## 3 Results
(**a**) Homogeneity, (**b**) contrast, (**c**) energy, (**d**) contrast, (**e**) dissimilarity and (**f**) entropy. Figure 6: Six textural features vs. image contrast for VOI\({}_{\text{true}}\) for acquisition duration 900 s and quantization level 64. (**a**) Homogeneity, (**b**) contrast, (**c**) energy, (**d**) contrast, (**e**) dissimilarity and (**f**) entropy. Volumes estimated from all methods for all contrasts are shown in Figure 7. VOI\({}_{\text{40T}}\), estimated using I\({}_{\text{40T}}\), are always bigger compared to VOI\({}_{\text{true}}\) for 2:1 contrast and low noise represented by longer acquisition duration. VOI\({}_{\text{40T}}\) for contrast 4:1 are similar to VOI\({}_{\text{true}}\), especially for volumes bigger than 5.58 cm\({}^{3}\) and less dependent on noise, indicating that I\({}_{\text{40T}}\) is optimal for 4:1 contrast. VOI\({}_{\text{40T}}\) are always overestimated for contrast 2:1 for all noise levels for volumes less than 5.58 cm\({}^{3}\). For bigger volumes, VOI\({}_{\text{40T}}\) are underestimated for high noise cases for contrast 2:1. As the contrast goes down, the dependency on the volume and noise increases and the discrepancies between VOI\({}_{\text{A}}\) and VOI\({}_{\text{true}}\) become noticeable, especially for smaller volumes and higher noise. The relationships between textural features and noise represented by acquisition durations at contrast level 2:1 for VOI\({}_{\text{true}}\) with VOI\({}_{\text{40T}}\) and VOI\({}_{\text{A}}\) are shown in Figures 8 and 9, respectively. For smaller volumes, textural features extracted from VOI\({}_{\text{40T}}\) are significantly different compared to those of VOI\({}_{\text{True}}\) (Figure 8). With the increase in volumes, the differences between the features extracted from these two volumes also reduce. For the case of VOI\({}_{\text{40T}}\), the textural features show dependency on acquisition duration. However, for VOI\({}_{\text{A}}\), the dependency on the noise is reduced for volume greater than 2.57 cm\({}^{3}\) and the extracted features closely match with the VOI\({}_{\text{True}}\) features (Figure 9). Figure 7: Log of volumes vs. acquisition durations for all six spheres for three segmentation methods (true volume (VOI\({}_{\text{True}}\)), 40% threshold (VOI\({}_{\text{40T}}\)), and adaptive threshold (VOI\({}_{\text{A}}\))) for contrast 2:1 (**a**) and 4:1 (**b**). Negative sign on y axis represents volume smaller than 1 cm\({}^{3}\) in log scale. Figure 8: Six textural features vs. acquisition durations for two different segmented volumes (VOI\({}_{\text{true}}\) and VOI\({}_{\text{40T}}\)) for contrast 2:1 and quantization level 64. (**a**) Homogeneity, (**b**) contrast, (**c**) energy, (**d**) contrast, (**e**) dissimilarity and (**f**) entropy. Figure 9: Six textural features vs. acquisition durations for two different segmented volumes (VOI\({}_{\text{true}}\) and VOI\({}_{\text{A}}\)) for contrast 2:1 and quantization level 64. (**a**) Homogeneity, (**b**) contrast, (**c**) energy, (**d**) contrast, (**e**) dissimilarity and (**f**) entropy. Figure 10 shows the six textural features for 2.57 and 26.52 cm\({}^{3}\) cylindrical, ellipsoidal, and spherical volumes. The results indicate that energy and entropy are more sensitive to change in volumes compared to the other four textural measures. However, for similar volumes, none of the textural feature shows any dependency on the shape of the volume. Figure 11 shows the textural features comparison between the six homogenous spheres of contrast 4:1 with the two heterogeneous spheres of the same contrast for three different segmentation methods. Due to PVE, the smaller heterogeneous sphere appears less heterogeneous in the reconstructed image for 900 s acquisition durations (Figure 2). Because of that, all the textural features generated using VOI\({}_{\text{true}}\) for smaller heterogeneous sphere agree with the homogeneous spheres of similar volumes except correlation, which is dependent on the intensity.