## 4 Analysis of the Results
### Analysis of the Experimental Results
#### 4.2.2 Quantitative Analysis  
In this paper, the pixel accuracy, cross-ratio, and time complexity were used as the quantitative metric for the evaluation of segmentation results. In the following analysis, we assumed that the actual segmented image was P and the reference segmented image was G.  
1. Pixel accuracy  
Pixel Accuracy (PA) is expressed as the ratio of correctly labeled pixels to total pixels. Assume that \(P_{i}=\left\{p_{i1},p_{i2},\ldots,p_{im}\right\}\) is the number of pixels with the correct marks, and \(G_{j}=\left\{g_{j1},g_{j2},\ldots,g_{jm}\right\}\) is the gold standard number of pixels. The higher the pixel accuracy, the better the image segmentation; the formula is as follows:  
\[\text{PA}=\frac{\sum_{i=0}p_{i1}}{\sum_{i=0}\sum_{j=0}g_{j1}} \tag{9}\]  
According to formula (9), the higher the value of PA, the more overlapped the results and the gold standard. The PA curve for lung parenchymal image segmentation with juxtapleural nodules is shown in Figure 8.  
It is clearly shown that either RG or Watershed had a lower curve than the other methods. Thus, both methods lost some juxtapleural nodules, resulting in a \(P_{i}\) with less pixels. However, the overall trend of the PA of the rolling-ball method was toward higher values than that of other algorithms. In a number of previous experiments, \(r=65\) was usually used. When comparing with the algorithm described in this paper, the repair result of the juxtapleural inden  
Figure 7: Comparison between the proposed algorithm and the rolling-ball method to repair the same sequence: (**a**) Six consecutive CT images; (**b**) The gold standard; (**c**) r = 35 patch results; (**d**) r = 65 patch results; (**e**) patch results of our method. The PA curve values obtained with the method described in this paper represent the most accurate segmentation results. 2. Intersection over Union  
Intersection over Union (IoU) is a probability value used to compare the similarity and dispersion between sample sets and reflect the degree of coincidence between two segmented images. The higher the cross ratio, the better the image segmentation results. Assuming that the gold standard of the nodules in the image is \(G\) and the segmentation result of an automated method is P, the calculation of IoU is represented by formula (10). \[\text{IoU}=\frac{Area(G\cap P)}{Area(G\cup P)} \tag{10}\]  
From Figure 9, it is evident that the IoU curve of the proposed algorithm and that of the rolling method were significantly higher than those of the RG and Watershed methods. Furthermore, the IoU curve of the algorithm described in this paper was slightly higher than that of the ball-rolling method. At the same time, the segmentation results of the algorithm proposed in this paper were the most similar to the gold standard results. Figure 8: Comparison of the curves of pixel accuracy for the four methods. Figure 9: Comparison of the curves of Intersection over Union (IoU) for the four methods. 3. Time complexity  
The algorithm was also evaluated for time complexity. In this paper, taking \(i\) of the correlation of sequential images into account, we compared the shortest time, the longest time, and the average time that was consumed for segmenting the sequence of CT images. The results are shown in Figure 10.  
As shown in Figure 10, the proposed method had the shortest processing time. The watershed algorithm had the longest processing time and the region-growing algorithm had a processing time between the previous two, to some extent. The average time for processing leaflets was 0.75 s in Figure 10a and 0.63 s in Figure 10b. These average times were significantly shorter than those of the other two methods. Moreover, the average processing time decreased with the increase of the number of sequence images. This feature demonstrated that the automated threshold transfer took the correlation of the adjacent images into consideration and was able to find the threshold to adapt all the images and speed up the sequence image segmentation.