Experimental results

Tables 3.1, 3.2, 3.2, 3.3, 3.4, 3.5, and 3.6 list the performance evaluation results of BET, BSE, HWA, ISTRIP and the proposed method for different data sets. In addition to the Table 3.1, in other cases, although HWA has the highest S_e, its poor performance of S_p results in its worse performance of JSC.

Since some of the brain volumes in the first IBSR data set has apparent intensity inho-mogeneity and artifacts, as shown in the Figure 3.2. Therefore, not all brain volumes have the satisfied result. As [25], Table 3.1 excludes the extracted brains which the JSC value is below 0.6 or the result is blank. The number of excluded brains are four, three, and five for the BSE, HWA, and the proposed method, respectively. Performance evaluation using the first IBSR data set without including all the failure cases as shown in Table 3.2, and the number of excluded cases is seven. In Table 3.1 and Table 3.2 we has the similar JSC value with ISTRIP, In terms of Seand Sp, the proposed method has better sensitivity than ISTRIP. However, ISTRIP can extract the all brain volumes in the first IBSR data set.

The proposed method outperforms others for the second IBSR set, in terms of JSC, S_e, and Sp. As listed in Table 3.3, compared to HWA, our method maintains the high sensitivity of HWA as much as possible and improves the low specificity of HWA to the highest one.

Our method achieves the highest JSC, the second highest Se, and the highest Sp. In this data set, the total amount of voxels in an MR volume is 8388168, and the brain region is about one-eighth of the total voxels. Therefore, 0.01 voxels Se of the value means there are about 10000 of the extracted brains overlapped with the ground truth. The 0.01 voxels S_pof the value means there are about 70000 of the extracted non-brain regions overlapped with the non-brain regions of the ground truth. The 0.01 voxels JSC of the value means there are more than 10000 of the extracted brains overlapped with the ground truth.

When using the VGHTPE data set, although BSE has the highest S_p and JSC values,

The performance evaluation using the BrainWeb phantom data set and only considering WM and GM is listed in Table 3.5. Although BSE has the highest S_p, but has the lowest Se. The proposed method has the best performance compared with BET and ISTRIP, in terms of JSC, S_e, and S_p.

Since the ground truth of the CSF region provided by BrainWeb contains peripheral CSF area, the values of Sp when considering CSF, as listed in Table 3.6, higher than those in Table 3.5. In Table 3.6, the higher S_e means that the segmentation result may contain more peripheral CSF voxels. Therefore, we only concern the Sp value with this data set, and we have the similar S_p of BET which has the highest value.

The parameters of the second IBSR data set are as same as those used in [25]. For each brain extraction method, except BSE, the parameters of the VGHTPE and BrainWeb phantom data sets are the same. The fractional intensity threshold of BET was set as 0.7;

the parameters of HWA were set to the default values with surface-shrink option turned on; the intensity contrast of ISTRIP was set as 0.08 with ”further remove non-brain tissues with high intensity” option turned on; the weight of intra n-link was set as 0.35, t-link was set as 0.65 and the distance term was set as 0.07 in the proposed method. The edge constant, diffusion iteration, and diffusion constant, erosion size of BSE when using the VGHTPE (BrainWeb phantom) data set were set to be 25 (increased with the degree of non-uniformity), 3 ,0.62 and 1 (2), respectively.

The extracted brain images using the proposed method with the subject in the first/second IBSR data set, VGHTPE, and BrainWeb phantom image are shown in Figure 3.3, Figure

Figure 3.2: The example of brain volumes with apparent intensity inhomogeneity and arti-facts in the first IBSR data set.

BSE⁴ 0.900 (0.025) 0.954 (0.035) 0.993 (0.003) 0.044 (0.034) 0.055 (0.017) ISTRIP 0.910 (0.018) 0.986 (0.013) 0.991 (0.005) 0.013 (0.013) 0.077 (0.027) HWA³ 0.752 (0.037) 0.974 (0.068) 0.970 (0.008) 0.022 (0.056) 0.226 (0.026) Our method⁵ 0.910 (0.021) 0.989 (0.012) 0.991 (0.003) 0.010 (0.011) 0.079 (0.020) The superscripts in the first column indicate the excluded cases.

Table 3.2: Performance evaluation using the first IBSR data set without including all the failure cases.

Method JSC S_e S_p P_m P_f

BET⁷ 0.881 (0.017) 0.981 (0.026) 0.988 (0.003) 0.017 (0.024) 0.102 (0.021) BSE⁷ 0.905 (0.025) 0.954 (0.035) 0.994 (0.002) 0.044 (0.034) 0.051 (0.010) ISTRIP⁷ 0.911 (0.014) 0.988 (0.015) 0.991 (0.004) 0.012 (0.014) 0.077 (0.023) HWA⁷ 0.762 (0.012) 0.999 (0.001) 0.967 (0.008) 0.001 (0.001) 0.237 (0.014) Our method⁷ 0.910 (0.021) 0.991 (0.008) 0.991 (0.003) 0.009 (0.007) 0.081 (0.020) The superscripts in the first column indicate the excluded cases.

