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Extra resources for A Boundary Value Problem for Hypermon Genic Functions in Clifford Analysis
The MRF prior has overregularized the segmentation and should therefore not be used in this form. 13: A 3-D volume rendering of the gray matter segmentation of the data of Fig. 12 with bias ﬁeld correction and MRF. (Source: Ref. ) 26 Leemput et al. 3 Validation and Conclusions The method was validated on simulated MR images of the head that were generated by the BrainWeb MR simulator , for varying number of MR channels, noise, and severity of the bias ﬁelds. 8) k denotes the volume of the voxels classiﬁed as tissue k by both raters, where V12 and V1k and V2k the volume of class k assessed by each of the raters separately.
1 Intensity and Contextual Constraints r Since MS lesions appear hyperintense on both the PD- and the T2-weighted images, only voxels that are brighter than the mean intensity of gray matter in these channels are allowed to be outliers. r Since around 90–95% of the MS lesions are white matter lesions, the contextual constraint is added that MS lesions should be located in the vicinity of white matter. In each iteraction, the normal white matter is fused with the lesions to form a mask of the total white matter.
The bias (Fig. 8(e)) is then estimated as a weighted least-squares ﬁt through the residue image using the weights W (Fig. 8(d)), each voxel’s weight being inversely proportional to the variance of the class that voxel belongs to. As can be seen from Fig. 8(d), the bias ﬁeld is therefore computed primarily from voxels that belong to classes with a narrow intensity distribution, such as white and gray matter. The smooth spatial model extrapolates the bias 3 For more general expressions for the multispectral case we refer to ; in the unispectral case yj = yj , µk = µk , and Σk = σk2 .