Validation on Real MR Images

This section shows validation results with real expert-classified MR images. We obtained this data set from the IBSR website [1]. The data set comprises T1-weighted brain MR images for 18 subjects. Figure 6.5 shows an example from the data set. We observe that the data have lower contrast and possesses certain acquisition-related artifacts that makes the classification task more challenging than that for the BrainWeb dataset. Figure 6.5 also shows an example of a classification generated by the proposed method and compares it to the ground truth.

Figure 6.5: Qualitative analysis of the proposed algorithm with IBSR data [1]. The voxel size for this image is 0.9375 $\times$ 0.9375 $\times$ 1 (coronal). (a) An axial slice of the data. (b) The classification produced by the proposed method. (c) The expert-classified ground truth.

Figure 6.6 compares the performance of the proposed method using the two different atlas-based priors. Figure 6.6(a) shows that the 2-class prior, relative to the scaled-atlas prior, biases the classification more in favor of the white matter. With the 2-class prior, which gives equal weight to all three brain tissue types, the Dice metric for the white matter is better than that for the gray matter because of lower inherent variability of the intensities in the white matter. The scaled-atlas prior imposes a stronger constraint which tends to shift this bias, as seen in Figure 6.6(b). Empirical evidence confirms that as the parameter $v$ varies from $0.0$ to $1.0$, the bias shifts away from white matter towards gray matter. Nevertheless, with the average Dice metric, Figure 6.6(c) shows that both priors perform equally well.

Figure: Validation, of the proposed method with two different atlas-based priors, on IBSR data. Dice metrics for (a) white matter: $D_{\mathrm{white}}$, (b) gray matter: $D_{\mathrm{gray}}$, and (c) their average: $(D_{\mathrm{white}} + D_{\mathrm{gray}})/2$. Note: In the graphs, Prior1: 2-class prior, Prior2: scaled-atlas prior.

For the proposed algorithm using the 2-class prior, Table 6.2 gives the mean, median, and the standard deviation for the Dice metrics over the entire dataset. The proposed method yields a higher mean (by a couple of percent) and lower standard deviation for the Dice metrics over both white matter and gray matter classes, as compared to the results reported by Ruf et al. [146] for the state-of-the-art method of Leemput et al. [94] as well as their own method.

Table 6.2: Mean, median, and standard deviation for the gray-matter and white-matter tissue classes in the IBSR data set using the proposed method with the 2-class prior.

Statistical measure	White matter	Gray matter
Mean	0.8868	0.8074
Median	0.8913	0.8009
Standard deviation	0.0179	0.0426

The results in the chapter empirically confirm that the piecewise stationary-ergodic Markov model conforms well to brain MR images. It shows that it is possible to learn these models via nonparametric density estimation in the high-dimensional spaces of MR-image neighborhoods. These results also suggest that the statistical structure in these spaces capture important tissue properties in brain MR images. The mathematical and engineering components in this chapter are appropriate for any kind of densely-sampled medical data, including vector-valued images (e.g., multimodal MR data) and images with higher-dimensional domains (e.g., a sequence of volumetric MR images over time).