Measuring noise/variation in an image

I'm wondering if there's some way to measure the amount of noise/variation in an image (or video frame). I'm not sure exactly how to describe what I want to measure, which is why I'm having trouble measuring it! Put simply, I want the image equivalent of measuring the "noisiness" of an audio sample -- that is, measuring its spectral flatness. My idea is that a "noisy" image would have lots of variation between neighboring pixels, while "flat" images would have little variation between neighboring pixels.

Is there something like this, or am I desiring something that just doesn't make sense?