# Evaluation of Metamorphic Testing for Edge Detection in MRI Brain Diagnostics
## 5 Results and Discussion
of test cases violating MR\({}_{2}\) for T1, T2, and flair images. \begin{table}
\begin{tabular}{c c c} \hline \hline
**MR** & **0 = 0.95** & **FDR** \\ \hline MR\({}_{1}\) & 24 & 27.27\% \\ MR\({}_{2}\) & 32 & 3.03\% \\ MR\({}_{3}\) & 25 & 24.24\% \\ MR\({}_{4}\) & 24 & 27.27\% \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Fault detection rate of flair type images. Figure 7: No. of test cases violating MR\({}_{1}\) for T1, T2, and flair images. identifying faults in T2-weighted images by satisfying 21 test cases. It is concluded that MR\({}_{2}\) is recommended for only T2-weighted images by violating the MR on 8 test cases. Let us talk about the third MR which is reflection at the ordinate. The result of MR\({}_{3}\) is given in Figure 9.  
Figure 9 shows that the capability of MR\({}_{3}\) to detect faults is low for flair-type images by violating only 8 test cases, whereas the capability of MR\({}_{3}\) to detect faults is high for T1- and T2-weighted images by violating 12 and 13 test cases, respectively. It is concluded that MR\({}_{3}\) is recommended for all the categories of images. The fault detection capability of this MR is low for flair-type images when comparing with T1- and T2-weighted images, but it is still able to detect faults. The last MR is reflection at abscissa. Figure 10 shows the statistics of MR\({}_{4}\). Figure 10 shows that the FDR of MR\({}_{4}\) is very high for T1- and T2-weighted images when \(\theta\) is set to 0.95. Both of the image types violate the relation on 21 test cases each. At the same \(\theta\) value, flair-type images violate the relation on 9 test cases, which is neither too low nor too high. Hence, it is concluded that MR\({}_{4}\) is useful for all the three types of images but highly recommended for T1- and T2-weighted images. The FDR of all four MRs against all the three types of images is shown in Figure 11.  
It is concluded from Figure 11 that for each image type, MR\({}_{4}\) is considered the best among all the MRs by achieving the highest FDR. The FDR of MR\({}_{4}\) for T1, T2, and flair-type images is 63.63%, 72.41%, and 27.27%, respectively. On the other hand, the FDR of MR\({}_{2}\) is considered the lowest in all three types of images, with an FDR value of 12.12%, 27.54%, and 3.03%, respectively. Hence, it is observed that for T1, T2, and flair images, MR\({}_{4}\) should be preferred to enhance the credibility of MRI diagnostics. On the other hand, MR\({}_{2}\) produced a low FDR and is not suggested for the diagnostics purpose, especially in flair-type images. Figure 10: No. of test cases violating MR\({}_{4}\) on T1, T2, and flair images. Figure 9: No. of test cases violating MR\({}_{3}\) for T1, T2, and flair image. A comparison of the proposed methodology with existing techniques is given in Table 10.  
As shown in Table 10, random camera images are used for the testing of IPAs. We have used a dataset of brain MRIs. To the best of our knowledge, no prior work has been conducted using an MRI dataset in MT. In the literature, there is no systematic way to ascertain that the generated test cases are actually random and have diversity to represent all different type of attributes or full coverage. If the sample is not a full representation of the population, then we would obtain biased results affecting the final outcome. In the proposed framework, we have precisely defined procedures to generate source test cases randomly by using black-box and white-box testing. In the existing literature, the outputs of two images are compared either manually or pixel by pixel. Sometimes, when comparing the images pixel by pixel, they may have differences which cannot be seen with the naked eye. In the proposed methodology, SSIM is used for the comparison, so we obtain the exact match between the two images.