Stage Two: Multi-spectral Histogram Thresholding

 

Given an intra-cranial mask from Stage One, there are three primary tissue types: pathology (which can include gadolinium-enhanced tumor, edema, and necrosis), the brain parenchyma (white and gray matter), and CSF. We would like to remove as many pixels belonging to normal tissues as possible from the mask.

Each MR voxel of interest has a $\langle T1, PD, T2 \rangle$ location in $\Re^{3}$, forming a feature-space distribution. Based on the knowledge in Table 2, and the fact that pixels belonging to the same tissue type will exhibit similar relaxation behaviors (T1 and T2) and water content (PD), they will then also have approximately the same location in feature space [38]. Figure 5(a) shows the signal-intensity images of a typical slice, while (b) and (c) show histogram for the bivariate features T1/PD and T2/PD, respectively, with approximate tissue labels overlaid. There is some overlap between classes because the graphs are projections and also due to ``partial-averaging'' where different tissue types are quantized into the same voxel.

  

Figure 5: (a) Raw T1, PD, and T2-weighted Data. The distribution of intra-cranial pixels are shown in (b) T1-PD and (c) PD-T2 feature space. C = CSF, Pa = Parenchymal Tissues, T = Tumor

  

Figure 6: Histograms for Tumor and the Intra-Cranial Region. Solid black lines indicates thresholds in T1 and PD-weighted space.

The typical relationships between enhancing tumor and other brain tissues can also be seen in Figure 6, which are histograms for each of the three feature images. These distributions were examined and interviews were conducted with experts concerning the general makeup of tumorous tissue, and the behavior of gadolinium enhancement in the three MRI protocols. From these sources, a set of heuristics were extracted that could be included in the system's knowledge base:

1.

Gadolinium-enhanced tumor pixels occupy the higher end of the T1 spectrum.

2.

Gadolinium-enhanced tumor pixels occupy the higher end of the PD spectrum, though not with the degree of separation found in T1 space [39].

3.

Gadolinium-enhanced tumor pixels were generally found in the ``middle'' of the T2 spectrum, making segmentation based on T2 values difficult.

4.

Slices with greater enhancement had better separation between tumor and non-tumor pixels, while less enhancement resulted in more overlap between tissue types.

Analysis of these heuristics revealed that histogram thresholding could provide a simple, yet effective, mechanism for gross separation of tumor from non-tumor pixels (and thereby an implementation for the heuristics). In fact, in the T1 and PD spectrums, the signal intensity having the greatest number of pixels, that is, the histogram ``peaks,'' were found to be effective thresholds that work across slices, even those with varying degrees of gadolinium enhancement. An example of this is shown in Figure 6. The T2 image had no such property that was consistent across all training slices and was excluded.

  

Figure 7: Multi-spectral Histogram Thresholding of Figure 6. (a) T1-weighted thresholding; (b) PD-weighted thresholding; (c) Intersection of (a) and (b); (d) Ground truth.

For a pixel to survive thresholding, its signal intensity value in a particular feature had to be greater than the intensity threshold for that feature. Figures 7(a) and (b) show the results of applying the T1 and PD histogram ``peak'' thresholds in Figures 6(b) and (c). In both of these thresholded images a significant number of non-tumor pixels have been removed, but some non-tumor pixels remain in each thresholded image. Since the heuristics listed above state that gadolinium enhanced tumor has a high signal intensity in both the T1 and PD features, additional non-tumor pixels can be removed by intersecting the two images (where a pixel remains only if it's present in both images). An example is shown in Figure 7(c).