**3. Results**

#### *3.1. Synthetic Image Experiments*

To conduct an objective quantitative study, the synthetic MR brain images containing multiple sclerosis (MS) lesions obtained from the MR imaging simulator of McGill University, Montreal, Canada were used for experiments [24]. MS lesions are typically hyperintense on T2W or FLAIR sequence image. Figure 4a–c shows a slice MR brain image along with the ground truth of MS lesion shown in Figure 4d. The MR brain images are acquired by the modalities of T1W, T2W and PD with specifications

provided in BrainWeb site [24]. The thickness of slice is 1 mm with size of 181 × 217 × 181. Each slice is specified by INU (intensity non-uniformity) 0% or 20%, denoted by rf0 and rf20 with six different levels of noise, 0%, 1%, 3%, 5%, 7% and 9%. The noise in the background of the simulated images is simulated by Rayleigh statistics and signal regions are simulated by Rician statistics. The "percentage (%) of noise" represents the ratio of the standard deviation of the white Gaussian noise to the signal for a reference tissue [24] in terms of %. There were 23 MR images from 91 to 113 slices for our study. To implement ICEM, we need to know the desired target signature **d**. Two ways were suggested to select training samples to calculate **d**. One is called all slices-selected training samples, which selects a small set of training samples from all MR image slices. The other is called single slice-selected training samples, which selects a small set of training samples from a particular single MR image slice that can be further used to find training samples for entire MR image slices. Its idea was derived from the extrapolation process used in volume sphering analysis (VSA) developed in [14,15]. Table 1 specifies the values of parameters used for experiments where two Gaussian filters using window sizes of 3 × 3 and 5 × 5, and two different σ = 0.1 and 0.5. The experiments were conducted for all MR image slices according to Table 1 where the results obtained by Gaussian window of 5 × 5 with σ = 0.5 are tabulated in parentheses.

**Figure 4.** Three MR images containing MS lesions acquired by T1W, T2W and PD with 0% noise and 0% INU. (**a**) T1W; (**b**) T2W; (**c**) PD; (**d**) ground truth (lesions)


To further evaluate the performance of the proposed NBE-ICEM, a commonly used segmentation approach, called lesion segmentation tool (LST) [25,26], was used for comparative study. It was originally developed for the segmentation of MS lesions and has also been proven to be useful for the segmentation of brain lesions. Table 2 tabulates DSI values calculated by Equation (1) averaged over 23 MR image slices 91–113 of lesion detection produced by CBEP-ICEM1, CBEP-ICEM2 and LST for six different noise levels and two INU levels where all slices-selected training samples were used to find the knowledge of **d**. The shaded DSI values in Table 2 are the best results. As we can see from the table, CBEP-ICEM1 performed better than CBEP-ICEM2 when noise level is low. However, when noise level is high, CBEP-ICEM2 performed better than CBEP-ICEM1. Nonetheless, both NBE-ICEM-based methods, i.e., CBEP-ICEM1 and CBEP-ICEM2, performed better than LST. It should be also noted that, since LST produced real-valued gray scale images, it required a threshold value to segmen<sup>t</sup> WMH lesions. The LST results in Table 2 were obtained by manually adjusting threshold values in order to yield the highest detection rate.


**Table 2.** Averaged DSI values of lesions detection by CBEP-ICEM1, CBEP-ICEM2 and LST over MR image slices 91–113.

Similarly, Table 3 also tabulates DSI values calculated by Equation (1) averaged over 23 MR image slices 91–113 of lesion detection produced by CBEP-ICEM1, CBEP-ICEM2 and LST for six different noise levels and two INU levels where single slice-selected training samples were used to find the knowledge of **d** and the slice 102 was chosen as the desired single slice. The selection of slice 102 is empirical as long as it includes sufficient tissue information, in which case the middle MR image slice can serve as this purpose. The same conclusions drawn from Table 2 were also valid for Table 3, even though the results in Table 3 were slightly degraded compared to the results in Table 2 because the single slice-selected training samples were used. It should be noted that the results of LST in Tables 2 and 3 were the same because LST did not allow users to select training samples. This disadvantage is further offset by a need of finding an appropriate threshold value to segmen<sup>t</sup> lesion out from the background.


**Table 3.** Averaged DSI values of lesions detection by CBEP-ICEM1, CBEP-ICEM2 and LST over MR image slices 91–113 using slice 102 to select training samples.

For an illustrative purpose, Figures 5–10 only show detection results of WMH lesions of the 97th MR image slice with six levels of noise and 0% INU by two versions of CBEP-ICEM, using the Gaussian window size of 3 × 3 specified by σ = 0.1 and the Gaussian window size of 5 × 5 specified by σ = 0.5, referred to as CBEP-ICEM1 and CBEP-ICEM2, respectively, where two sets of training samples selected by all slices and the single 102nd slice were used to calculate the desired target signatures **d** to implement NBE-ICEM. As we can see by visual inspection against the ground truth in Figure 4d, CBEP-ICEM1 and CBEP-ICEM2 using two sets of training samples, i.e., all slices-selected and single slice-selected training samples, produced very close results and they both also performed better lesion detection than LST did.

**Figure 5.** Lesion detection of Slice 97 with 0% noise and 0% INU by CBEP-ICEM1 and CBEP-ICEM2. (**a**) CBEP-ICEM1; (**b**) CBEP-ICEM2; (**c**) Lesion detection LST.

**Figure 6.** *Cont*.

**Figure 6.** Lesion detection of Slice 97 with 1% noise and 0% INU by CBEP-ICEM1 and CBEP-ICEM2. (**a**) Original 97th slice of MS MR brain images with 1% noise and 0% INU; (**b**) CBEP-ICEM1; (**c**) CBEP-ICEM2; (**d**) Lesion detection LST.

