MeshPAD: Payload-aware mesh distortion for 3D steganography based on geometric deep learning

Abstract

Minimizing distortion while embedding specific payloads is a critical challenge in 3D steganography task. The traditional methods usually involve two steps: first, calculating embedding change probabilities for each vertex using a heuristic distortion formula, and then embedding the secret data according to these probabilities. This paper introduces a novel approach called Payload-Aware Mesh Distortion (MeshPAD), which utilizes a geometric deep learning framework tailored for 3D steganography. MeshPAD directly learns embedding change probabilities while maintaining the minimal distribution distance. The framework is built on three main components: (1) a graph auto-encoder that captures edgewise sensitivity based on topological data; (2) a mechanism that using the edge sensitivity and different payload rates to predict embedding change probabilities, creating a payload-aware distortion process; and (3) a combination consisting of a trainable data embedding mechanism and a discriminator, which work in an adversarial manner to refine the distortion process and enhance security. Experimental results show that MeshPAD achieves superior undetectability compared to heuristic methods. For instance, MeshPAD improves undetectability by about 3% at a payload rate of 0.5 over heuristic methods on the Manifold40 dataset. Across various payload settings, it consistently matches or surpasses existing methods in mesh steganography scenarios, demonstrating its effectiveness and improved security. This development not only enhances the robustness of data protection in 3D environments but also suggests potential applications in areas such as virtual reality security and digital asset management within the information security field.