## 1 Introduction  
The development of three-dimensional (3D) printing technology has recently led to the explosive growth of 3D models. 3D printing services are therefore increasing rapidly [1; 2]. However, the copyright infringement of 3D models has become an issue for the 3D printing ecosystem of product distribution websites, 3D scanning, and design-sharing [3; 4]. To prevent the unauthorized use of copyrighted 3D models, we should find out which copyrighted 3D models which are distributed on the internet, thus, the issue of identification of 3D models remains. Various methods of extracting 3D model features have been proposed by many researchers [5; 6; 7; 8; 9; 10; 11; 12]. Because of the highly discriminative property of 3D skeleton-based features for 3D model representation, 3D skeleton-based approaches have attracted much attention [5; 6; 7; 8; 9; 10]. A 3D skeleton is not only an abstraction of the model at the center-line of the model but also a compact representation of the model, which is used for shape description, 3D model identification, and many other applications. The skeletons preserve the geometric and topologic properties of 3D models and are useful for 3D model matching, recognition, and retrieval [8]. There are three major skeletonization methodologies used in the literature: distance transform field-based methods [13; 14; 15], Voronoi diagram-based methods [16; 17; 18], and thinning-based methods [19; 20; 21; 22; 23]. The field-based methods extract a skeleton with missing branches. The Voronoi diagram-based methods extract a great number of spurious skeletal branches that are not essential for compact representation of the model [8; 16; 17; 18]. Moreover, the computations of the Voronoi diagram are a time consuming process. The thinning-based methods are faster than the Voronoi diagram-based methods and extract more detailed skeletons than do those extracted by the field-based methods [24]. A thinning process is to erode an object's surface layer by layer until only a skeleton remains. However, the existent thinning-based algorithms cannot preserve the connectivity of the skeletons of 3D mesh models. They accidentally remove some voxels that should be retained. Because they create new cavities and change the topology, an incorrect skeleton will be extracted. Figure 1 shows an example of removing a voxel that leads to the creation of a cavity during several continuous thinning procedures. To illustrate the disconnection more clearly, the figures are shown in a 3D and 2D \(xz\)-plane. Figure 1b,e shows a result after thinning the voxels in Figure 1a,d. They show that a cavity is created. Figure 1c,f shows a result after three times of thinning procedures. The cavity becomes larger, and the distance between the two separated branches becomes longer. The shape and topology of the skeleton are seriously damaged. Figure 1: An example of a damaged skeleton. (**a**) An initial state of a part of a 3D model shown in 3D; (**b**) A result shown in 3D after a thinning procedure; (**c**) A result shown in 3D after three times of thinning procedures; (**d**) The initial state of the part shown in 2D; (**e**) The result shown in 2D after a thinning procedure; (**f**) The result shown in 2D after three times of thinning procedures. In [21], the authors modified and improved the fully parallel 3D thinning algorithm described in [22]. The fully parallel thinning algorithm is based on four types of removing templates (classes A, B, C, and D). The target voxel, which is the currently investigated voxel, will be removed if the neighborhoods of the target voxel match one of the templates and satisfies another criterion. However, the skeletons extracted by the modified algorithm may be disconnected when thinning the 3D mesh models. A correct skeleton can increase the precision of skeleton-based 3D model identification. In the meantime, it can help to prevent copyrighted 3D models from being distributed illegally. Therefore, it is important to extract a correct skeleton.