## 3 Results and Discussion
### Detection of Protein Overexpression in Gels Using the IPBBIS Algorithm
#### 3.3.7 IPBBIS Study on the Image Dataset Using the Confusion Matrix

Table 7: Confusion matrix obtained by analyzing 1561 samples with GPN protein expressed at different concentrations on heterogeneous SDS-PAGE gels. \begin{table}
\begin{tabular}{c c c c} \hline \multicolumn{2}{c}{**Accuracy of Homogeneous Gels**} & \multicolumn{2}{c}{**Accuracy of Heterogeneous Gels**} \\ \hline
0.985052 & 0.91736 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Confusion matrix obtained by analyzing 1561 samples with GPN protein expressed at different concentrations on heterogeneous SDS-PAGE gels. \begin{table}
\begin{tabular}{c c c} \hline \multicolumn{2}{c}{**Predicted**} \\ \hline  & & **Positive** & **Negative** \\ \hline \multirow{2}{*}{Real} & Positive & TP = 310 & FN = 8 \\  & Negative & FP = 2 & TN = 349 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Confusion matrix obtained by analyzing 669 samples expressing GPN protein at different concentrations on homogeneous SDS-PAGE gels. For the manual measurements, K-means segmentation and Otsu segmentation, it was necessary to cut out each of the bands and separate them from the gel image as neither of these methods can analyze the whole gel. The results of the measurements of each of the bands at different concentrations are aggregated in Table 4, indicating the type of methodology used in the row. The data in Table 4 were normalized to verify the functionality of the methodologies used to assess protein overexpression within the gel in the different samples (Figure 14D). The data in Table 4, corresponding to the intensity values in Figure 14D, were sorted according to the amount of expressed protein from lowest to highest overexpression and placed in Table 8, normalized (see Table 9), and used to measure the correct level of GPN protein overexpression for each of the methods used by the following operation:  
Let \(\mathrm{x_{n}}\) be the n-th value of the measured area, and \(\mathrm{x_{m}}\) be the value of the measured area in the band with the highest protein concentration. If \(\mathrm{x_{m}}>\mathrm{x_{n}}\Rightarrow\mathrm{x_{m}}-\mathrm{x_{n}}>0\). This expression indicates that the measurement of the overexpression level is correct since positive values are expected if the concentration is increasing. On the other hand, if \(\mathrm{x_{m}}<\mathrm{x_{n}}\Rightarrow\mathrm{x_{m}}-\mathrm{x_{n}}<0\), it indicates that the overexpression level was miscalculated. The analyzed method presents errors in its measurement because the protein concentration is increasing and not decreasing. As seen in Table 10, the results of the above analysis, applied to each of the measurements, indicate that the proposed image profiling method based on binarized image segmentation (ROI-GPN) does not show any negative values. In contrast, the manual method shows two negative values (lanes 4 and 8 in Table 10), the K-means segmentation shows two negative values (lanes 4 and 8 in Table 10), and the Otsu segmentation shows two negative values (lanes 8 and 9 in Table 10). Figure 16: (**A**) Manual calculation of the band area by outlining the spot contour. (**B**) Area calculated by K-means segmentation. (**C**) Area calculated by Otsu segmentation. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline Concentration mg/mL & 0 & 2 & 9.5 & 14 & 14.5 & 18 & 18.5 & 26 & 27 & 30 \\ \hline Lane & 3 & 2 & 5 & 11 & 4 & 7 & 9 & 10 & 6 & 8 \\ ROI-GPN & 0 & 10.38 & 18.67 & 20.11 & 20.55 & 22.87 & 23.08 & 27.26 & 27.34 & 28.82 \\ Manual Area & 0 & 513.6 & 680.1 & 869.25 & 830.25 & 830 & 934.5 & 983.5 & 1373.8 & 1061.5 \\ K-means segmentation & 0 & 495.5 & 933 & 993.13 & 969.62 & 1132 & 1134.9 & 1422.1 & 1457.2 & 1336.2 \\ Otsu segmentation Area & 0 & 535.8 & 1023 & 1174.6 & 1189.8 & 1318 & 1269.1 & 1585.9 & 1646.8 & 1557.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The data in Table 4 are ordered according to the amount of protein expressed from lowest to highest overexpression.