Radiomics analysis of [18F]-fluorodeoxyglucose ([18F]-FDG) PET images could be leveraged for personalised cancer medicine. However, the inherent sensitivity of radiomic features to intensity discretisation and voxel interpolation complicates its clinical translation. In this work, we evaluated the robustness of tumour [18F]-FDG-PET radiomic features to 174 different variations in intensity resolution or voxel size, and determined whether implementing parameter range conditions or dependency corrections could improve their robustness. Using 485 patient images spanning three cancer types: non-small cell lung cancer (NSCLC), melanoma, and lymphoma, we observed features were more sensitive to intensity discretisation than voxel interpolation, especially texture features. In most of our investigations, the majority of non-robust features could be made robust by applying parameter range conditions. Correctable features, which were generally fewer than conditionally robust, showed systematic dependence on bin configuration or voxel size that could be minimised by applying corrections based on simple mathematical equations. Melanoma images exhibited limited robustness and correctability relative to NSCLC and lymphoma. Our study provides an in-depth characterisation of the sensitivity of [18F]-FDG-PET features to image processing variations and reinforces the need for careful selection of imaging biomarkers prior to any clinical application.