**4.2 Implementation and anlaysis**

By using SGLCM, approximately two dozen co-occurrence features can be obtained [16]. Consideration of the number of distance angle relations also will lead to a potentially large number of dependent features. In this study, we restrict the representation to four features, which we hypothesize from Table 1 would provide useful information for texture characterization. These are entropy, correlation, contrast and homogeneity. For soft textures, the second order measurement distributions change very slightly with distance, while for coarse textures, the change in the distribution is rapid [16].

Characterization of Hepatic Lesions

Cyst

Tumor

Healthy

Cyst

Tumor

Healthy

Table 2. Entropy results for cyst, tumor and healthy liver.

Table 3. Correlation results for cyst, tumor and healthy liver.

Using Grid Computing (Globus) and Neural Networks 277

ROI Direction, *θ* Entropy

ROI 0° 45° 90° 135° Min Max T1 5.802 5.724 6.425 6.484 5.802 6.484 T2 5.487 5.524 5.925 6.183 5.487 6.183 T3 5.477 6.554 6.072 7.854 5.477 7.854 T4 5.339 6.774 6.241 7.692 5.339 7.692 T5 5.174 6.694 6.131 7.911 **5.174 7.911**  T6 5.477 5.884 6.082 7.054 5.477 7.054 T7 5.884 6.145 6.281 7.692 5.884 7.692

T8 2.802 2.724 2.925 4.284 2.802 4.284 T9 2.487 2.719 2.919 4.183 **2.487** 4.183 T10 2.677 2.794 2.999 4.254 2.677 3.254 T11 2.539 2.724 2.802 4.192 2.539 4.192 T12 2.494 2.894 2.994 4.291 2.494 **4.291**  T13 3.327 3.484 3.792 4.054 3.327 4.054 T14 3.124 3.145 3.381 4.102 3.124 4.102

T15 0.054 0.692 1.054 1.692 **0.054** 1.692 T16 0.082 0.281 1.082 1.954 0.082 **1.954**  T17 0.554 0.784 1.054 1.281 0.554 1.281 T18 0.887 0.231 1.607 1.784 0.887 1.784 T19 0.574 0.884 1.177 1.231 0.574 1.231 T20 0.114 0.145 1.484 1.884 0.114 1.884 T21 0.774 0.954 1.074 1.145 0.774 1.145

ROI Direction, *θ* Correlation

ROI 0° 45° 90° 135° Min Max T1 5.962 6.403 6.825 6.854 **5.962** 6.854 T2 6.127 6.241 6.325 6.483 6.127 6.483 T3 6.493 6.554 6.610 6.854 6.493 6.854 T4 6.384 6.774 6.941 6.997 6.384 **6.997**  T5 6.128 6.694 6.910 6.111 6.128 6.910 T6 6.773 6.884 6.904 6.341 6.773 6.904 T7 6.237 6.345 6.431 6.562 6.237 6.562

T8 2.302 2.924 3.164 4.269 2.302 4.269 T9 2.300 2.811 3.119 4.702 **2.300** 4.702 T10 2.321 2.703 2.321 4.164 2.321 4.164 T11 2.370 2.718 3.860 4.718 2.370 4.718 T12 2.410 2.843 2.994 4.932 2.410 **4.932**  T13 3.156 3.481 3.494 4.156 3.156 4.156 T14 2.186 2.916 3.994 4.321 2.186 4.321

T15 0.110 0.241 1.314 1.500 0.110 **1.500**  T16 0.120 0.231 1.312 1.431 0.120 1.431 T17 0.152 0.214 1.224 1.322 0.152 1.322 T18 0.133 0.231 1.167 1.311 0.133 1.311 T19 0.142 0.284 1.437 1.410 0.142 1.410 T20 0.071 0.145 1.224 1.374 **0.071** 1.374 T21 0.140 0.254 1.284 1.350 0.140 1.350

Fig. 7. Automated segmentation of image block in a cyst liver boundary using (a) 5 x 5 (b) 8 x 8 (c) 10 x 10 image block (d) shows the liver region in MRI abdomen image.

Table 2 shows the statistical results achieved for entropy calculated based on spatial cooccurrence matrices generated using SGLCM on cysts, tumor and healthy liver of the training set (*T1, T2, …, Tn*). Entropy is consistent within a specific range from 5.174-7.911 for cyst classification and 2.487- 4.291 for tumor classification. In healthy liver, entropy ranges from 0.054-1.954. As the entropy ranges are distinct for each of the 3 categories tested, entropy could be a suitable feature for successful liver lesions classification.

Table 3 provides the results for the correlation calculated using SGLCM. As observed, correlation is consistent within a specific range from 5.962-6.997 for cyst and 2.300-4.932 for tumor and 0.071-1.500 for healthy liver. Being different for the 3 categories, correlation may also be deemed a suitable classification feature.

The statistical results for two more features, homogeneity and contrast, calculated based on SGLCM on healthy liver ROI were inconsistent as shown in Table 4 and Table 5. As all the ranges for the 3 categories overlap, these features cannot be used to classify the liver MRI images.
