Why the Smoothing is Eliminated 87

In another point of view, the advantage we mentioned above tends to be drawbacks dur-ing the analysis. First of all, the consideration of neighbor voxels may be bad when voxels are near the borders of GM WM and CSF. We may sum up the wrong voxel information with each other, which are not in the same tissue, that is smoothing can always sum all in-formation to be together without checking them and it reduces the correctness of the VBM result. The other is the subtle difference may be weakened during smoothing the data. The small variance of brain structures may not be detected with smoothed data. In the last, it is hard for every of us to decide the smoothing kernel size. It is always a problem with the size of the kernel. However, it is recommended that the size of the smoothing kernel should be comparable to the size of the expected regional differences between the groups.

In our previous work [16], we have proved that the result of using the smoothed data or non-smoothed data will either reach the maximum of the Fisher’s criterion, which means that the use of the smoothing data would not improve the discrimination of the discriminant map.

Chapter 6

Conclusions

In this study, we proposed a reformatory method which is a parcellation-based mul-tivariate method for characterizing brain discrepancy of different populations. The proce-dures of parcellation-based multivariate morphometry are similar to one of the most popular morphometry method which is called voxel-based morphometry (VBM), it includes image preprocessing and parcellation-based multivariate analysis. In image preprocessing, several tools are used to maximize the performance of each step. The main idea of the proposed method is parcellation-based analysis, that is, we divide brain into several pieces before the multivariate analysis. we adopted the discriminative common vector method to detect the most discriminant hyper-plane which represents the discrimination of each region or voxel.

Finally, we combine each region back into the original brain to identify group discrepancy in an unbiased way. According to our experiment, we have demonstrated that the perfor-mance of the parcellation-based multivariate method is better than VBM. The multivariate result is shown that it detects more subtle and widely distributed pattern of brain structures which are often not detectable by VBM.

There are several important characters of parcellation-based multivariate method. First of all, the most important point is, all voxels in same region are simultaneously taken into consideration with multivariate analysis by using parcellation-based approach rather than using all features in brain. Obviously, features may be redundant especially for those region which is not important in group difference. Moreover, with an imperfect registration may cause some regions failed to spatial normalize to a template, these regions may also reduce the ability of characterizing group differences. Another important character is that feature reduction is omitted owing to the discriminative common vector method which can deal with plenty of features simultaneously. Therefore, the information of each voxel may not loss with feature reduction, every voxel will be in analysis instead. That enables the proposed method superior to other multivariate analysis which uses feature reduction within analysis. At last, the smoothness is not included in the preprocessing of the proposed method since the smoothness may mix up or reduce the information of each voxel. It has been proved that the maximums of Fisher’s criterion is equivalent with smoothing or not.

These are still some defects within the proposed method. In VBM analysis, that the

ef-Conclusions 91

fect of spatial normalization is different between each subject. Therefore, the global mean voxel value is included as a confounding covariate in an analysis of covariance (ANCOVA).

Different from VBM analysis, the proposed method take no consideration with this effect.

Another defect is about the discriminant map. The resulting discriminant map of VBM analysis provides a t-test map, which means the value of each voxel represent a significant level by a t statistic value. The discriminative map of our proposed method is a discrim-ination weight which is lack of statistic result. Although, we still provide a result with two-sample t test which is calculated by projecting all subjects onto the most projection vector we have found, then all the subjects will be indicated by a value for two sample t test. However, our proposed method has shown that the parcellation-based multivariate morphometry analysis has a good performance on subtle and widely-distributed structural difference and it is more flexible within analysis.

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