Robots taking over won't happen for a looooong time. Not bc they can't, but b/c our society just isn't mentally prepared for that. Docs make mistakes, and people accept this (though often suing the pants off them in the process), but the tolerance for mistakes from machines is MUCH lower.
For example: Human drivers cause tens of thousands of fatalities annually. But just 1 or 2 caused by failed brake override tech in toyotas triggered a national uproar. All it takes is a few robot surgeons to cut a major artery, a few automated radiology programs to miss a tumor, a few misdiagnosis by robot Dx programs and the backlash will be tremendous, even if the robots are statistically "better" then a human doc.
What is far more likely (and what we are starting to see already) is computer assistance rather than computer replacement. The computer will perform a prelim-read of the radiographic study and highlight areas for the rads doc to focus, but the final read will be done by a radiologist. The computer will spit out a probability weighted Ddx based on a set of symptoms and management recommendations, but actual decisions will be made by the internist. Also remember that someone has to properly identify said symptoms + perform a good/accurate physical exam.