# A 2D-View Depth Image- and CNN-Based 3D Model Identification Method
## 3 Experimental Results
### 3D Model Identification  
Here, we test the 3D model identification performance of our method on the data that is described in Section 2.2. We will first show the identification results on default settings of our method, and then we will demonstrate how the number of depth images and the number of 3D models in each category that used for training affect identification results. As described in Section 2.2, from 50 categories in dataset of SHREC'15 _Non-Rigid 3D Shape Retrieval_, we use 20 pose-deformed 3D models for each category, which are 1000 models in total, to train the GoogLeNet. Each 3D model is represented by 42 depth images, and each depth image is assigned the label of the corresponding category. These depth images and corresponding labels are put into the GoogLeNet, for which the last softmax layer is changed to output 50-way prediction values. The training used momentum with a decay of 0.9, a learning rate of 0.001, and every epoch is decayed using an exponential rate of 0.96 with a dropout ratio in the last fully connected layer set to 0.5. After the GoogLeNet is trained, the remaining four pose-deformed 3D models in each category and 200 irrelevant 3D models are used for testing. Each test 3D model is also represented by 42 depth images and input to the trained GoogLeNet, which will output \(42\times 50\) prediction values. These are averaged on each dimension to generate a 50-dimensional final prediction. Then, by setting a threshold to the final prediction, we can yield an identification result. Regarding the experiment in this section as from the point of view of the 3D model identification system for copyright protection, it can be considered that there are 50 original copyrighted 3D models in the database of the identification system. Thus, in the following article, we define the query 3D model that is deformed version of an original copyrighted 3D model as \(Q_{c}\) and define the query that is irrelevant to the original copyrighted 3D models as \(Q_{i}\). To evaluate performance, we use True Positive (\(tp\)), True Negative (\(tn\)), False Positive (\(fp\)), False Negative (\(fn\)), and Accuracy (\(Acc\)). * True Positive: If a query 3D model is a deformed version of an original copyrighted 3D model (\(Q_{c}\)) and the identification system correctly identifies the query 3D model. * True Negative: If a query 3D model is irrelevant (\(Q_{i}\)) and the identification system correctly identifies it as irrelevant. * False Positive: If a query 3D model is irrelevant (\(Q_{i}\)) but the identification system wrongly identifies it as one of the 3D models in the database, or if a query 3D model is a deformed version of an original copyrighted 3D model (\(Q_{c}\)), but the identification system identifies it as a wrong one in the database, which means the query is not the deformed version of the 3D model that was identified by the system. * False Negative: If a query 3D model is a deformed version of an original copyrighted 3D model (\(Q_{c}\)), but the identification system identifies it as irrelevant. * Accuracy: \(Acc=\frac{tp+tn}{tp+tn+fp+fn}\)  
The calculation process is written in pseudo code in Table 1. Table 2 shows the identification results that using the 400 test 3D models, and Figure 5 shows the corresponding graph between accuracy and threshold. From the table and graph, we can see that the method works best when the prediction threshold is 0.7, yielding 93.5% accuracy: 183 3D models are correctly identified from the 200 \(Q_{c}\) 3D models and 191 irrelevant 3D models are correctly rejected from the 200 \(Q_{i}\) 3D models. If users do not want to miss any deformed versions of their 3D models from a target database, they can set a lower threshold, such as 0.4, which correctly identified 199 out of the 200 deformed 3D models. However, there would be more false positive cases. In other words, without the premise of an ideal 3D model identification system existing, users are free to select the threshold to adjust the performance of the identification system to meet their own needs.