# A Voxel-Based Watermarking Scheme for Additive Manufacturing
## 1 Introduction  
Additive manufacturing (AM) techniques have been widely used in scientific, engineering, medical, and other applications [1, 2, 3]. An AM process is composed of three stages: geometrical modelling, G-code generation, and 3D printing [2, 3]. The resultant geometric models, G-code programs, and physical objects consume valuable resources, including human efforts, computing costs, energies, and raw materials. If these contents are illegally distributed, reproduced, and modified, the owners may encounter significant economic losses [4, 5], and they will hesitate to invest additional resources in AM. Consequently, the innovation and progression of AM industries will be in danger. In some volunteer AM communities, their members are willing to share their work and knowledge with others. Thus, ownership protection is not a concern [6, 7, 8]. However, in this situation, authentication and annotation of contents are still required to avoid misuse of the products.  
Watermarking procedures had long been used to enhance the securities of digital data, including texts, music, images, and videos [9, 10, 11]. By analogy, in AM industries, people inserted identification signals into digital and physical models to secure their intellectual properties [12, 13, 14]. Nonetheless, mechanisms for protecting G-code programs were seldom discussed in these publications. In an AM process, the quality of the resultant objectis mainly decided by the G-code program. Thus, we spend a lot of efforts to decide the printing direction, construct the supporting structures, slice the geometric model, select the hatching patterns, and schedule the toolpaths before generating the G-code program. Besides, to ensure a high-quality 3D printing, we must also conduct experiments, calculations, and simulations to obtain feasible printing parameters, including the nozzle temperature, raw material type, printing speed, etc. Therefore, for the sake of economy, G-code programs are valuable properties. Furthermore, well-tuned G-code programs can be used to repeatedly produce physical models to reduce production costs. Thus, G-code programs are one of the key gradients for mass-production in AM applications. Based on these reasons, G-code programs should be carefully protected too.  
In most of the published watermarking algorithms, the digital models are presumed to be expressed in polygonal representations, for example, stereolithography (STL) and OBJ formats [2; 3; 4; 5]. However, tissues and organs, segmented from 3D medical image data, are composed of voxels [15]. They are not polygonal models and cannot be watermarked by using these conventional methods. To protect or authenticate them, we must invent new watermarking techniques. In some conventional watermarking procedures, watermarks are created on the surfaces of digital models. These watermarks could be damaged in the G-code generation, printing, and post-processing stages and become hard to verify [4; 5]. Some other researchers proposed to insert watermarks inside digital models [16; 17]; thus, the printing and post-processing processes would not remove these signals. However, these algorithms possess weakness too. For example, the geometrical complexities of the regions for inserting watermarks are usually simple. Secondly, these methods lack the techniques to uncover watermarks in digital models, thought they are capable to reveal watermarks in printed results. Thirdly, special facilities are required to uncover and verify watermarks. Hence, it will be beneficial to design an adaptive watermarking scheme which can insert fingerprints anywhere in digital and physical models and can adjust the encoding process to accommodate the shapes of the target models, the underlying 3D printing platforms, and the intended applications of the products.