Imaging of tumors is a standard step in diagnosing cancer and making subsequent treatment decisions. The emerging field of radiomics aims to extract quantitative features from these images which can be used for downstream modeling. Much of the current work in radiomics relies on methods that do not lend themselves to communicating results to physicians. In order for radiomics to be used in clinically accepted tools, there is a motivation to move away from black box methods towards more interpretable approaches. In this thesis, we present two projects that aim to address the need for meaningful features in radiomic analyses. In the first project, we develop a hierarchical tree structure on the image pixels, creating a feature that captures intra-tumor heterogeneity. We demonstrate that this feature can be used in the classification of adrenal lesions. In the second project, to classify subjects on the basis of their radiomic features, we propose a Bayesian variable selection approach that favors the inclusion of more reliable features, and can additionally identify relevant genomic covariates if available. We apply this model to radiomic data from CT scans of head and neck cancer patients, using as our prior information a reliability metric obtained from a study on the impact of different scanners on feature stability.