## 4 Experiments and Results
### Effects of the Proposed Methods  
In order to quantitatively analyze our proposed MSH-CNN method, we designed the following CNNs for comparison:  
(1) MSH-CNN-RI: The 3D multi-scale gradual integration module (I1-I2-I3 and I3-I2-I1) in MSH-CNN was replaced with the radical integration I1\(||\)I2\(||\)I3 in the same layer. The \"\(||\)\" symbol indicates concatenation by channel, as shown in Figure 5.  
Figure 4: The free receiver operation characteristic (FROC) curves of different methods. Figure 3: Examples of candidate nodule classification by our algorithm. Each example is a transverse plane of candidate nodules; P is the probability that the algorithm predicts an example as real nodule. (2) MSH-CNN-IC: II-I2-I3 (\"Input 1\") and I3-I2-II (\"Input 2\") in the MSH-CNN were interchanged, and Input 1 was input into Archi-2, while Input 2 was input into Archi-1, and the structure was similar to that shown in Figure 2d. (3) MSH-CNN-AF: The fusion method of the MSH-CNN was modified to addition fusion without weights. (4) MSH-CNN-II: In MSH-CNN, the network in Archi-1 was replaced by that in Archi-2 (including 3D inception), so that both branches contained 3D inception. (5) MSH-CNN-EI: In MSH-CNN, the network in Archi-2 was replaced by that in Archi-1 (excluding 3D inception), so that neither branch contained 3D inception. (6) MSH-CNN-LT: The training and test sets were expanded, and the MSH-CNN model was trained and tested on the datasets of LUNA16 + Tianchi. The Tianchi dataset was provided by the Aliabad Cloud of Intelligent Diagnosis of Pulmonary Nodules. The training and validation sets contained a total of 800 CT samples and 1245 nodules. Table 5 summarizes the best performance of each network. Our method had higher average CPM score than other networks, which can be seen by applying each network to the same dataset. Our algorithm also performed better on the extended dataset, whether it was on the average CPM score or the sensitivity corresponding to different false-positive rates. The following conclusions could be drawn:  
(1) MSH-CNN was 0.025 higher than MSH-CNN-RI (average CPM). At the 1 FP/scan, the sensitivity of MSH-CNN exceeded 0.9, but MSH-CNN-RI was a little worse than 0.9. This shows that, at the nodule block integration stage, 3D multi-scale gradual integration can make better use of the structural information of the nodules and its neighboring organs than the radical integration method at the same level. (2) Comparison between MSH-CNN-IC with MSH-CNN. The sensitivity difference between the two structures was smaller than that of other networks. The sensitivity of MSH-CNN-IC was slightly higher than that of MSH-CNN at 0.125 and 1 FP/scan, but the sensitivity of MSH-CNN was high when  
Figure 5: The network structure of multi-scale heterogeneous three-dimensional (3D) convolutional neural network with radical integration (MSH-CNN-RI): radical integration of nodule blocks on the same layer. The two branches of the network have the same structure as the MSH-CNN. The numbers above the thick arrows represent kernel size, e.g., \(3\times 3\times 3\) (s: stride, p: padding, Conv: 3D convolution). The figure after @ denotes the number of channels. The parameters \(\gamma_{1}\) and \(\gamma_{2}\) are weights automatically learned from the training dataset. the FP/scan was other values. This shows that different networks concern different input characteristics, and that a heterogeneous structure is useful. (3) This part analyzed the influence of the fusion method on the classification task of the nodule. The average CPM scores of MSH-CNN-AF and the sensitivity of different false-positive rates were lower than those of MSH-CNN. This shows that using a set of weights which are automatically determined by back propagation can better complement the two branches. (4) To verify the role of the 3D inception layer, we compared MSH-CNN-II and MSH-CNN-EI. As can be seen from Table 5, MSH-CNN-II had high sensitivity at low FP/scan.