## 2 Materials and Methods
In this segmentation method, the threshold intensity (IA) is given by [34]:  
\[\text{I}_{\text{A}}=(\alpha\times\text{I}_{\text{70}})+\left(\beta\times\text {I}_{\text{bg}}\right) \tag{2}\]  
I70 is defined as the average intensity in a 3D contour containing all voxels with a value greater than 70% of the Imax within the roughly delineated VOI. Ib\({}_{\text{bg}}\) is the average background intensity. To avoid spill in effects from the nearby hot spheres, the background is determined by placing a 26.52 mL VOI away from all the spheres. Before carrying out the threshold-based segmentation, six roughly delineated VOIs containing a sphere with different size each were generated. Fixed and adaptive threshold methods were then applied separately on these roughly delineated VOIs to generate the corresponding VOIs. The adaptive threshold method parameters (\(\alpha\) and \(\beta\)) were calculated using the mean value of optimal cutoff intensities (Ioptimal) of five realizations using all contrasts for each acquisition duration. Ioptimal of each hot sphere is calculated using optimal threshold (Toptimal) and Imax. Toptimal is estimated as the percentage threshold value of Imax which provides the best matched thresholded volume with the VOItrue for the uniform sphere phantom. To investigate the individual effect of size and segmentation on GLCM features, six similar size spherical VOIs were also placed on the background away from the hot spheres to remove the variability arising from inconsistent segmentation of VOI. For investigating the effects of shape, three different shaped (cylinder, ellipsoid and spheres) VOIs with the same volume of 26.52 cm\({}^{3}\) were delineated in the background (Figure 2). Figure 2: One reconstructed slice of the NEMA PET phantom with homogeneous spheres for contrast 2:1 (**a**–**c**) and 4:1 (**d**–**f**). The heterogeneous spherical inserts with cold inner core (**g**–**i**). (**a**,**d**,**g**) For 900 s reconstructions; (**b**,**e**,**h**) for 2000 s reconstructions; and (**c**,**f**,**i**) for 7200 s reconstructions. Red circles represent VOIture and green circles represent spherical background VOIs with different volumes. (**j**–**l**) represent cylindrical-, ellipsoidal-, and spherical-shaped VOIs with the same volumes that were delineated in the uniform background. Since it has been reported that FBN has several advantages over FBS in many circumstances [21], it was implemented in this study. In FBN-based quantization, the intensities of each VOI is first normalized between 0 and 1 and then multiplied by different quantized values (Q = 8, 16, 32, 64, 128 and 256)  
\[\mathrm{N(x)=Q\times\left(\frac{I(x)-[I(x)]_{min}}{[I(x)]_{max}-[I(x)]_{min}}\right)} \tag{3}\]  
where I(x) is the intensity of voxel \(x\) in the original image, \([I(x)]_{min}\) and \([I(x)]_{max}\) are the minimum and maximum value in the VOI, and Q is the quantization level (4, 8, 16, 32, 64, 128 and 256). Before deriving grey level co-occurrence matrix (GLCM), each VOI was normalized and quantized separately. Six second-order heterogeneity measures (homogeneity, correlation, energy, contrast, dissimilarity, and entropy were then calculated from the GLCM data. The textural features are given as  
\[ \begin{array}{l}\mathrm{Homogeneity}=\sum\limits_{i,j}\frac{1}{1-(i-j)^{2}} p(i,j)\\ \mathrm{Correlation}=\sum\limits_{i,j}\frac{(i-\mu_{i})(i-\mu_{j})p(i,j)}{ \sigma_{i}\sigma_{j}}\\ \mathrm{Energy}=\sum\limits_{i,j}p(i,j)^{2}\\ \mathrm{Contrast}=\sum\limits_{i,j}\abs{i-j}^{2}p(i,j)\\ \mathrm{Dissimilarity}=\sum\limits_{i,j}\abs{i,j}p(i,j)\\ \mathrm{Entropy}=-\sum\limits_{i,j}p(i,j)\log(p(i,j))\end{array}  \tag{4}\]  
where (i,j) indicates cell location of the GLCM matrix, p(i,j) is the cell value at (i,j), and \(\mu\) and \(\sigma\) are mean and standard deviation, respectively. The ranges of homogeneity, energy, and entropy are [0, 1]. Homogeneity calculated using GLCM is high (with maximum limit of 1) in the case when the diagonal elements of GLCM have higher values.