 Single slice-selected training samples (**b**)

 **Figure 7.** *Cont*.

**Figure 7.** Lesion detection of Slice 97 with 3% noise and 0% INU by CBEP-ICEM1 and CBEP-ICEM2. (**a**) Original 97th slice of MS MR brain images with 3% noise and 0% INU; (**b**) CBEP-ICEM1; (**c**) CBEP-ICEM2; (**d**) Lesion detection LST.

(**a**) 

**Figure 8.** *Cont*.

1st iteration 3rd iteration (final) Lesions detection by Otsu's method Single slice-selected training samples 

**Figure 8.** Lesion detection of Slice 97 with 5% noise and 0% INU by CBEP-ICEM1 and CBEP-ICEM2. (**a**) Original 97th slice of MS MR brain images with 5% noise and 0% INU; (**b**) CBEP-ICEM1; (**c**) CBEP-ICEM2; (**d**) Lesion detection LST.

(**b**) 

**Figure 9.** *Cont*.

(**d**) 

**Figure 9.** Lesion detection of Slice 97 with 7% noise and 0% INU by CBEP-ICEM1 and CBEP-ICEM2. (**a**) Original 97th slice of MS MR brain images with 7% noise and 0% INU; (**b**) CBEP-ICEM1; (**c**) CBEP-ICEM2; (**d**) Lesion detection LST.

1st iteration 4th iteration (final) Lesions detection by Otsu's method All slices-selected training samples

**Figure 10.** *Cont*.

1st iteration 4th iteration (final) Lesions detection by Otsu's method Single slice-selected training samples 

**Figure 10.** Lesion detection of Slice 97 with 9% noise and 0% INU by CBEP-ICEM1 and CBEP-ICEM2. (**a**) Original 97th slice of MS MR brain images with 9% noise and 0% INU; (**b**) CBEP-ICEM1; (**c**) CBEP-ICEM2; (**d**) Lesion detection LST.

Two comments are noteworthy.


#### *3.2. Real Image Experiments*

Real MRI brain images were acquired at the Taichung Veterans General Hospital (TCVGH) by Siemens Magnetom Aera 1.5 Tesla (Erlangen, Germany) MR scanner with a 16-channel phase-array head coil. MR imaging protocol included T1W with 3D MPRAGE, T2W and FLAIR. Since T1W, T2W and FLAIR images used for experiments were collected by 3D high resolution sequences with each voxel of size, 1 × 1 × 1 mm3, the interpolation artifacts and partial volume do not have much effect on imaging. However, as a part of trade-off, this also requires additional 2 min for image acquisition. Other imaging parameters used for data acquisition were voxel size of 1 × 1 × 1 mm3, matrix size = 256 × 256 × 176, NEX = 1. According to a clinical visual inspection criterion [27], the WMH lesions can be graded by Fazekas with three grades of Fazekas shown in Figure 11 for illustration.

**Figure 11.** Lesion categorized by three grades of Fazekas shown in FLAIR images. (**a**) Fazekas grade 1; (**b**) Fazekas grade 2; (**c**) Fazekas grade 3

A total of 111 cases were collected and all the participants have been well-informed and signed their consents. In addition, the study conducted in this paper was approved by the Ethics Committee of Clinical Research, Taichung Veterans General Hospital (IRB number: CE16138A). Among all the 111 cases there are 58 cases of Fazekas grade 1, 44 cases of Fazekas grade 2 and 9 cases of Fazekas grade 3. Thus, in this study, we selected 10 cases from Fazekas grade 1, 11 cases from Fazekas grade 2, and 9 cases from Fazekas grade 3.

As demonstrated by synthetic image experiments, CBEP-ICEM2 was shown to be a better WMH detection technique. Thus, CBEP-ICEM 2 was used in real image experiments. Table 4 tabulates the values of parameters used by CBEP-ICEM2 where two sets of training samples selected by all slices and the single 90th slice were selected to calculate the desired target signature **d** to implement NBE-ICEM.



Figures 12–14 show the WMH lesion detection results produced by CBEP-ICEM2 and LST for three Fazekas grades, respectively, where Figures 12a, 13a and 14a are original T1W, T2W and FLAIR MR images; Figures 12b, 13b and 14b are iterative WMH lesion detection images by CBEP-ICEM2 along with final WMH lesion detection by Otsu's method; and Figures 12c, 13c and 14c show comparisons between lesion detections by CBEP-ICEM2 and LST.

**Figure 12.** Lesion detection of Fazekas grade 1 by CBEP-ICEM2 and LST (**a**) Original MR images (T1W, T2W, FLAIR) with lesions of Fazekas grade 1; (**b**) CBEP-ICEM2-detected lesion of Fazekas grade 1; (**c**) Comparison between lesion detections by CBEP-ICEM2 and LST.

**Figure 13.** Lesion detection of Fazekas grade 2 By CBEP-ICEM2 and LST. (**a**) Original MR images (T1W, T2W, FLAIR) with lesions of Fazekas grade 2; (**b**) Lesion detection by CBEP-ICEM2; (**c**) Comparison between lesion detections by CBEP-ICEM2 and LST.

**Figure 14.** Lesion detection of Fazekas grade 3 By CBEP-ICEM2 and LST. (**a**) Original MR images (T1W, T2W, FLAIR) with lesions of Fazekas grade 3; (**b**) Lesion detection by CBEP-ICEM2; (**c**) Comparison between lesion detections by CBEP-ICEM2 and LST.

As demonstrated in Figures 12–14, our proposed NBE-ICEM using two sets of training samples performed very similarly and also better than LST according to clinical visual evaluation criterion, Fazekas grades [27].