3.4, Figure 3.5, and Figure 3.6, respectively. In our method we bring up three points, dis-tance term at the highest level, pre-determined foreground and application of graph cuts algorithm localized by using smaller cubes to local estimation of intensity histogram. The left column of Figure 3.7 illustrations the extracted brains without using the distance term,

Table 3.3: Performance evaluation using the second IBSR data set.

Method JSC S_e S_p P_m P_f

BET 0.891 (0.052) 0.959 (0.042) 0.989 (0.005) 0.038 (0.038) 0.071 (0.031) BSE 0.838 (0.083) 0.957 (0.042) 0.973 (0.030) 0.041 (0.041) 0.119 (0.104) ISTRIP 0.915 (0.018) 0.978 (0.011) 0.990 (0.003) 0.021 (0.011) 0.064 (0.022) HWA 0.814 (0.040) 0.9997 (0.0003) 0.965 (0.016) 0.0002 (0.0002) 0.186 (0.040) Our method 0.930 (0.011) 0.981 (0.016) 0.991 (0.005) 0.018 (0.015) 0.052 (0.017)

Table 3.4: Performance evaluation using the VGHTPE data set.

Method JSC S_e S_p P_m P_f

BET 0.921 (0.009) 0.971 (0.013) 0.994 (0.001) 0.028 (0.012) 0.051 (0.011) BSE 0.933 (0.008) 0.958 (0.011) 0.997 (0.001) 0.041 (0.011) 0.026 (0.008) ISTRIP 0.915 (0.011) 0.984 (0.012) 0.991 (0.002) 0.015 (0.011) 0.07 (0.015) HWA 0.847 (0.019) 0.998 (0.002) 0.979 (0.003) 0.002 (0.002) 0.151 (0.019) Our method 0.920 (0.010) 0.982 (0.009) 0.992 (0.002) 0.017 (0.009) 0.063 (0.017)

and the right column is the extracted brain using distance term. The difference is obvi-ous, the border of the extracted brains in the right column are more smooth. Figure 3.8 shows the extracted brain of the proposed method overlaid by another without considering pre-determined foreground. The brain region of proposed method is larger than the one without using pre-determined foreground. Some brain extraction methods segment brain volume in a slice-by-slice manner, however we use smaller cubes to do this work. The left column of Figure 3.9 shows the extracted brain of the proposed method overlaid with a brain extracted by graph cuts algorithm in a slice-by-slice manner, and the right column

HWA 0.696 (0.005) 0.9995 (0.0001) 0.876 (0.003) 0.0003 (9.00947E-05) 0.304 (0.005) Our method 0.840 (0.025) 0.997 (0.001) 0.946 (0.011) 0.003 (0.001) 0.157 (0.026)

Table 3.6: Performance evaluation using the BrainWeb phantom data set and consid-ering WM, GM and CSF.

Method JSC S_e S_p P_m P_f

BET 0.928 (0.009) 0.944 (0.011)) 0.993 (0.001) 0.055 (0.011) 0.017 (0.003) BSE 0.870 (0.031) 0.897 (0.009) 0.988 (0.018) 0.0999 (0.012) 0.030 (0.041) ISTRIP 0.934 (0.001) 0.963 (0.004) 0.988 (0.001) 0.036 (0.004) 0.031 (0.003) HWA 0.850 (0.003) 0.993 (0.002) 0.936 (0.002) 0.006 (0.002) 0.144 (0.004) Our method 0.912 (0.007) 0.934 (0.017) 0.991 (0.005) 0.064 (0.0178) 0.024 (0.013)

shows the extracted brain of proposed method. The brain region of proposed method is larger than the one using the slice-by-slice manner. Since the upper part of the image in the right column of Figure 3.9 is darker than the bottom part of image in transverse view, therefore, applying graph cuts algorithm localized by using the local estimated histogram is preferable than slice-by-slice manner.

The performance evaluations of the proposed method without distance term/predetermined term and in a slice-by-slice manner using the second IBSR data set are listed in Table 3.7.

Although the proposed method without predetermined term has the highest JSC value and specificity, but it has lower sensitivity than the proposed method with the three factors.

According to the value of JSC, Se, and Sp, distance term, pre-determined foreground and application of graph cuts algorithm localized by using smaller cubes to local estimated intensity histogram are important factors in our method.

Table 3.7: Performance evaluation of the proposed method without distance term/predetermined term and in a slice-by-slice manner using the second IBSR data set.

