The thresholding process in Stage Two provides a good initial tumor segmentation, such as the one shown in Figure 7(c). Comparing it with the ground truth image Figure 7(d), a number of pixels in the initial tumor segmentation are not found in the ground truth image and should be removed. Additional thresholding is difficult to perform, however, without possibly removing tumor as well as non-tumor pixels.
Pixels belonging to the same tissue type will have similar signal intensities in the three feature spectrums. Because normal tissue types have a more or less uniform cellular makeup [33,34,35], their distribution in feature space will be relatively concentrated [38]. In contrast, tumor can have significant variance, depending on the local degrees of enhancement and tissue inhomogeneity within the tumor due to the presence of edema, necrosis, and possibly some parenchymal cells captured by the partial-volume effect. Figures 5 (b) and (c) show the different spreads in feature space for normal and tumor pixels. Pixels belonging to parenchymal tissues and CSF are grouped more densely by intensity, while pixels belonging to tumor are more widely distributed.
By exploiting this ``density'' property, non-tumor pixels can
be removed without affecting the presence of tumor pixels.
Called ``density screening,'' the process begins by creating a 3-dimensional
histogram for all pixels remaining in the initial tumor segmentation
image after thresholding. The histogram array itself has a
size of
intensity bins. For each feature, the maximum and
minimum signal intensity values in the initial tumor segmentation are found and
quantized into the histogram array (i.e., the minimum T1 intensity value
occupies T1 Bin 1, the maximum T1 intensity value occupies
T1 Bin 128), with all T1 values in between ``quantized'' into one of
the 128 bins. This quantization was done for two reasons.
First, sizes of a three-dimensional histogram quickly became
prohibitively large to store and manipulate. Even a 2563 histogram
has nearly 17 million elements. Secondly, levels of quantization can
make the ``dense'' nature of normal pixels more apparent while still
leaving tumor pixels relatively spread out.
For the 12-bit data studied here, after thresholding, slices had
a range of approximately 800 intensity values in each feature. The
actual value of 128 was empirically selected.
Using 64 bins blurred
the separation of tumor and non-tumor pixels in training slices
where the tumor boundary was not as well defined. Values
similar to 128, such as 120 or 140, are unlikely to
significantly change the ``quantization'' effect and should yield
similar results. The histograms and scatterplots shown in
Figure 8 were created using 128 bins.
From the 3D histogram, three 2D projections are generated: T1/PD, T1/T2, and PD/T2. An example 2D projection is shown in Figure 8(a), which was generated from the slice shown in Figure 7(c). A corresponding scatterplot is shown in Figure 8(b). The bins with the most pixels (the highest ``peaks'' in Figure 8(a)) can be seen in the lowest T1/PD corner and are comprised of non-tumorous pixels that should be removed. In contrast, tumor pixels, while greater in number, are more widespread and have lower peaks in their bins.
In each projection, the highest peak is found and designated as the starting point for a region growing [40] process that will ``clear'' any neighboring bin whose cardinality (number of pixels in that bin) is greater than a set threshold (T1/PD=3, T1/T2=4, PD/T2=3). This will result in a new scatterplot similar to that shown in Figure 8(c). A pixel is removed from the tumor segmentation if it corresponds to a bin that has been ``cleared'' in any of the three feature-domain projections. Figures 8(d) and (e) are the tumor segmentation before and after the entire density screening process is completed. Note that the resulting image is closer to ground truth.
The thresholds used were determined from training slices by creating a
3D histogram, including 2D projections, using only pixels contained in
the initial tumor segmentation. Then the ground truth tumor pixels
for each slice were
overlaid on the respective projections. So, given a
3D histogram of an initial tumor segmentation, all pixels not in
the ground truth image are removed, leaving only tumor behind without
changing the dimensions and quantization levels of the histogram. The
respective 2D projections of all training slices were examined. It
was found that the smallest bin cardinality bordering a bin occupied by known
non-tumor pixels made an accurate threshold for the given projection.
It should be noted, however, that the thresholds were based on the
images used in this research and would need to be
scaled to accommodate images of different sizes, such as
.
