Blind 3D-Printing Watermarking Using Moment Alignment and Surface Norm Distribution

Abstract

The recent development of 3D printing technology has brought concerns about its potential misuse, such as in copyright infringement and crimes. Although there have been many studies on blind 3D mesh watermarking for the copyright protection of digital objects, methods applicable to 3D printed objects are rare. In this paper, we propose a novel blind watermarking algorithm for 3D printed objects with applications for copyright protection, traitor tracing, object identification, and crime investigation. Our method allows us to embed a few bits of data into a 3D-printed object and retrieve it by 3D scanning without requiring any information about the original mesh. The payload is embedded on the object's surface by slightly modifying the distribution of surface norms, that is, the distance between the surface and the center of gravity. It is robust to resampling and can work with any 3D printer and scanner technology. In addition, our method increases the capacity and resistance by subdividing the mesh into a set of bins and spreading the data over the entire surface to negate the effect of local printing artifacts. The method's novelties include extending the vertex norm histogram to a continuous surface and the use of 3D moments to synchronize a watermark signal in a 3Dprinting context. In the experiments, our method was evaluated using a public dataset against center, orientation, minimum and maximum norm misalignments; a printing simulation; and actual print/scan experiments using a standard 3D printer and scanner.

Levenberg–Marquardt deep neural watermarking for 3D mesh using nearest centroid salient point learning

“…Delmotte et al 8 introduced a novel blind watermarking algorithm designed specifically for 3D printed objects that employed subtle modifications to the distribution of surface norms, particularly focusing on the distance between the surface and the center of gravity. Furthermore, the algorithm subdivides the mesh into bins and disperses the data across the entire surface, effectively reducing the impact of local printing artifacts.…”

A Robust Scheme for 3D Point Cloud Copy Detection

“…Hou et al [16] estimated the print axis by analyzing the layering artifact and added a sinusoidal frequency signal to the vertex coordinates calculated from the watermark. Delmotte et al [6] computed the norm histogram continuously over the entire surface instead of a discrete set of vertices and shifted the mean of each bin of the norm histogram to indicate the watermark value (0 or 1). These methods eliminate the adverse effects of sampling in the scanning process.…”

“…The key is the decomposition of the complex matrix into a low-rank matrix and a sufficiently sparse error matrix shown in Eq. (6).…”