Method JSC Se Sp Pm Pf

Our method 0.930 (0.011) 0.981 (0.016) 0.991 (0.005) 0.018 (0.015) 0.052 (0.017) Our method without distance term 0.911 (0.023) 0.975 (0.017) 0.989 (0.007) 0.024 (0.016) 0.066 (0.026) Our method in slice-by-slice manner 0.904 (0.020) 0.953 (0.024) 0.991(0.006) 0.045 (0.023) 0.051 (0.022) Our method without predetermined term 0.933 (0.012) 0.979 (0.016) 0.992 (0.004) 0.020 (0.016) 0.047 (0.016)

Figure 3.3: The extracted brain images of subject in the first IBSR data set and using the proposed method are shown in (a) transverse, (b) coronal and (c) sagittal views.

Figure 3.4: The extracted brain images of subject in the second IBSR data set and using the proposed method are shown in (a) transverse, (b) coronal and (c) sagittal views.

Figure 3.5: The extracted brain images of subject in the VGHTPE data set and using the proposed method are shown in (a) transverse, (b) coronal and (c) sagittal views.

Figure 3.6: The extracted brain images of subject in the BrainWeb phantom data set and using the proposed method are shown in (a) transverse, (b) coronal and (c) sagittal views.

Figure 3.7: The result of extracted brain without using distance term at the highest level.

The left column is the extracted brain without considering the contour factor. The right column is the extracted brain and consider the contour factor corresponding to the left column.

Figure 3.8: The extracted brain of proposed method overlaid by another without consider-ing pre-determined foreground factor.

Figure 3.9: The left column shows the extracted brain of proposed method overlaid with a brain extracted by graph cuts algorithm in a slice-by-slice manner, and the right column shows the extracted brain of proposed method.

Discussion

Figure 4.1: The left column is the extracted brain with excluded cerebellum voxels by HWA and the right column is the corresponding ground truth volume segmented manually.

In this work we use an initial brain with high sensitivity and low specificity segmented by HWA and trim the brain into a more accurate one. If the initial brain extraction fails then our method fails too. In most cases HWA is a method with high sensitivity for brain extraction, but it sometimes excludes parts of the cerebellum, The example is shown in Figure. 4.1.

The program execution speed of the existing methods for brain extraction which com-pared in this work are fast (less than a minute). The program execution speed of the pro-posed method is about 5 minutes for an MR volume. Regarding to the performance eval-uation for brain extraction, our method outperforms others for the second IBSR data set.

Therefore, the time cost of the proposed method is not expensive. The compared method

Figure 4.2: An example of the possible disadvantage by using localized graph cuts. The red window shows the inconsistent border.

in this work, BET, HWA, and ISTRIP are performed on Genuine Intel CPU 2.93GHz×16 processor running Linux, BSE and our method are performed on Intel Core2 Quad XP 2.83GHz processor on Windows system. Most of the running time of our method spent on the Otsu’s method, since it was performed frequently. Although the speed of multires-olutional graph cuts with narrow band should be faster, but we use multiresmultires-olutional graph cuts to extracted brain instead of using multiresolutional graph cuts with narrow band. The reason is that the multiresolutional graph cuts with narrow band will limit the refinement of the results in a band and may miss the thin structure.

In our method we perform graph cuts algorithm individually for each cube, the advan-tage is to consider the influence of the intensity inhomogeneity. In the finest level, when the cube contains only a small portion of brain region. The intensity of foreground seeds may be similar to the non-brain region. Therefore the results may contain non-brain and have irregular border, as shown in the red window of Figure. 4.2. The distance term can correct this problem, but if the distance term is too big then the result may not be smooth.

According to our experiences, the result of adding the WM voxels to the pre-determined foreground will be better than pre-determined foreground only. Because the pre-determined foreground is eroded and upsampled from the extracted brain at the coarser level, in the

Figure 4.3: An example of the possible disadvantage by using the distance term in the finest level. (a) The extracted brain at the highest level and the red windows show the non-brain voxles. (b) The yellow line shows the contour used in distance term at the highest level, and the positions corresponding to the red windows in (a) are inconsistent with the brain area. (c) The extracted brain at middle levels. (a) and (b) are shrunk as the size of (c).

process of erosion may lose some thin structure or other details. But considering the time cost of WM region growing, we did not apply the WM region as pre-determined foreground at middle levels.

The advantage of the distance term at the finest level is its capability to constrain the shape of brain boundary. However, it has disadvantages. In some cases the extracted brain at middle levels are better than that at the highest level. Since the contour used in distance term is upsampled from the coarser level, the contour may not be entirely consistent with the border of the brain at the highest level, as illustrated in Figure 4.3.

Conclusions

We have compared to the existing methods and compared with our method by using four data sets. Regarding the performance evaluation for brain extraction, our method outperforms others for the first/second IBSR data set and BrainWeb phantom data set, and comparably with the BET and ISTRIP methods for the VGHTPE data sets.

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