A Lossless Watermarking for 3D STL Model Based on Entity Rearrangement and Bit Mapping

Introduction

With the prosperous development of 3D image processing and 3D modeling technology, 3D model has been widely used in medical diagnosis, 3D printing, product design and industrial manufacture. Meanwhile, the conflict of copyright of 3D model is becoming a serious problem. For example, in the collaborative design, it is challenging to determine the copyright belongings for design attenders.

Recently, watermarking has been implemented for the copyright protection for text, image and engineering graphics, and many advancements have been achieved. However, as the topology relation is complicated, model data is in disorder and the attack means for the model is various, the research on watermarking for 3D model is still limited. After Ohbuchi, Masuda, and Aono (1997) first proposed a watermarking scheme for 3D model, some works have been put forward in the past few years. The existed 3D model watermarking can be classified into the methods in space domain (Jhou, Pan & Chou, 2007; Wu & Dugelay, 2008; Yang & Ivrissimtzis, 2010; Choi, Kim, Kwon, Moon, Park, Shin, & Sohn, 2010; Wang, Lavoué, Denis & Baskurt, 2011; Luo & Bors, 2011) and the methods in transform domain (Ohbuchi, Mukaiyama & Takahashi, 2004; Wu & Kobbelt, 2005; Konstantinides, Mademlis, Daras, Mitkas & Strintzis, 2009; Ai, Liu, Zhou, Yang & Xie, 2009). As for the former, they can achieve high capacity and small computation, but the robustness is limited; while for the later, a good robustness can be obtained, but the capacity is limited and the computation is large.

3D model generally has special process precision, especially for medical diagnosis, military investigation and aerospace applications. Any slight modification to the data may results in serious consequences. Thus, watermarking for 3D model should keep the precision of it. As traditional watermarking introduces distortion to the host, it cannot be used for the occasions with high requirements in data precision. Since lossless watermarking/reversible watermarking can completely recover the original host after the watermark extraction, it is well suited for the content protection of 3D model.

Currently, reversible watermarking for 3D model was accomplished by modifying the geometric information (topology relation or vertex coordinates), which will introduce distortion in the watermarked 3D model. Generally, the more the embedded information is, the larger the distortion is. Although reversible embedding can recover the host to a certain, it still cannot completely resolve the geometric distortion. Recently, entity rearrangement was proposed for data hiding (Artz, 2001; Cheng & Wang, 2006; Lin, Tan & Tai, 2009; Tan, Lin, Tai & Chang, 2009; Lin, Chao, Chen, Yu & Hsu, 2013; Luo, Lu & Wang, 2010; Bogomjakov, Gotsman & Isenburg, 2008; Huang, Li & Wang, 2009; Tu, Tai, Isenburg & Chang, 2010; Tu, Hsu & Tai, 2010; Tu & Tai, 2012), which does not introduce geometric distortion. However, there still exists obvious contradiction between capacity and time complexity. Although Tu & Tai’s (2012) methods can achieve a capacity which is larger than that of the standard rearrangement method, the time complexity is high. In order to strike a good balance between capacity and time complexity, a lossless watermarking for 3D model based on entity rearrangement and bit mapping is proposed in this paper.

The rest of the paper is organized as follows: entity rearrangement and bit mapping is firstly presented. After that, the proposed watermarking scheme is described. Then, experimental results and analysis are provided. Finally, conclusions are drawn.