# 3D Model Identification Using Weighted Implicit Shape Representation and Panoramic View
## 5 Experimental Results  
In this section, some experimental results about the shape normalizations are shown first. To achieve high precision of 3D model identification, how to accurately normalize the shapes of the models is of great significance in practice. Figure 3a,c are original sumotori and tortoise models. Figure 3b is deformed version of sumotori model by articulating around its joints in different ways. Figure 3d is partially removed version of tortoise model. There is a certain extent of difference between the original models and deformed and removed models. If we extract 6 range images from each view point of six degree of freedom, we can obtain 24 possible poses of a 3D model [8]. We only selected the most representative range image from all possible poses of a model. Figure 4a-l show the range images which have the most representative surface of the models using PCA, ISR, and WISR, respectively. The main body and face in Figure 4b are oblique. Figure 4d shows left side of the model. Figure 4f,h show the range images were viewed obliquely from above. Both Figure 4j,l show their fronts to a view point, which means the deformed and removed models were well normalized using WISR.  
Figure 2: The cylinder around a model and its panoramic view-based range image; (**a**) Cylinder; (**b**) Panoramic view-based range image.  
We evaluated the proposed identification method with 1200 non-rigid 3D models in SHREC 2015 benchmark. The models consist of 24 deformed versions of 50 classes. We selected one model for each class to compose 50 query models. We also experimented with the other 3D model identification methods: combination of PCA and SIFT (PCAS) [9], that of continuous PCA, normal PCA, 2D discrete  
Figure 4: The most representative range images of shape normalized models using PCA (**a–d**): original and deformed sumotori model, original and partially removed tortoise model; ISR (**e–h**): original and deformed sumotori model, original and partially removed tortoise model; and WISR (**i–l**): original and deformed sumotori model, original and partially removed tortoise model.  
Figure 3: Original, deformed and partially removed 3D models; (**a**): original sumotori model; (**b**): deformed sumotori model; (**c**): original tortoise model; (**d**): partially removed tortoise model.  
Fourier transform, and 2D discrete wavelet transform (CPCA) [10], and that of dodecahedron and SIFT (DODE) [11]. Two types of experiments were performed to evaluate the performances of the methods. First one is to identify the 50 original query models. Then we removed some parts of the models such as arms and legs. Second experiment is to identify the 50 partially removed query models. The percentage of removal ranges from 6.1% to 33.6%. The average percentage is 13.8%. We set the range of the number of clusters from 1 to 10, which means the \(K\) is set to 10. Both the sample rate \(F\) and the number of rays \(M\) are set to be 180. We performed the experiments on an IBM compatible computer with a 3.4 GHz CPU and a 4 GB random-access memory. The average feature size and matching time of the corresponding method for 1200 models are shown in Table 1. Because of using only one range image, the proposed method provides small size of feature and fast matching speed. Figure 5 shows the precision of identification for each method. Although the feature size is greatly reduced, the precision is still greater than those of the other 3 methods even with the removed versions.