Let's take image A: 2560*1920 pixel image in perfect focus. Sharp as a razor. That's 5 Mpix.
Let's take image B: image A resized to 5120*3840. It's now a 20 Mpix file, but there's no new data in the image, so - using common sense - it's still just a 5 Mpix file, just "bloated".
Theoretically, one should be able gradually to reduce image B's dimensions until reasonable sharpness is detected (bringing it as close to image A as possible, although without actually comparing them at this point), and thus derive the image's "true" megapixel count: the size below which imagery is starting to lose its details.
This value could easily be used to determine the usefulness of a photo - if I shoot it slightly out of focus, I can still print it in a smaller size, and no-one will notice. Or, it could help with assessing lens or sensor quality - if a 24 Mpix camera is unable to capture an image with more than "true" 8 Mpix, then something isn't right.
So, cutting to the chase: is there a software program that does just that? Or am I doomed to writing my own?
From a comment by the OP to one of the answers:
I need to measure how much detail is my positive transparency scanner really getting, before I scan a collection of about 2000 old slides and consider it digitized. If I set it to optical 19200 dpi or something, and it keeps producing images with detail lost, equal to, say, a 5 Mpix camera, then I'll know it's bad.
This is the actual problem the question wants to solve. Everything above is about one perceived solution to that root problem.
Answer
One approach might be to compute the two-dimensional Fourier transform of the image and try to decide the spatial frequency above which the transform (or, say, it's power) becomes noise, that is, uncorrelated and small. Never tried anything like this, but it must be connected in some way with a rigorous definition of resolution?
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