Robust watermarking through gradient-based topological encoding and geometric localization

With the rapid rise of generative artificial intelligence (AI), defensive watermarking has become a hotspot for distinguishing synthetic from real images. However, frequency-domain attacks such as UnMarker undermine the reliability of existing schemes. To address this, we shift to the spatial domain and propose a robust watermarking method based on topological stability to resist removal and restore trust in provenance. A topological mesh built from robust keypoints is used to geometrically localize the embedding regions. Within these regions, a gradient-based topological encoding scheme is employed to enhance the robustness of the watermark. Experimental results demonstrate that the proposed method achieves a normalized correlation (NC) above 0.99 across diverse attack types and their combinations. Even under a combined scenario involving three high-intensity distortions—scaling (0.5×), Gaussian noise (0.05), and JPEG compression (Q=50)—the method achieves an NC of 0.9878, substantially surpassing the average robustness of the compared methods. The method effectively exploits geometric-topological information of the image, offering a viable solution for robust watermarking in complex and adversarial environments while also providing a reliable tool for the detection and protection of AI-generated content.