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I need to evaluate if the picture was resized (upscaled). Are there any approaches to that already? If not, what do you recommend me to start with?

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    $\begingroup$ I'm not sure this is really a computer science question. What do other people think? $\endgroup$ – David Richerby Feb 28 '15 at 21:49
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    $\begingroup$ It does not seem to be, but I think it can be. What have you tried and where did you get stuck? Do you want a mathematical model, an algorithm or a program? (cc @DavidRicherby) $\endgroup$ – Raphael Feb 28 '15 at 23:38
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    $\begingroup$ I think this is an information theoretical question: If it was possible to decide whether some representation of a picture is a possible output of any algorithm from an informally defined class, can you tell that not only the input to go with both "is a picture", but that the representation is indeed the output of such a process? $\endgroup$ – greybeard May 24 '16 at 10:24
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As Raphael already said, in general it's impossible.

There is the field of image forensics where people look for methods to detect tampering with images. For JPEG images for example, there is a paper about detecting resizing: A new approach for JPEG resize and image splicing detection.

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On the conceptual level, the task is clearly impossible: you won't be able to detect size changes of mono-coloured images. Patterns with only right angles will always be identical modulo dimensions as well.

So you need assumptions on the image and knowledge about the specific algorithm used for upscaling. Something may be possible for specific combinations, but it's impossible to tell in general.

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