The torso phantom data were provided by Dr. Tai-Been Chen from I-Shou University. It is designed for comparing the accuracy of different segmenting methods in this study. The information of phantom container is shown below. The region of the simulated heart container is injected a large amount of medicine. This makes the image appear in high intensity on PET images.
Figure 3.1: The information of phantom container.
PET and CT both have 114 slices where pixel size is 256 256 in the phantom experiment. The PET images which contain high intensity identify the area with high activity in the simulator. Different segmenting methods are used to segment the region of the highest activity in the simulator. The aim of this phantom study is to compare the accuracy of the highest region by these different segmenting methods. The following is the 43th slice of PET and CT images.
Figure 3.2: (A) The 43th slice of 114 PET images. (B) The 43th slice of 114 CT images.
The region of high activity can be observed in the PET image. From CT image, the profile and organ can be observed very clearly. Therefore, we can find the boundary of the simulated heart container from CT image. Because the region of the boundary of simulated heart container is injected a large amount of medicine, the true highest activity region can be selected by CT images’ good outlining effect. It is shown as follow:
Figure 3.3: (A) The boundary of simulated heart container can be found from CT images. (B) The region of the true highest activity of 43th slice of CT image.
A B
A B
After obtaining the true highest activity region, we can compare the accuracy by F-measure (van Rijsbergen, 1979). First, the GMM is used to segment PET images. The following is kernel density curve of PET image data.
0 500 1000 1500 2000 2500 3000 3500
0.0000.0020.0040.0060.008
Kernel density for the PET data
intensity
Density
-20 -15 -10 -5 0 5 10
0.000.050.100.150.20
Kernel density for the PET data
log(intensity)
Density
Figure 3.4: (A) The kernel density curve of PET image (B) Take log of data and plot density curve. These peaks are more obvious.
By the kernel density curve from Figure 3.4, the initial values of GMM can be determined. And the model with minimum value of BIC can be selected as k 6 (the number of clusters) from Figure 3.5 shown as follow.
738000740000742000744000746000748000
PET
BIC
(A) (B)
The results of segmenting PET image by GMM shown as following. It obviously overestimates the real highest region.
Figure 3.6: k 6, The result of segmenting PET image by GMM with KDE.
Next, the fusion image of PET and CT is segmented by GMM. The following is kernel density curve of fusion image data.
0.0 0.2 0.4 0.6
05101520
Kernel density for the Fusion data
intensity
Density
-5 -4 -3 -2 -1 0
0.00.51.01.5
Kernel density for the Fusion data
log(intensity)
Density
Figure 3.7: (A) The kernel density curve of fusion image of PET and CT. (B) Take log of data and plot density curve. These peaks are more obvious.
(A) (B)
The initial values of GMM can be determined by the kernel density curve from Figure 3.7. And the model with minimum value of BIC can be selected as k 8 from Figure 3.8 shown as follow.
6 7 8 9 10
-413500-412500-411500-410500
Fusion
clusters (k)
BIC
Figure 3.8: The BIC values of different clusters for GMM (Fusion). k is the number of clusters.
The result of segmenting fusion image by GMM is shown as following. It is better than the result of only implementing segmenting PET image at the highest region.
Finally, the two-dimensional GMM is fitted to the PET and CT data. And the 1st order and the 2nd order spatial dependence are used to in GMM as shown Figure 2.3.2 and Figure 2.3.3 on Chapter 2. The followings are the BIC values of different clusters of these three
1st spatial dependence in GMM(PET & CT)
clusters (k)
BIC
10 11 12 13 14 15
-11300000-11260000-11220000
2nd spatial dependence in GMM(PET & CT)
clusters (k)
BIC
Figure 3.10: The BIC values of different clusters. (A) GMM(PET & CT). (B) 1st spatial dependence in GMM(PET & CT). (C) 2nd spatial dependence in GMM(PET & CT).
(A)
(B) (C)
From Figure 3.10, the cluster sizes can be selected k 13 for GMM(PET & CT), and k 14 for the 1st and 2nd spatial dependence GMM. These clustering results and accuracy are shown as following.
Figure 3.11: (A) k 13, the result of GMM (PET & CT). (B) k 14, the result of 1st spatial dependence GMM(PET & CT). (C) k 14, the result of 2nd spatial dependence GMM (PET & CT).
A
B C
Table 3.1: Comparison for the accuracy of the highest activity region of different methods by F-measure.
Recall (TRR) Precision (PPV) F-measure
PET + GMM 1.0000 0.5256 0.6891
Fusion + GMM 0.9682 0.9346 0.9511
GMM (PET&CT) 0.8962 0.9976 0.9442
1st order spatial GMM (PET&CT) 1.0000 0.7307 0.8444 2nt order spatial GMM (PET&CT) 0.9322 0.9692 0.9503
The comparison from Table 3.1 shows that the results of Fusion + GMM, GMM (PET&CT), 1st order spatial GMM (PET&CT) and 2nd order spatial GMM (PET&CT) all have higher accuracy than PET + GMM. Although GMM (PET&CT), the 1st and 2nd order spatial GMM (PET&CT) have slightly lower F-measure values than Fusion + GMM, they provided more information for the data. We can find the correlation of PET and CT on the regions of interesting. The correlation of the result of PET and CT could be used to detect the association pattern between the pixels of these two images. The correlation is positive as the area of a PET image has high (or low) isotope radioactivity and the area of a CT image has high (or low) X-ray absorption overlap very much. The correlation is negative as the area of a PET image with high (or low) isotope radioactivity and the area of a CT image with low (or high) X-ray absorption overlap very much. In addition, the correlations of neighbor points on PET and CT images also can be obtained by using spatial dependence in GMM. The following is some correlations of PET and CT on the result of using 2nd order spatial dependence in GMM.
Figure 3.12: The red regions show different correlations of PET and CT on the result of using 2nd order spatial dependence in GMM. (A) The correlation is -0.7575. (B) The correlation is 0.3704. (C) The correlation is -0.7540.
From Figure 3.12, the correlations of (A) and (C) are negative. It represents that the area of the PET image with high (or low) isotope radioactivity and the area of the CT image with low (or high) X-ray absorption overlap very much.
(C) A
B C