## 3 Proposed Tumor Visualization and Identification Framework
The second step (image fusion module) of the proposed overall scheme proceeds with fusing the results of the three individual image processing techniques applied in the first step and enables us to form the binary mask containing pixels that are active (non-zero intensity value) in more than one segmented images, resulting to a robust estimation of the \"strong and consistent components\" of tumor margins, i.e., the pixels that are detected as tumor belonging ones by at least two of the three adopted segmentation techniques. The final step of the overall pipeline of algorithms proceeds by applying mathematical morphology (image closing and region filling) to the fused quantized image, acting as a noise/outliers filter, filling out holes and refining borders, and derives the reconstructed geometry of the overall cancerous area as a closed and compact region, illustrating the potential for numerical computations regarding the tumor size, area, shape, and depth. The notion of \"Otsu thresholding\" was initially introduced as a non-parametric and unsupervised approach based on the assumption that an image is formulated by pixels from two principal classes (background region and foreground one containing the object/scene of interest), indicating that the image can be represented via a bimodal histogram [46]. Having established this image model, the method defines an optimal threshold value, under an iterative calculation procedure, in order to binarize the image. The threshold value is adaptively determined so that the intra-class divergence (variability between data points belonging to one class) is minimized and, at the same time, the inter-class deviation (differentiation between individuals of the two distinct classes) is maximized. This condition imposes efficient segmentation of the image, because the variance is considered a reliable index for determining the homogeneity of a region. The intra-class divergence is determined as the weighted sum of the variances within any of the two dominant classes, with \"weight\" representing the a priori likelihood of that particular class. On the contrary, the inter-class variance reaches its maximum by initializing a \"starting point\" value (threshold) and repeatedly updating it to attain the maximum differentiation between the two pixel distributions. Another thresholding technique exploited in this study is based on information theory and Shannon entropy maximization. Entropy can be considered as an index that represents the uncertainty of a random variable, thus it quantifies the information present in a dataset or a message [47]. The principal objective of this approach is to partition the image histogram (pixel intensity values considered as the probability distribution) into two different (independent) distributions via the determination of an optimal threshold value that maximizes the randomness of both image region classes, and, thus, enriched information content can be extracted [48, 49]. Let \(\mathrm{P}_{1}\), \(\mathrm{P}_{2}\),..., \(\mathrm{P}_{n}\) be the probability distributions of different pixel intensity values (levels of grey) represented within the image. Let \"\(s\)\" be the threshold value determined for binarizing the image (binary image segmentation). Thus, two independent classes (probability distributions) are outlined; the first one corresponds to pixel intensities varying from 0 to \"\(s\)\" and the second one representing grey levels from \"\(s\)+1\" to \"\(n\)\". Let these sets be defined as A and B, respectively, according to the following representation:  
\[A:\left\{ \begin{array}{l}\frac{P_{1}}{P_{s}},\frac{P_{2}}{P_{s}},\ldots, \frac{P_{s}}{P_{s}}\end{array}