## 9 Results and Discussion
In addition to the subjective evaluation, the liver segmentation method was evaluated objectively by comparing the results obtained by the manual segmentation with the results obtained by the proposed method. Only three data set of three subjects were included in the objective evaluation process due to the difficulty of the manual segmentation of the liver in non-contrast-enhanced CT data  
Figure 10: Samples of the original CT images and the results of fat segmentation and classification. and the extensive time required. The true positive rate was used to express the percentage of a true segmented liver, while the false positive rate was used to express the percentage of the non-liver tissues that were mistakenly segmented by the proposed method. Table 2 shows the obtained true positive and false positive rates for the three subjects. Figure 11 shows side and front views for two subjects where the liver is bounded by black contours. A general observation of the total results of applying the proposed liver segmentation method to the entire 30 subjects shows that the method successfully implements the segmentation operation. Additionally, the proposed method shows robustness in the capability to separate non-liver tissues from liver tissues. The volumetric information for the total abdomen fat, SF, and VF does not provide realistic information about obesity due to the variation in the sizes of people. Therefore, the  
Figure 11: Two samples of the results of the liver segmentation method. (**a**) Front view, (**b**) side view. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Subjects** & **Accuracy (Average)** & **Mean Error Rate (Average)** \\ \hline Subject \#1 & 83.49\% & 0.027\% \\ Subject \#2 & 85.13\% & 0.1\% \\ Subject \#3 & 84.59\% & 0.031\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Abdomen fat segmentation and classification method results. following ratios were used as an indication of obesity. For each subject, CT slices between the first and fifth lumbar vertebrae (L1-L5) were used. Figure 12 shows two samples that highlight the area where the CT slices were selected from. The region of interest is bounded by the two white lines. The segmented and classified non-contrast CT slices for each subject were used to calculate the following ratios (total fat ratio \"\(TFR\)\", subcutaneous fat ratio \"\(SFR\)\", and visceral fat ratio \"\(VFR\)\"):  
\[TFR=\frac{\#\,of\,fat\,pixels}{\textit{abdomen\,pixels}\,(organs+tissues)} \tag{4}\]  
\[SFR=\frac{\#\,of\,SF\,pixels}{\textit{abdomen\,pixels}\,(organs+tissues)} \tag{5}\]  
\[\text{VFR}=\frac{\#\,of\,VF\,pixels}{\textit{abdomen\,pixels}\,(organs+tissues)} \tag{6}\]  
The reason for using the ratios mentioned above instead of the actual number of pixels is the subjects' size variety. The number of fat pixels in a tall, non-obese subject might be greater than the number of fat pixels in a short, obese subject. Therefore, the ratios were used as an indication of obesity (percentage of fat in the abdominal region) for a subject. Liver density is inversely related to liver fat, according to [PERSON] et al. [7]. The mean of the liver HU values for the used data set was employed as an indicator for the level of diffused fat in the liver. Figure 13 illustrates two examples of two CT images (two different subjects) where the liver is bounded by black contours using the proposed liver segmentation method. The liver in each example shows different tissue densities. To study the relationship between the accumulated abdomen fat ratios and the liver diffused fat, the correlation coefficient (R) and the \(p\)-value were used. Correlation is a statistical measurement of the relationship between two (or more) variables. Correlation coefficients range from \(+1\) to \(-1\). A zero correlation indicates that there is no relationship between the variables. A correlation of \(-1\) indicates a perfect negative correlation, meaning that as one variable goes up, the other goes down.