# A 2D-View Depth Image- and CNN-Based 3D Model Identification Method
## 3 Experimental Results
### Deformable 3D Model Retrieval with Missing Parts  
In this section, we present the comparative performance of the proposed method on SHREC'17 _Deformable Shape Retrieval with Missing Parts_. We named our method the 2D-view depth image- and CNN-based method (2 VDI-CNN) and participated this test. As described in Section 2.2, there are two challenges in the contest: irregular holes and range data, and both have 10 categories. Hence, in the training part, for each challenge we trained a GoogLeNet and also used default settings of our method, except the last softmax layer of the GoogLeNet was changed to output 10-way prediction values. The training used momentum with a decay of 0.9 and a learning rate of 0.01, and every epoch is decayed using an exponential rate of 0.96 with the dropout ratio in the last fully connected layer set to 0.1. In the test part, as the test is about comparing retrieval accuracy, each 3D model is supposed to be represented by feature vectors, and it is simply generated in our method by averaging prediction values of 42 depth images of a 3D model in each dimension. Thus, a 3D model is represented by a 10-dimensional feature vector, and the dissimilarity between two 3D models is given by the Euclidean distance of the corresponding feature vectors. In the end, for each challenge we were asked to calculate the dissimilarity between each pair of 3D models in the test set to construct a dissimilarity matrix \(\left(d_{ij}\right)_{n\times n}\), where \(n\) is the number of 3D models in the test set and \(d_{ij}\) denotes the dissimilarity between the 3D model \(i\) and 3D model \(j\). With the matrices, retrieval performance is compared based on the precision-recall (P-R) curve and four quantitative measures: nearest neighbor (NN), first tier (1-Tier), second tier (2-Tier) and discounted cumulative gain (DCG). * Nearest neighbor: The percentage of best matches that belong to the query's class. * First tier and second tier: The percentage of models belonging to the query's class that appear within the top \((K-1)\) and \(2(K-1)\) matches where the number of models in the query's class is K.
* Discounted cumulative gain: A statistic that weights correct results near the front of the list more than correct results later in the ranked list. * Precision-recall curve: Precision is the ratio of retrieved models that are relevant to a given query, while recall is the ratio of relevant models to a given query that have been retrieved from the total number of relevant models. Thus, a higher P-R curve indicates better retrieval performance. The four quantitative measures range from 0 to 1, and higher values indicate better retrieval performance. For more details about the metrics, we refer readers to [29]. In the contest, there are 11 participating methods (if including runs with different parameters, there are totally 15 algorithms), where six are supervised learning-based and the others are not learning-based. These methods also can be roughly divided into the Laplace-Beltrami operator-based method, the bag-of-word framework-based method, and the 2D view-based method. Readers can refer to [28] for a detailed description of each method. Tables 3 and 4 shows the four quantitative measures for irregular holes and range data, respectively. Figure 8 shows P-R curves for all methods on the two challenges. In the irregular holes challenge, from the left side P-R curve graph in Figure 8, we can obviously see the top three performing methods among 11 competing methods (without counting different runs): DLSF is the best, followed by BoW+RoPS and our 2 VDI-CNN. From Table 3, it can be observed that in terms of 1-tier, 2-tier, and DCG, 2 VDI-CNN is ranked third after DLSF and BoW-RoPS. The NN is ranked second. In the range data challenge, from the right side P-R curve graph in Figure 8, we can see that 2 VDI-CNN and BoW+RoPS are the best-performing methods among the six competing methods.