Being a radiologist, I mostly work on medical images. There are tons of interesting challenges working with these. But the potential impact is huge. We are still in the very early days of application of deep learning to medical imaging.
Globally, high resolution, single channel, noise, weak labeling and/or low number of samples are the frequent challenges when applying deep learning to medical imaging. What is really exciting for the algorithmic dl research in medical imaging is that each problem has usually a different optimal solution.
To answer your specific question about resizing, it depends on the context. If the computer vision problem that you are trying to solve doesn’t really need high resolution, then it should be fine to resize. But if you try to solve a problem that usually needs high resolution (eg. identifying microcalcifications on a digital mammography) than resizing can completely broke the potential performance. Involvement from an interested domain expert (radiologist) can usually help to get a hint for a useful direction.