Feature-Imitating-Networks (FINs) are neural networks with weights that are initialized to approximate closed-form statistical features. In this work, we perform the first-ever evaluation of FINs for biomedical image processing tasks. We begin by training a set of FINs to imitate six common radiomics features, and then compare the performance of networks with and without the FINs for three experimental tasks: COVID-19 detection from CT scans, brain tumor classification from MRI scans, and brain-tumor segmentation from MRI scans; we find that FINs provide best-in-class performance for all three tasks, while converging faster and more consistently when compared to networks with similar or greater representational power. The results of our experiments provide evidence that FINs may provide state-of-the-art performance for a variety of other biomedical image processing tasks.