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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.
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