The Lobe Fissure Tracking by the Modified Ant Colony Optimization Framework in CT Images

1. Introduction

Figure 1. The lung CT image for (a) axial slice (whole lung) and (b) sagittal slice (right lung). Whole information of lung lobe is more suitable than axial views or coronal view.

2. Related Works

2.2. Robinson Filter and Kirsch Filter

In this study, we also applied two powerful filters to enhance the region edges, such as Robinson filter and Kirsch filter [14]. Robinson filter and Kirsch filter are the compass masks. In their methods, each point of the image is used by the convolution algorithm with eight parts, as shown in Figure 2 and Figure 3. The maximum response of each part is produced only corresponding to a certain given edge direction. The maximum of all of the eight directions can be regarded as the output of the image edge amplitude. The serial numbers of the part with the maximum response are the codes of edge direction.

Figure 2. The masks of Robinson filter.

Figure 3. The masks of Kirsch filter.

3. Tracking Framework for Lobe Fissure Based on Modified ACO Algorithm

3.2. Design of the Modified ACO Method

The modified ant colony optimization (ACO) algorithm is used to track the lobe fissures in lung CT images. The idea of ACO is that the ants will find a best path to walk by their pheromone. The procedure of modified ACO algorithm is listed in Figure 4, where R is the number of path-tracking rounds and N is the number of ants. First, the input images are transferred to the sagittal slices from each axial CT cases. Second, we marked two points to be the start and end points on the boundary of lung; the ants can use the initial pheromone table to search and create the candidate paths. In each round, the pheromone table will be updated by the updating rules and the local optimal path will also be found. Last, the lobe fissure is the final optimal path through R rounds and N ants. Figure 5 shows the flowchart of proposed system.

Figure 4. The procedure of modified ACO algorithm.

Figure 5. The flowchart of proposed ACO framework.

3.3. Define the Initial Pheromone

Figure 6a,d are the original sagittal views of lung CT images. We can see that the intensity of lobe fissure is higher than the lung region, but is lower than the lung tubes. Therefore, we use Otsu’s method [15] to be a location map to find out lung tubes, as shown in Figure 6b,e. The initialized pheromone can be set by the intensity function (IF):

$$IF(I)=\alpha {\left(\frac{(\max (I)-I(x,y))}{\max (I)}\right)}^k$$

(1)

Where I(x,y) is the intensity of image I, max(I) is the maximum intensity in the image, and k is a positive constant that can control the intensity [16]. Figure 6c,f show the example results by the intensity function. The intensity function can increase contrast of image; the weak edges on the image can be enhanced. According to the definition of intensity function, a corresponding pheromone table PHM can be created as:

$$PHM(x,y)=\frac{I{F}_i(x,y)}{\max (I{F}_i)}$$

(2)

Where i of pheromone table is the number of images, IF_i is the i-th processing by the intensity function. The location map (LM) is defined as:

$$LM(x,y)=\frac{\max (OtsuMethod)-OtsuMethod(x,y)}{\max (OtsuMethod)}$$

(3)

Figure 6. The examples for the definition of initial pheromone: (a,d) The sagittal view of a lung CT image; (b,e) after Otsu’s method; (c,f) after intensity function.

3.4. Edge Enhancement

In the proposed ACO procedure, we use Robinson filter and Kirsch filter to assist increasing the efficiency of proposed methods. In our study, the amplitude of Robinson filter (RFA) on the lobe fissure is lower than other regions of lung, as shown in Figure 7a,b. The amplitude of Kirsch filter (KFA) of lobe fissure is almost high, as shown in Figure 7e,f. Figure 7c,d show the orientation of Robinson filter (RFO); Figure 7g,h show the orientation of Kirsch filter (KFO). Because the identified lobe fissures always have the same direction, the shortest path may not be the optimal in proposed ACO algorithm. In order to avoid this problem, we define the equation to find the optimal path in each round. RFO and KFO have eight directions in each processing result. We denote RFO of the path as Path_RFO, and KFO of the path as Path_KFO. C_RFO and C_KFO are the counts of Path_RFO and Path_KFO to correspond with eight directions. Moreover, the path amplitudes of RFA and KFA are denoted as Path_RFA and Path_KFA, respectively. Those can calculate the count number of the maximum direction with two amplitude results of compass filters, and determine lobe fissure correctly.

$$\begin{array}{c}{C}_{RFO}=count(Pat{h}_{RFO})\\ C_{KFO}=count(Pat{h}_{KFO})\\ Robinson\times Kirsch=\frac{sum(Pat{h}_{RFA})}{sum(Pat{h}_{KFA})\times \max (C_{RFO})\times \max (C_{KFO})}\end{array}$$

(4)

Figure 7. Examples of edge enhancement after (a,b) the amplitude of Robinson filter (RFA); (c,d) the orientation of Robinson filter (RFO); (e,f) the amplitude of Kirsch filter (KFA); (g,h) the orientation of Kirsch filter (KFO).

3.6. Optimal Path Detection

According to Euclidean distance formula, the distance D_i is 8-neighbor of I(x₁,y₁) to I(x₂,y₂). The parameter i can provide the direction information that can be calculated as following:

$$D_i=\sqrt{{(neighbo{r}_i-IF(x,y))}^2}$$

(9)

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 τ_i to find out the minimum of D_i and intensity function. The parameter τ_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:

$$\begin{array}{l}A{M}_i=\{\begin{array}{l}\begin{array}{cc}{\tau }_i=\min (\frac{D_i}{PHM}),& \hspace{0.17em}if p>T_p\end{array}\\ \begin{array}{cc}\left[RandomStep\right]\hspace{0.17em},& \hspace{1em}if p\end{array}\le T_p\end{array}\\ \begin{array}{cc}\left[Random\hspace{0.17em}Step\right]:\hspace{1em}\{\begin{array}{l}V,\hspace{1em}\hspace{1em}\hspace{1em}if q>T_q\\ Random, if q\le T_q\end{array}& \end{array}\end{array}$$

(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:

$$OP=\min (\frac{P(A{M}_i)}{Robinson\times Kirsch})$$

(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 Figure 8 and Figure 9.

Figure 8. The first example for optimal path of ant movement with N = 10, where (a) R = 1; (b) R = 2; (c) R = 3; and (d) R = 5.

Figure 9. The second example for optimal path of ant movement with N = 10, where (a) R = 1; (b) R = 2; (c) R = 3; and (d) R = 5.

4. Experimental Results

Figure 10. The details of proposed ACO framework for lung fissure tracking.

Table 1. The values of parameters for the proposed ACO framework.

Figure 11. The first experimental result for the left lung CT by the proposed ACO framework.

Figure 12. The second experimental result for the right lung CT by the proposed ACO framework.

Figure 13. The conception of trustful region for lobe fissure tracking.

Figure 14. The relationship of parameters: false lobe fissure (FLF), true lobe fissure (TLF), and false real lobe fissure (FRLF).

Table 2. The experimental results of precision, recall and F-measure by the proposed ACO method for 15 left lung cases.

Table 3. The experimental results of precision, recall and F-measure by the proposed ACO method for 15 right lung cases.

5. Discussion

6. Conclusions

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