We have proposed new methods to segment dynamic microPET images by MLEM reconstruction with k-mean or mixture clustering. The MLEM reconstruction is more precise than the FBP reconstruction with fewer artifacts.
K-mean or mixture clustering can perform the segmentation automatically. Tests of homogeneity of variances are used to decide k-mean or mixture clustering. BIC is used to select the cluster size from the data adaptively. Dimension reduction techniques can be integrated to reduce the computation cost in determining the cluster size by BIC.
If the activities of various clusters have different temporary patterns, then regression in time is useful to distinguish them via dimension reduction. Otherwise, the principal component analysis is a general tool for dimension reduction. Besides simple linear regression, we can also consider polynomial or nonlinear regression in time.
Because the images of MLEM reconstruction may be still noisy, noise reduction filters can be applied to remove noises. For example, the median filter can be applied as demonstrated in Figure 38. Other filters that can remove noises and preserve edges are important for this purpose.
For further investigation of these methods, it will be of great interest to evaluate the quality and quantity performance by more phantom studies and empirical studies with the judgments from medical experts in the future.
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Appendix
Figure 1: Four clusters in Simulation 1 within the size of 128 by 128 are displayed.
Figure 2: Time-activity curves in Simulation 1 are plotted.
Figure 3: PCA loadings of simulation 1 are plotted.
Cluster 4
Cluster 3 Cluster 2
Cluster 1
Figure 4: The BIC plot of k-mean clustering in Simulation 1 by PCA is displayed.
Figure 5: The BIC plot of k-mean clustering in Simulation 1 by regression is displayed.
Figure 6: The results of 3 clusters in
Simulation 1 by k-mean clustering are shown.
Figure 7: The results of 4 clusters in
Simulation 1 by k-mean clustering are shown.
Figure 8: The results of 5 clusters in
Simulation 1 by k-mean clustering are shown.
Figure 9: The results of 6 clusters in
Simulation 1 by k-mean clustering are shown.
K-mean Cluster 1 Cluster 2 Cluster 3 Cluster 4 Sum of Errors
True Cluster 1 3492 0 0 0 0
True Cluster 2
1
(
6 10 %× −3)
11350 5(
0.03%)
104(
0.63%)
110 0.67%( )
True Cluster 3 0
163
( )
1% 505 48(
0.3%)
211 1.28%( )
True Cluster 4 0
198
(
1.2%)
0 518 198 1.2%( )
Figure 10: The BIC plot of k-mean clustering in Simulation 1 for the original data by k-mean clustering is plotted.
Figure 11: The BIC plot of normal mixture in Simulation 1 by PCA is displayed.
Figure 12: The BIC plot of normal mixture in Simulation 1 by regression is displayed.
Table 1: Classification errors and error rates of k-mean clustering in Simulation 1 are shown.
Figure 13: The results of 3 clusters in Simulation 1 by normal mixture are shown.
Figure 14: The results of 4 clusters in Simulation 1 by normal mixture are shown.
Figure 15: The results of 5 clusters in Simulation 1 by normal mixture are shown.
Figure 16: The results of 6 clusters in Simulation 1 by normal mixture are shown.
Figure 17: The BIC plot of normal mixture in Simulation 1 for the original data by normal mixture is plotted.
Normal mixture
Cluster 1 Cluster 2 Cluster 3 Cluster 4 Sum of Errors
True Cluster 1 3492 0 0 0 0
True Cluster 2
64
(
0.4%)
11211 12(
0.07%)
173(
1.05%)
249 1.52%( )
True Cluster 3 0
85
(
0.52%)
520 111(
0.68%)
196 1.2%( )
True Cluster 4 0
112
(
0.68%)
0 604 112 0.68%( )
Table 2: Classification errors and error rates of normal mixture clustering in Simulation 1 are shown.
Figure 18: Four clusters in Simulation 2 are displayed.
Cluster 4 Cluster 3
Cluster 2
Cluster 1
Figure 19: Time-activity curves in Simulation 2 are plotted.
Figure 20: The results of 3 clusters in Simulation 2 by k-mean clustering are shown.
Figure 21: The results of 4 clusters in Simulation 2 by k-mean clustering are shown.
Figure 22: The results of 5 clusters in Simulation 2 by k-mean clustering are shown.
Figure 23: The results of 6 clusters in Simulation 2 by k-mean clustering are shown.
Figure 24: The results of 3 clusters in Simulation 2 by normal mixture are shown.
Figure 25: The results of 4 clusters in Simulation 2 by normal mixture are shown.
k_mean 3 4 5 Figure 26: The results of 5 clusters in
Simulation 2 by normal mixture are shown.
Figure 27: The results of 6 clusters in Simulation 2 by normal mixture are shown.
Table 3: Classification errors and error rates of k-mean and normal mixture clustering in Simulation 2 are shown.
Figure 28: Experiment data are displayed
Figure 29: PCA loadings of experiment data are plotted.
Figure 31: The BIC plot of k-mean Figure 30: The BIC plot of k-mean
groups P-Value
Bartlett test 3 58141 0
Bartlett test 4 68401.68 0
Bartlett test 5 68969.65 0
Bartlett test 6 68180.45 0
Bartlett test 7 67808.42 0
Bartlett test 8 67689.87 0
Bartlett test 9 68524.84 0
Bartlett test 10 68193.19 0
Bartlett test 11 67974.98 0
Bartlett test 12 70109.08 0
Table 4: The results by the Bartlett test are reported.
Figure 32: The results of 4 clusters in experiment data by k-mean clustering are shown.
Figure 33: The results of 5 clusters in experiment data by k-mean clustering are shown.
Figure 34: The results of 3 clusters in experiment data by normal mixture are shown.
Figure 35: The results of 4 clusters in experiment data by normal mixture are shown.
a1
Figure 36: The results of 5 clusters in experiment data by normal mixture are shown.
Figure 37: The results of 6 clusters in experiment data by normal mixture are shown.
Figure 38: Reduce noises by a median filter.
Figure 39: Time-activity curves of experiment data are plotted.