# Collusion Attack Resilient 3D Mesh Watermarking Based on Anti-Collusion Fingerprint Code
## 1 Introduction  
Digital watermarking is the process of hiding digital information in a noise-tolerant signal such as multimedia data. The watermark can be used to determine authorship when a copyright dispute occurs, and can be used as a fingerprint to track a distribution path when a prototype in the hands of only a few people, is leaked. Digital watermarking technology have been applied to various kind of multimedia contents such as 3D mesh watermarking [1], and 2D and 3D video watermarking [2, 3]. Collusion attack is one of the main techniques used for unauthorized removal of embedded marks [4]. Attackers can exploit different versions of the fingerprinted content to estimate the original content. Moreover, a simple averaging process of some different protected contents can be used to disable detection of the embedded pattern. To cope with collusion attacks, two categories of countermeasure techniques were previously researched. The first technique works by pre-warping at the signal-processing level, so that each copy of the multimedia content is varied in a slightly different way [5, 6]. However, in the case that the method fails to protect against collusion attack, it cannot provide information useful for tracking the attackers. The second countermeasures are based on the averaging-resilient fingerprint, which theoretically guarantees robustness against several attackers [4, 7, 8, 9, 10]. In contrast to pre-warping-based methods, the anti-collusion-based-techniques work passively by providing explicit clues for tracking the attackers.  
Recently, the demand for 3D mesh watermarking has increased due to the emergence of low-cost 3D printers. On the other hand, copyright issues will inevitably occur with the expansion of 3D model sharing platforms such as Thingiverse, Pinshape, and Sketchfab. In spite of various watermarking methods [1, 11, 12, 13], mesh watermarking techniques resilient to collusion attack wererarely considered [6; 14]. [PERSON] et al. [6] proposed anti-collusion watermarking for 3D meshes by pre-warping, which changes the vertices ordering and the associated faces. However, there is no algorithm that utilizes the averaging-resilient fingerprint code into 3D mesh watermarking.  
This paper is an extension of our previous work [15]. Our previous work proposed a mesh watermarking algorithm based on a mesh Laplacian matrix [16] with group-divisible partially balanced incomplete block design (GD-PBIBD). In this extension, we used two anti-collusion fingerprint code system: one is based on the GD-PBIBD [9], and another one is based on [PERSON]'s fingerprint code [17], and the codes were changed as a form of unsigned random pattern to prevent the attenuation of embedded signal by collusion attack. By modeling the detector response of the proposed method, we theoretically determined a threshold to minimize the detection error. As a result of our tests, we experimentally demonstrate that the proposed method does not lose recipient information during collusion attack.  
The rest of this paper is organized as follows. Section 2 is a brief introduction of the necessary background knowledge, and Section 3 explains the details of the proposed method. To demonstrate the performance of the proposed scheme, we tested our method with mesh benchmark sets, and report the results in Section 4. In Section 5, the conclusions are presented.