## 2 Proposed Method
### Detect AD Area
#### 2.3.2 Improved PCNN  
The traditional PCNN model has a large number of parameters to be set. The setting of these parameters has a great influence on the detection AD. In order to ensure the stability of the AD accuracy, based on the simplified PCNN model in [34], we incorporate the improved Otsu into the initial threshold setting of the model, only three parameters need to be manually set, which are \(\beta\), \(a_{\theta}\) and \(V_{\theta}\). Each neuron in the model consists of three parts: input field, modulation field and spike generator. The structure of the model is shown in Figure 6.  
In Figure 6, \(S_{ij}\) is the gray value of the pixel \((i,j)\) of the input image, and \((k,l)\) is the pixel adjacent to \((i,j)\); \(F_{ij}\) is the feeding channel; \(L_{ij}\) is the linking channel; \(\beta\) is the linking strength coefficient; \(U_{ij}\) is the internal activation signal; \(\theta_{ij}\) is the threshold; \(Y_{ij}\) is the pulse outputs of the input pixel; \(Y_{kl}\) is the pulse output of the neighborhood pixel; \(w\) is the linking weight matrix of channel \(L\); \(V_{\theta}\) is the amplification coefficient of the threshold \(\theta_{ij}\); and \(a_{\theta}\) is the time decay coefficient of threshold \(\theta_{ij}\). The mathematical iterative equation for the PCNN model is as follows:  
\[F_{ij}(n)=S_{ij} \tag{15}\]  
\[L_{ij}(n)=\sum_{kl}W_{ijkl}Y_{kl}(n-1) \tag{16}\]  
\[W_{ijkl}=\left\{\begin{array}{cc}0&(i,j)=(k,l)\\ \frac{1}{\|(i,j)-(k,l)\|_{2}}&(i,j)\
eq(k,l)\end{array}\right. \tag{17}\]  
\[U_{ij}(n)=F_{ij}(n)\Big{(}1+\beta L_{ij}(n)\Big{)} \tag{18}\]  
\[Y_{ij}(n)=\left\{\begin{array}{cc}1&U_{ij}(n)>\theta_{ij}(n-1)\\ 0&\text{others}\end{array}\right. \tag{19}\]  
\[\theta_{ij}(n)=e^{-a_{\theta}}\theta_{ij}(n-1)+V_{\theta}Y_{ij}(n) \tag{20}\]  
Here, \(W_{ijkl}\) is the reciprocal of the Euclidean distance between two adjacent pixel points of the image. It can be seen in the iterative equation of the model that the variable parameters in the model only have \(\beta\), \(a_{\theta}\) and \(V_{\theta}\). The PCNN parameters are set as shown in Table 3 and Figure 7.  
Figure 6: Simplified PCNN model.  
It shows in Table 3 and Figure 7, as the value of \(V_{\theta}\) increases, the contour of the detection result becomes clearer; as the value of \(\beta\) and \(a_{\theta}\) increases, the area of the detection result becomes larger and more noise points appear. Moreover, there would be no results can be detected when the value of \(\beta\) and \(a_{\theta}\) are small. In this section, the optimal threshold calculated by Otsu is set as the initial threshold of the PCNN model, which reduces the impact of manual setting parameters. After a lot of experiments for parameters setting, we set the \(\beta\) to 1.2, \(a_{\theta}\) to 0.5, and \(V_{\theta}\) to 28. However, there are some isolated points in the detection results. In order to obtain the accurately detection results, the maximum connected region is employed to remove these isolated points. The final result is shown in Figure 8.  
In Figure 8d, the area within the red line is the AD area marked by the expert, and the area within the yellow line is detection result by proposed method, it can be seen that the proposed detection method can accurately detect AD and the contour of the lesion is clear.