Knowledge-Based Vs. Ground Truth

A total of 120 slices, including the 17 training slices described in Section 2.1, were within the slice range of the system and known to contain tumor. After processing by the system, the slices were compared with ``ground-truth'' tumor segmentations that were created by radiologist hand labeling [41]. Error was found between the two segmentations, both false positives (where the system indicated tumorous pixels where ground truth did not) and false negatives (where ground truth indicated tumorous pixels that the system did not).

To compare how well (on a pixel level) the KB method corresponded with ground truth, two measures were used. The first, ``percent match,'' is simply the number of true positives divided by the total tumor size. The second, is called a ``correspondence ratio,'' and was created to account for the presence of false positives:

$$\mbox{Correspondence~Ratio} = \frac{\mbox{\small True Pos.}... ...lse Pos.})} {\mbox{\small Number Pixels in Ground Truth Tumor}}$$

For comparing on a per volume basis, the average value for Percent Match was generated using:

$$\mbox{Average~\%~Match} = \frac {\sum_{i=1}^{\mbox{\small sl... ...small slices in set}} \mbox{(number ground truth pixels)}_{i}}$$

The average value for the Correspondence Ratio is similarly generated.

  

Patient Scan True False False Tumor Percent Corr. ``True'' False

Positive Positive Negative Size Match Ratio Positive

1 Base 6921 2700 234 7155 0.97 0.78 80

1 R1 7038 3879 196 7234 0.97 0.70 467

1 R2 7285 4869 176 7461 0.98 0.65 496

1 R3 6206 3261 166 6372 0.97 0.72 227

1 R4 5930 3130 48 5978 0.99 0.63 47

2 Base 7892 5976 408 8300 0.95 0.54 18

2 R1 10092 3481 1059 11151 0.91 0.75 66

2 R2 14822 4961 1012 15834 0.94 0.78 219

3 Base 8917 1635 581 9498 0.94 0.85 47

3 R1 5003 2619 169 5172 0.97 0.71 89

4 Base 3054 1536 75 3129 0.98 0.73 124

4 R1 3627 2082 659 4286 0.85 0.43 1092

4 R2 2506 1020 1103 3609 0.69 0.46 495

5 Base 829 573 173 1002 0.83 0.54 161

6 Base 1425 624 1425 0.96 0.78 53

7 Base 177 175 177 1.00 0.51 54

Table 5 lists the results of the KB system on a per-volume basis. The results show that the KB system performs well overall. We note that 89 of the 120 slices had a Percent Match rating of 90% or higher. Slices that showed significant False Negative presence were primarily the result of two situations. Some tumor could be lost during the intra-cranial extraction stage. One test slice (from Patient 4 Repeat Scan 2) had significant tumor pixels lost during the morphological operations following tumor recovery from the quadrangle test. In four uppermost test slices (all from Patient 1), part of the tumor had grown beyond the intra-cranial region into an area normally occupied by surrounding meningial membranes, which have an increased percentage presence in the uppermost slices. The tumor's location within these membranes, combined with the reduced brain size complicated extraction. Other instances of tumor loss occurred when the system captured the tumor borders, but not its interior, possibly due to more subtle gadolinium enhancement (still detected by the radiologist, but not clear enough in feature space) [42], or cases where necrosis prevented circulation of the enhancing agent, but the radiologist made a conservative diagnosis and marked the area as tumor.

Overall, the KB approach tended to significantly overestimate the tumor volume. Only one volume in Table 5 shows underestimation (Patient 4 Repeat Scan 2), and that can be traced to one test slice with significant tumor underestimation (described above). The tendency to over-estimate is consistent with the system's paradigm, since only those pixels positively believed to be non-tumor are removed, defaulting areas of uncertainty to be labeled as tumor.

To show the nature of the false positives in the knowledge-based system, an additional measurement, ``true'' false positives, were added to Table 5 to indicate how many of the false positives were actually not connected spatially to any ground truth tumor. This number is less than 15% of the false positives with 2 exceptions. An examination of the process of creating ground-truth images revealed a 5% inter-observer variability in tumor volume [41]. We also note that all brain tumors have micro-infiltration beyond the borders defined with gadolinium enhancement. This is especially true in glioblastoma-multiformes, which are the most aggressive grade of primary glioma brain tumors, and no one can tell the exact tumor borders without invasive histopathological methods [24,42,43] and these were unavailable. As a result, ground truth images mark the areas of tumor exhibiting the most angiogenesis (formation of blood vessels, resulting in the greatest gadolinium concentration). Therefore, the knowledge-based system may capture tumor boundaries that extend into areas showing lower degrees of angiogenesis (which would still be treated during therapy) [43].