disruptions, and robust performance under diverse distortions, with a compression-aware fine-tuning strategy further enhancing robustness. Overall, DiM provides a principled, generalized framework for interpreting and designing watermarking systems with clarified trade-offs and richer functionality.

Abstract

Deep watermarking methods often share similar encoder-decoder architectures, yet differ substantially in their functional behaviors. We propose DiM, a new multi-dimensional watermarking framework that formulates watermarking as a dimension-aware mapping problem, thereby unifying existing watermarking methods at the functional level. Under DiM, watermark information is modeled as payloads of different dimensionalities, including one-dimensional binary messages, two-dimensional spatial masks, and three-dimensional spatiotemporal structures. We find that the dimensional configuration of embedding and extraction largely determines the resulting watermarking behavior. Same-dimensional mappings preserve payload structure and support fine-grained control, while cross-dimensional mappings enable spatial or spatiotemporal localization. We instantiate DiM in the video domain, where spatiotemporal representations enable a broader set of dimension mappings. Experiments demonstrate that varying only the embedding and extraction dimensions, without architectural changes, leads to different watermarking capabilities, including spatiotemporal tamper localization, local embedding control, and recovery of temporal order under frame disruptions.
Paper Structure (32 sections, 12 equations, 25 figures, 4 tables, 1 algorithm)

This paper contains 32 sections, 12 equations, 25 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background
  3. DiM: Unified Watermarking Framework
  4. Multi-dimensional Payload Space
  5. Dimension-aware Mapping
  6. DiM-V: DiM for Video Watermarking
  7. Payload Instantiation
  8. Input Construction
  9. Unified Watermarking Pipeline
  10. Experiments
  11. Experimental Setup
  12. Same-dimensional Mapping: $\mathcal{M}\{d_e = d_d\}$
  13. Low-to-High Mapping: $\mathcal{M}\{d_e<d_d\}$
  14. High-to-Low Mapping: $\mathcal{M}\{d_e>d_d\}$
  15. Conclusion
  16. ...and 17 more sections

Figures (25)

  • Figure 1: Dimension-aware embedding-extraction mappings across multi-dimensional watermark payloads. Watermark information is represented at different dimensionalities, and each mapping $\mathcal{M}\{d_e,d_d\}$ is defined by the dimensional relationship between embedding and extraction. Same-dimensional mappings operate within a single space, while cross-dimensional mappings bridge different dimensional spaces.
  • Figure 2: Illustration of the proposed multi-channel mask encoding for spatiotemporal payloads. Each frame is assigned a distinct, permutation-invariant binary code along the channel dimension, where each channel map is spatially uniform within a frame (all-0 or all-1). This encoding scheme enables frame-wise localization and temporal order recovery under arbitrary frame permutations.
  • Figure 3: Comparison with baseline methods on local extraction (top) and tamper localization (bottom) in the same-dimension mapping setting. Results are evaluated under five distortion scenarios, and we select the average value for each interval’s ratios to stand for the interval (e.g., 5% represents the average over the 1--10% interval).
  • Figure 4: Comparison with baseline methods on local extraction (top) and tamper localization (bottom) in the cross-dimension mapping setting. Results are evaluated under five distortion scenarios, and we select the average value for each interval’s ratios to stand for the interval (e.g., 5% represents the average over the 1--10% interval).
  • Figure 5: Effect of mask channel count and dimensional mapping on global mIoU under diverse distortions. Comparing $\mathcal{M}\{3,3\}$ and $\mathcal{M}\{3,2\}$ reveals that increasing mask dimensionality degrades volumetric extraction, while high-to-low mapping restores robustness under multi-channel payloads.
  • ...and 20 more figures

Theorems & Definitions (3)

  • Definition 3.1: 1D Binary Payload
  • Definition 3.2: 2D Spatial Payload
  • Definition 3.3: 3D Spatiotemporal Payload