Knowledge-Based Vs. kNN

**Table 6:** Comparison of kNN (k=7) Tumor Segmentation Vs. Hand Labeled Segmentation Per Volume.
Patient	Scan	True	False	False	Percent	Corr.
		Positive	Negative	Positive	Match	Ratio
1	Base	6430	782	3592	0.89	0.64
1	R1	6548	781	5410	0.89	0.52
1	R2	6544	925	5032	0.88	0.54
1	R3	5643	751	5227	0.88	0.47
1	R4	5274	935	5500	0.85	0.41
2	Base	6227	2167	3287	0.74	0.55
2	R1	5933	5217	6840	0.53	0.23
2	R2	7905	8199	7498	0.49	0.26
3	Base	6972	2570	4027	0.73	0.52
3	R1	3695	1476	2903	0.71	0.43
4	Base	2191	938	1716	0.70	0.43
4	R1	2105	2193	3432	0.49	0.09
4	R2	1988	1614	2869	0.55	0.15
5	Base	874	144	1490	0.86	0.13
6	Base	319	116	1085	0.22	-0.16
7	Base	175	1	1128	0.99	-2.21

One of the advantages of this KB approach is that human based training regions of interest (ROI's), currently required for supervised techniques [44], are not necessary after rule acquisition. Yet, results can be as good, if not better, than those obtained from supervised methods, without the need to for time-consuming ROI selection, which make such methods impractical for clinical use and do not guarantee satisfactory performance. Table 6 shows how well the supervised k-nearest neighbors (kNN) algorithm (k=7) [45] performed on the same slices processed by the KB system. The kNN method finds the k=7 labeled pixels from the ROI's closest to a test pixel and classifies the test pixel into the majority class of the associated ROI's. The kNN algorithm has been shown to be less sensitive to ROI selection than seed-growing, a commercially available supervised approach (ISG Technologies, Toronto, Canada) [44,46].

It must be noted that the kNN results include extra-cranial pixels in the tumor class because kNN is applied to the whole image. No extraction of the actual tumor is done, which would require additional supervisor intervention. The kNN numbers shown here were the mean results over multiple trials of ROI selection, meaning that all kNN slice segmentations were effectively training slices. Furthermore, kNN introduces the question of inter and intra-observer variability, which was rated at approximately 9% and 5% respectively [47]. In contrast, the KB system was built from a small subset of the available slices and processed 103 slices in unsupervised mode with a static rule set allowing for complete repeatability.

**Table 7:** Tumor Volume Comparison (Pat. = Patient, GT = Ground Truth Volume, KB = Knowledge Based, kNN SD = kNN Standard Deviation, kNN Trial = Number of Trials, kNN Obs. = Number of kNN Observers.)
Pat.	Scan	GT	KB	kNN	kNN	kNN	kNN
		Volume	Volume	Volume	SD	Trials	Obs.
1	Base	7155	9621	10022	732	5	2
1	R1	7234	10917	11958	2236	5	2
1	R2	7461	12154	11576	1615	5	2
1	R3	6372	9467	10870	4395	5	2
1	R4	5978	9060	10774	891	5	2
2	Base	8300	13868	9514	1635	5	2
2	R1	11151	13573	12773	2375	5	2
2	R2	15834	19783	15403	1942	5	2
3	Base	9498	10552	10999	1323	5	3
3	R1	5172	7622	6598	1830	5	3
4	Base	3129	4590	3907	643	4	2
4	R1	4286	5709	5537	592	4	2
4	R2	3609	3526	4857	727	4	2
5	Base	1002	1042	2364	N/A	1	1
6	Base	1425	2049	1404	N/A	1	1
7	Base	177	352	1303	207	4	2

**Figure 12:** Tracking Tumor Growth/Shrinkage Over Repeat Scans. KB=Knowledge-Based System. kNN=k-Nearest Neighbors. GT=Ground Truth.
$\begin{figure} \centerline{ \parbox{3in}{ \centerline{\psfig{figure=/home/daffy4... ...al/nasa5a.ps,width=3in,height=2.5in}} \centerline{(d) Patient 4} } }\end{figure}$