**7. Experimental results**

108 Liver Tumors

criteria: (1) size, (2) shape of each slice, (3) regional variation among the slices, (4) location in

In this study, we assume that the shape of a tumor is approximately spherical. Therefore, for the second criteria, we use a shape filter as shown in Fig. 5. For each tumor candidate, we first find a center of gravity, and then calculate distances from it to the 12 points which are on the edge of tumor candidate as shown in Fig.5. 4 points are cross points with the bounding box (line of a rectangle), which are shown in Fig.5 as diamond points. 8 points are boundary points sampled at intervals of 45 degree, which are shown in Fig.5 as small circle points. The ratio of maximum distance and minimum distance is used as a measure of shape. The ratio is a value larger than or equal to 1. If the candidate's shape is like a circle, the ratio will be 1. Since the tumor is considered having a spherical shape, the candidates are rejected if their ratio is larger than a pre-defined threshold (in our research, the threshold is

Though most false positive candidates can be rejected by the use of above 5 criterions, some tumor points will also be rejected. In order to recover the rejected true tumors, we use a new criterion, which is shown in Fig. 6 to check the rejected candidates. For each rejected tumor candidate, we first generate an edge image, and then superimpose it with two circles *L*in and *L*out having radius *r*in and *r*out, respectively, and centers corresponding to the center of the

tumor candidate's 2D ROI. Their parameters are defined in Eq. 4.

the image, and (5) numbers of connectivity among the slices.

set as 4).

Fig. 5. Illustration of a shape filter

Fig. 6. Illustration of a shape filter for recheck

We applied our proposed method to five sets of CT images. Information on each image is shown in Table 1. Data sets 1, 2, and 3 were used in the JAMIT CAD contest in July 2010, while Data sets 4 and 5 were used in the MICCA Liver Tumor Segmentation Challenge 2008 [11]. Table 2 shows the results of tumor detection. In this study, if a part of a tumor is detected in the correct region, we consider the result as a true positive. Because only the ground truth for Data sets 1, 2, and 3 were known, Table 2 shows comparisons between the detected results and the ground truth for Data sets 1–3. The proposed method provides accurate detection results for Data sets 1 and 2. For Data set 3, the detection rate is about 50% because the image includes numerous minute tumors.


Table 1. Information on each dataset


Table 2. Number of detected tumors

Fig. 7 shows the results of tumor detection using the EM/MPM algorithm and the method based on [6]. It removed high intensities without employing Maximum likelihood method and applied the EM algorithm. The results show that our proposed method is superior to the previous one. The reason is considered to be the use of histogram transformation with PDFs. In the previous method, the EM algorithm took more time to converge compared with that in our proposed method; this was because the proposed method employs Maximum likelihood method. Moreover, irregular shapes could be removed by using the shape filter [Fig. 7(d)].

Fig. 7. (a) the original image (Data set 4). The tumor detection result obtained (b) using the method based on [6], (c) the proposed method, and (d) by the application of a shape filter to the image in (c). (In (b)–(d), the detected regions are white and the arrows indicate the locations of the detected tumors.)

Fig. 8 show the results of the experiments for Data set 3. We used four methods: EM with and without preprocessing (contrast enhancement) and EM/MPM with and without preprocessing. As we used different pre-processing for EM and EM/MPM, it may affect the result a little. However, Figures 8(c)–(f) are the images obtained after morphology operations. Figures 8(c), (d) demonstrate the effectiveness of our histogram transformation. Comparing Figs. 8(c), (e) with Figs. 8(d), (f), we find that using EM/MPM improves performance.

Fig. 8. Results after morphology (white lines) (a) Smoothed original image (b) answer (c) EM without preprocessing (d) EM with preprocessing (e) EM/MPM without preprocessing (f) EM/MPM with preprocessing

Next, we quantitatively evaluate the tumor segmentation performance in terms of the metrics proposed in the MICCAI Liver Tumor Segmentation Challenge 2008 [11]. The metrics are the volumetric overlap error (Overlap Error), absolute relative volume difference (Vol. dif.), average symmetric surface distance (Ave. Dist.), RMS symmetric surface distance (RMS Dist.), and maximum surface distance (Max. Dist.). For ideal segmentation, all metrics should be zero. Table 3 shows the results obtained for one slice of a segmented region in a tumor by the metrics given in [11]. For Data set 1, regions in which tumors are detected are not solely represented by dark regions but also by bright voxels around them. Our proposed method can detect dark tumor regions; however, it cannot detect the bright tumor regions. Therefore, we excluded the results for Data set 1 and included only the results for the other data sets. We compared the current method with the previous method on the basis of the abovementioned method [6]. It is obvious from the results that we have improved on all metrics.


Table 3. Performance comparisons
