# A Voxel-Based Watermarking Scheme for Additive Manufacturing
## 5 Conclusions  
In this article, we propose a watermarking scheme which prevents infringements of intellectual properties in AM industries. Our algorithm embedded watermarks into digital and physical contents, including geometric models, G-code programs, and printed parts. Hence, it widens the scope of copyright protection in AM. In the proposed watermarking method, the input geometric models can be expressed in polygonal formats as well as volumetric representations. Therefore, voxel models can be protected too. Besides embedding fingerprints, our encoder transforms digital models into distance fields. As a result, the contents obtain extra security. Because of using the SOM technique, our encoder is able to insert watermarks inside complex models and attach embossed as well as engraved signatures on the model surfaces. Thus, the proposed watermarking method is more flexible and adaptive than conventional ones.  
Experimental results validate the efficacy of the proposed watermarking scheme. The proposed procedure can embed and detect watermarks in models with complex shapes, for example, a tetrapod. In some experiments, we employed the encoder to create embossed and engraved marks on model surfaces such that quick verification of printed parts is possible. This functionality helps volunteers and hobbyists to share their creations and innovations. Other tests revealed that our method is able to insert watermarks in large curvy layers inside complicated objects. Hence, the watermarks are more resilient to attacks. In the proposed procedure, watermarks are implicitly encoded into G-code programs to protect these valuable properties. Hence, people can distribute their G-code programs to massively produce physical models. We presented three test cases to evaluate the efficiency of the watermark-detection methods. In all the test results, we found that the similarities between extracted and embedded watermarks are high even though the models had gone through digital-to-analog and analog-to-digital conversions. With these experiments, we showed that both the encoder and the decoder achieve the target goals of this research.  
The proposed watermarking process is performed in a voxel space. It invokes several specialized algorithms, including the SOM method, distance field computation, volume rendering, and virtual manufacturing procedures. These techniques possess potential applications in 3D modelling, 4D printing, and compliance mechanism creation. We plan to apply these algorithms in our future work to develop advanced modeling tools and mechanical facilities.  
Conceptualization, S.-K.U.; methodology, S.-K.U.; software, Y.-F.H. and Y.-C.K.; validation, S.-K.U., Y.-F.H. and Y.-C.K.; formal analysis, S.-K.U. and Y.-F.H.; investigation, S.-K.U. and Y.-F.H.; resources, S.-K.U. and Y.-F.H.; data curation, S.-K.U. and Y.-F.H.; writing--original draft preparation, S.-K.U.; writing--review and editing, S.-K.U.; visualization, S.-K.U., Y.-F.H. and Y.-C.K.; supervision, S.-K.U.; project administration, S.-K.U.; funding acquisition, S.-K.U. All authors have read and agreed to the published version of the manuscript.  
This research was funded by MOST Taiwan, grant number 109-2221-E-019-055-.  
Not applicable.  
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.