The objectives of the study are to develop a new way to assess stability and discrimination capacity of radiomic features without the need of test-retest or multiple delineations and to use information obtained to perform a preliminary feature selection. Apparent diffusion coefficient (ADC) maps were computed from diffusion-weighted magnetic resonance images (DW-MRI) of two groups of patients: 18 with soft tissue sarcomas (STS) and 18 with oropharyngeal cancers (OPC). Sixty-nine radiomic features were computed, using three different histogram discretizations (16, 32, and 64 bins). Geometrical transformations (translations) of increasing entity were applied to the regions of interest (ROIs), and the intra-class correlation coefficient (ICC) was used to compare the features computed on the original and modified ROIs. The distribution of ICC values for minimal and maximal entity translations (ICC10 and ICC100, respectively) was used to adjust thresholds of ICC (ICCmin and ICCmax) used to discriminate between good, unstable (ICC10 < ICCmin), and non-discriminative features (ICC100 > ICCmax). Fifty-four and 59 radiomic features passed the stability-based selection for all the three histogram discretizations for the OPC and STS datasets, respectively. The excluded features were similar across the different histogram discretizations (Jaccard's index 0.77 ± 0.13 and 0.9 ± 0.1 for OPC and STS, respectively) but different between datasets (Jaccard's index 0.19 ± 0.02). The results suggest that the observed radiomic features are mainly stable and discriminative, but the stability depends on the region of the body under observation. The method provides a way to assess stability without the need of test-retest or multiple delineations.