## 3 Tracking Framework for Lobe Fissure Based on Modified ACO Algorithm
### Optimal Path Detection  
According to Euclidean distance formula, the distance \(D_{i}\) is 8-neighbor of \(I\)(x\({}_{1}\),y\({}_{1}\)) to \(I\)(x\({}_{2}\),y\({}_{2}\)). The parameter \(i\) can provide the direction information that can be calculated as following:  
\[D_{i}=\sqrt{\left(neighbor_{i}^{-}-IF(x,y)\right)^{2}} \tag{9}\]  
Figure 7: Examples of edge enhancement after (a,b) the amplitude of [PERSON] filter (_RFA_); (c,d) the orientation of [PERSON] filter (_RFO_); (e,f) the amplitude of [PERSON] filter (_KFA_); (g,h) the orientation of [PERSON] filter (_KFO_). Then, we used two ant movement (_AM_) steps to create a new direction for each ant. Especially in random step, that can be eight random directions, or be only a chosen direction, which is controlled by \(q\). The other one is to compute \(\tau_{i}\) to find out the minimum of \(D_{i}\) and intensity function. The parameter \(\tau_{i}\) means the ant choose \(i\)-th direction to be a new direction, which is controlled by \(p\). The parameters, \(p\) and \(q\), are probability values to control the path direction during ant moving. \(T_{p}\) and \(T_{q}\) are the thresholds of \(p\) and \(q\), respectively. \(V\) is a vector connecting end point that is used to avoid the ant movement entering an infinite loop. The ant movement (_AM_) function is defined as:  
\[ \begin{split} AM_{i}=\begin{cases}\tau_{i}=\min(\frac{D_{i}}{ PHM}),&\text{if }\ p>T_{p}\\ \left[\text{\emph{RandomStep}}\right],&\text{if }\ p\leq T_{p}\\ \left[\text{\emph{Random Step}}\right]:&\begin{cases}V,&\text{if }\ q>T_{q}\\ \text{\emph{Random}},&\text{if }\ q\leq T_{q}\\ \end{cases}\end{split}  \tag{10}\]  
Finally, when ants completed all paths from start point to end point, we can choose the shortest one to be the optimal path. The optimal path (_OP_) is defined as:  
\[\text{\emph{OP}}=\min(\frac{P(AM_{i})}{\text{\emph{[PERSON]}}\times\text{ \emph{[PERSON]}}}) \tag{11}\]  
Where \(P(AM_{i})\) is the path length of \(AM_{i}\). Through the completed framework of proposed ACO method, the optimal path of lobe fissure can be detected by \(N\) ants with \(R\) rounds, as shown in Figures 8 and 9. In the analysis of system performance, we set the obtained lobe fissure by the proposed system to be \(LF_{ACO}\), and the artificial fissure path by the professional physician to be \(LF_{P}\). Ideally, these two parameters are compared with each other. However, the path widths of \(LF_{ACO}\) and \(LF_{P}\) are a single pixel. If we compared \(LF_{ACO}\) and \(LF_{P}\) directly, the results of performance may be inaccurate and unsatisfactory. Therefore, we applied the statistical conception of trustful region for lobe fissure comparison, shown in Figure 13. The conception of trustful region here is to broaden the widths of \(LF_{ACO}\) and \(LF_{P}\) from 1 pixel to 5 pixels, respectively. Then we can obtain the trustful region of \(LF_{ACO}\) and \(LF_{P}\), that are TR(\(LF_{ACO}\)) and TR(\(LF_{P}\)). If the points on TR(\(LF_{ACO}\)) are located in TR(\(LF_{P}\)), we can say that the points belonged to the path of lobe fissure. It can avoid the fault that only compared \(LF_{ACO}\) and \(LF_{P}\) by 1-pixel width. Figure 11: The first experimental result for the left lung CT by the proposed ACO framework. Figure 13: The conception of trustful region for lobe fissure tracking. In the analysis of performance metric, the precision, recall and F-measure [17; 18; 19; 20] are used to analyze the performance of the proposed ACO method.