# Estimation of the Prostate Volume from Abdominal Ultrasound Images by Image-Patch Voting
## 4 Experiments and Results
### Ablation Study  
We performed an ablation experiment with a subset of our data set. Instead of using all four patch scales, we used patches with pixel sizes (\(64\times 64\)) and (\(128\times 128\)). For each patch size, we trained a ResNet-18 network for the transverse and another one for the sagittal plane. In addition, we trained a Twin Deep Convolutional Neural Network (TDCNN) for the transverse and another one for the sagittal plane. A TDCNN is similar to the QDCNN but contains two DCNNs and gets two patches as inputs with sizes (\(64\times 64\)) and (\(128\times 128\)) pixels. The model outputs were the \(cd\) and the \(co\) values for each endpoint.  
The patch sizes we used for the ablation study were smaller than the prostate sizes in our data set. Thus, these patch sizes allow us to observe the effect of the quadruplet patch structure, which consists of patches both smaller and larger than the prostate.  
We compared the volume estimations of these individual ResNet-18 networks and TDCNN with the volume estimations of experts on AUS images. The average MAVD between experts and these models were 13.5 cm\({}^{3}\) for the \(64\times 64\) ResNet-18 network, 11.4 cm\({}^{3}\) for the \(128\times 128\) ResNet-18 network, and 8.92 cm\({}^{3}\) for the TDCNN. Figure 10 shows a bar chart where each group of bars show MAVD values between two different markings of two experts and a model. The first three models are the models of the ablation study. The fourth model is the baseline model, and the last model is the model of the proposed system. The proposed system, QDCNN, has the best MAVD values, which shows the effect of the quadruplet patches and the quadruplet model. TDCNN has better MAVD values than single networks, but it cannot achieve the MAVD values of the baseline system. These MAVD values of the TDCNN show us that using patches only smaller than the prostate is not enough to obtain results ranging among experts.  
Feature extraction is one of the usage areas of convolutional neural networks [46]. It is known that good deep classifiers can also be used as good feature extractors because good classification results can only come from good features. Thus, we examined the feature-extraction ability of the proposed QDCNN by visualizing the outputs of the last layer before the classification layer of our network as a feature vector. We visualized the feature vectors of the distance tasks for the QDCNN, the individual \(64\times 64\) ResNet-18, and the individual  
Figure 10: MAVD values between five models and the markings of two experts on AUS images at two different times.  
\(128\times 128\) ResNet-18. We used t-SNE graphs [47] for 2D visualization, and Figure 11 shows two examples of distance tasks for each network. Each color represents a distance class, and each colored point represents a feature vector. The color charts in each graph shows colors associated with class numbers. Smaller numbers show shorter distances, while larger numbers show longer distances. We observed that the class values, especially for the small distances, are nicely separated and grouped together for the quadruplet network. The same grouping cannot be observed for the single-scale networks. These visual results indicate the quality of the features extracted by our network.