Unlike many other things in image recognition, the measures of contrast can be objective; always solvable and easy to obtain. You can start here:
Contrast (vision) — Wikipedia, the free encyclopedia,
Display contrast — Wikipedia, the free encyclopedia.
Of course, you cannot use the measure operating the concepts of "feature" and "background" (Weber), because an image does not contain any predefined information of how to tell feature from background.
Now, I'm not quite sure that you have to apply the contrast measure to discriminate input images and rejecting them. In some cases, this approach is needed. Just one thing: one of the image transforms needed to apply before image recognition is boosting the image contrast; often (perhaps not always), you need to boost it to extremes. It depends on particular problem.
—SA