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 3D-printing 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.

We propose a new blind watermarking algorithm for 3D printed objects that has applications in metadata embedding, robotic grasping, counterfeit prevention, and crime investigation. Our method can be used on fused deposition modeling (FDM) 3D printers and works by modifying the printed layer thickness on small patches of the surface of an object. These patches can be applied to multiple regions of the object, thereby making it resistant to various attacks such as cropping, local deformation, local surface degradation, or printing errors. The novelties of our method are the use of the thickness of printed layers as a one-dimensional carrier signal to embed data, the minimization of distortion by only modifying the layers locally, and one-shot detection using a common paper scanner. To correct encoding or decoding errors, our method combines multiple patches and uses a 2D parity check to estimate the error probability of each bit to obtain a higher correction rate than a naive majority vote. The parity bits included in the patches have a double purpose because, in addition to error detection, they are also used to identify the orientation of the patches. In our experiments, we successfully embedded a watermark into flat surfaces of 3D objects with various filament colors using a standard FDM 3D printer, extracted it using a common 2D paper scanner and evaluated the sensitivity to surface degradation and signal amplitude.