## 7 Experimental Results  
In this section, we show some experimental results of extracting skeletons by different skeletonization algorithms. The proposed algorithm is compared with five other skeletonization algorithms. The first one was described in [13], which used fast marching methods (FMM). The second one was proposed in [19; 20], which built a skeleton via the 3D medial surface and axis (MSA). The third one was proposed in [23], which modified the templates and added two additional criteria (MTTAC). The fourth one was proposed in [21; 22], which used a fully parallel thinning algorithm (FPT). The last one was proposed in [26], which used the cell complexes and medial persistence (CCMP). The performances of the algorithms were evaluated with 100 3D mesh models in the SHREC 2015 benchmark. We show comparison results of three representative models of animals and humans. Figure 11 shows the three models: armadillo, centaur, and manta ray. The numbers of the triangles are 17,656; 18,868; and 20,000, respectively. Before thinning the models, we first voxelized the mesh models to \(50\times 50\times 50\) grids as in [27]. Figure 10: Correcting templates of class F.  
The skeletons extracted by the six algorithms are shown in Figure 12. Figure 12a-c shows the skeletons extracted by FMM. The skeletons of the armadillo's tail, the centaur's head and the manta ray model's wings are not extracted. Figure 12d-f shows the skeletons extracted by MSA. The skeletons of the armadillo's and the centaur's heads contain spurious branches. Especially in Figure 12f, the skeleton of the manta ray model has many branches that are not essential. Figure 12g-i shows the skeletons extracted by MTTAC. Because too many voxels of the skeletons are removed, the skeletons are widely scattered. Figure 12j-l shows the skeletons extracted by FPT. The skeletons of the armadillo's head and the centaur's tail are disconnected, and those of the manta ray model's wings are not extracted. Figure 12m-r shows the skeletons extracted by CCMP. We adjusted the MP score to extract a connected skeleton of the centaur. However, the skeleton contained some noises as shown in Figure 12n. With the same MP score, the extracted skeletons of the armadillo and the manta ray contained more noises as shown in Figure 12m,o. We also adjusted the MP score to extract a skeleton of the centaur without noise. However, the skeleton of the centaur's head is disconnected as shown in Figure 12q. With the same MP score, the skeleton of the armadillo's head is also disconnected as shown in Figure 12p. There was almost no skeleton extracted from the manta ray as shown in Figure 12r. Figure 12s-u show the skeletons extracted by the proposed algorithm. It extracts the skeletons of the manta ray model's wings and does not extract spurious branches. The connectivity of the skeletons of the models are also preserved. To evaluate the robustness of the proposed method, we reduced the number of triangles of the models to 50% and scaled the sizes of the models to 50%. If the number of triangles is decreased, the smooth surface of the 3D model becomes rough. Thus, the generated voxels are also rough like adding noises. Scaling the size of the 3D model means that the volume of the 3D model is reduced. Figure 13 shows the skeletons extracted from the changed models. They are very similar to those of the original models, which means that the proposed method is robust to the change in the number of patch faces and of scaling sizes. Figure 11: Models in SHREC 2015 benchmark. (**a**) Front of the armadillo; (**b**) Side of the armadillo; (**c**) Front of the centaur; (**d**) Side of the centaur; (**e**) Front of the manta ray; (**f**) Top of the manta ray. Figure 12: _Cont._  
Figure 12: Skeletons extracted by five algorithms.