## 3 Results and Discussions  
A total of 107 features (14 shape features, 18 first-order statistical features, and 65 texture features) were extracted from each PET study before and after co-registration with T1-weighted (for 15 patients because two T1 images were unavailable), and FLAIR (for all 17 patients) MRI sequences, for a total of three feature datasets for each lesion. Starting from an exploratory analysis of the difference percentage between the feature values obtained from original PET images and co-registered PET ones, the shape-based feature group showed a mean less than 5% for all features indicating that this group has significantly robust features (see Figure 2). This is because a similar VOI is used before and after co-registration, and as a result, the shape characteristics are not supposed to change significantly from each other after the co-registration process. Even the first-order statistical GLCM and NGTDM features showed a median of less than 20% (<10% for first-order statistical features); thus, they are quite robust (see Figure 3). Figure 3: _Cont_. Figure 2: Difference percentage between non-co-registered and co-registered PET with T1-weighted and FLAIR MRI (the median is indicated in orange, while mean in green) for shape-based features. Vice versa, significant differences were found for the remaining texture matrices with mean values above 40% (Figure 4). In the case of the GLSZM Large Area High Gray Level Emphasis feature, the main exceeded 70%. These results are consistent with previous results published in [33]. In addition, in GLSZM group, a peculiarly high difference percentage was obtained for one patient (DP = 546% for the Large Area Low Gray Level Emphasis feature). Once again, this result shows a similarity with [PERSON]'s findings [33], where the GLSZM class is the one with the highest variation. Specifically, a difference of 106.58% was reported for the Large Area Low Gray Level Emphasis feature. This value refers to the variability analysis of the PET features when image acquisition is repeated five times. Conversely, in our study, the comparison is not between PET phantom studies obtained at different times but between PET and co-registered PET studies. Consequently, we can expect that this difference increases in our study where image co-registration is considered. In other studies dealing with other types of images, i.e., CT imaging [17] where deformable image registration was applied, the shape-based features were 100% robust, while GLSZM and NGTDM were the most unstable feature groups. Furthermore, features from the categories of intensity and GLCM were considered as stable. This is in good agreement with our results. In a MRI study, [PERSON]'s [34] found that the variation of radiomics features were intermediate or high for Skewness, glcm-Autocorrelation, glcm-ClusterShade, glcm-Imc1, glrlm-LongRunLow (or High) GrayLevelEmphasis, firstorder-90 Percentile, glcm- ClusterTendency, glcm-Correlation, and ngtdm-Complexity. This also matches with our study. Figure 3: Difference percentage between non-co-registered and co-registered PET with T1-weighted and FLAIR MRI (the median is indicated in orange, while mean in green) for first-order, and GLCM, and NGTDM features, respectively. The next step was to verify if the same optimal set of radiomics features was obtained in the three groups of images after the selection process based on the Spearman rank correlation coefficient. This approach was replicated for all patient studies producing a matrix that showed the correlation coefficient for all extracted features (see Figure 5). Figure 4: Difference percentage between non-co-registered and co-registered PET with T1-weighted and FLAIR MRI (the median is indicated in orange, while mean in green) for GLRLM, GLSZM, and GLDM features. A threshold of 0.8 (see Table 1) was chosen to reduce the amount of radiomics features that are highly correlated. In this way, only uncorrelated features were considered.