## 4 Results and Discussion
### Evaluation of Detection Results
If \(z_{i}\) is a random variable indicating an intensity level contained in an image with \(L\) being the total number of intensity levels and \(p(z_{i})\) is the probability of occurrence of that intensity level, then \(p(z)\), where z ranges from \(z_{1}\) to \(z_{L}\), is the intensity histogram of the image, viewed as the probability density function. The expression for the mean or average intensity (\(m_{z}\)) is given as follows:  
\[m_{z}=\sum_{i=1}^{L-1}z_{i}p(z_{i}) \tag{11}\]  
The general expression for the nth statistical moment of the mean (\(\mu_{n}\)) is formulated as:  
\[\mu_{n}=\sum_{i=1}^{L-1}(z_{i}-m_{z})^{n}p(z_{i}) \tag{12}\]  
The standard deviation (\(\sigma\)) corresponding to the pixel intensity distribution correlates to the average contrast and can be calculated using the second-order statistical moment (\(\mu_{2}\)), as the variance (\(\sigma^{2}\)) of a distribution is given by the second moment. \[\sigma=\sqrt{\mu_{2}(z)}=\sqrt{\sigma^{2}} \tag{13}\]  
Looking at Table 1, we can see that entropy thresholding produces the highest contrast in examined cases but mean shift segmentation and Otsu thresholding also provide good contrast. This trend can also be seen in the first to fourth-order statistics. Entropy thresholding results possess increased entropy (lower value), indicating a larger amount of information that can be interpreted as a higher number of object pixels detected. The standard deviation between the resulting pixels is also higher for entropy thresholding compared to Otsu and mean shift segmentation. Nevertheless, all three techniques segment the image efficiently. The mean shift segmentation algorithm eliminates noise entirely and only the cancer region can be seen. This can also mean that it might have missed certain pixels pertaining to the tumor/object, even though it has the least amount of noise. As the final step of evaluating the potential of the proposed tumor visualization and delineation system, a comparison has also been made between the texture features of the background (normal tissue) and those of the tumor, as defined by a pathology expert on the one tissue sample available in our study. This shows that texture features can be used to characterize cancerous tumors to differentiate them from normal healthy tissue. Comparing the statistical texture parameters of the area selected from the tumor region and from the normal tissue region (Table 2), we can clearly see the trend in the difference between the two. The texture features of cancer differ markedly from those of normal tissue in terms of examined texture information metrics. The tumor region is brighter and possesses higher contrast than normal tissue. The entropy of the cancer part is also much higher in all cases than the normal tissue, as is the case with the standard deviation and kurtosis. This indicates that the intensity of the tumor region is more concentrated towards a certain value (demonstrated by the small amount of skewness or higher kurtosis). The normal tissue region is also more homogenous and \"even\" compared to the tumor region. The statistical quantification of texture shown above demonstrates that it can be used as a metric to characterize cancer and differentiate it from healthy tissue.