Hmm, I actually got the mention message even though the post doesn't link to me here. (And in the dmail, it is linked.)
If I had to guess, I'd say both posts came from a different source than they claim, rather than being upscales.
post #2436032 (tumblr): First point of interest, the listed source, although named .png, is actually a JPEG. The danbooru upload is a real PNG. But I don't think it's an upscale. The tumblr version has some artifacts that don't appear in the larger image. In fact, looking at the edges, the tumblr version resembles a downscale in a non-linear colorspace of the larger one. It could also be that the larger one was unsharp-masked, but that wouldn't have brightened the thin lines and would have amplified the jpeg artifacts as well. At the very least, if it is an upscale, it isn't an upscale of the tumblr image.
post #2517706 (twitter): Harder to tell, but I think again it's not upscaled. I can almost see it being a sharpened upscale, but I don't think the detail on the upper-left-corner knight's helmet would have be reproduced by that, and there's some jpeg-induced color distortion in the twitter one that would have infected an upscale and isn't present as much in the larger image.
We won't know what happened for sure unless we ask the uploaders. I'm not sure if this topic is the right place for that or not.
Mikaeri said:
Mmmm... quite honestly, I'm not sure if one can tell if such posts are third party resizes or artist resizes unless it's blatantly described in the source. Is the distinction that necessary though? It seems fairly unnecessary to me right now, although my mind may change if you can bring up a better reasoning.
Warning, wall of text incoming here.
Why the distinction is necessary: A different size produced by the artist is likely to be exported from the original (possibly vector) source at the new resolution rather than scaled. That's higher fidelity by definition than a raster scale and almost always subjectively better looking as well. Furthermore, research is always ongoing and technology always improving, but algorithms are unlikely to be forgotten, so if you do a resize now, you might be able to do it better in the future, but if you keep the original, you can always resize it at least as well as you can now whenever you need to. Also, if you need a different size later, it's better to resize from the original directly to the new size, rather than from an already-resized image, because the latter introduces rounding error every time you rasterize, as well as amplification of artifacts left by the scaling algorithm. (See first example below.) So archiving a third-party resize is generally not only wasteful but actually counter-productive - you could end up later in a situation where you could have produced an image using the original that is better than the previously scaled image. The original from the artist is the only non-reconstructable information, so it should absolutely be treated specially. You also can't trust third parties to resize with as high quality as they could. It's extremely common, for example, to downscale in a non-linear colorspace, which can destroy details such as the stars in a night sky. (See second example below.) Unfortunately, you can't always trust the artist in that respect either, but whatever you get from the artist is the best you're going to get.
How to tell: It's not always easy, which is one reason it's always nice to have the proper source of the image. But you can look for the artifacts caused by various resizing algorithms, or the amplification of jpeg artifacts if the original was a jpeg (or other lossy compression). In the case where you have a smaller image that you know is original, you can try upscaling that the best you can to the size of the maybe-original larger image, and see if it looks as good. If the larger image has actual detail that isn't present in the enlarged smaller one, it's more likely to at least not be an upscale of that image. You can also downscale the larger image to the size of the smaller one, and see if it looks better, which could happen if the smaller one was a starved jpeg, for example, but wouldn't happen if it had been created from the small one to begin with. It's still a big judgement call in the end, though, unless you can recognize some obvious tell-tale artifact. There's a huge rabbit hole to jump down here if you want to, but please be aware that you have to understand digital image stuff pretty well to make a good call, and even then some cases are hard to tell. Not to be obnoxious, but I just don't want someone to read this post and then start flagging all kinds of stuff saying they upscaled/downscaled it and it kinda looked different. (Haha, who am I kidding, nobody's going to read this whole post.)
Some examples of distortion caused by resizing:
post #2354838: resized directly to 800px wide and resized in 5px steps. What artifacts you would see in the second case depend on the algorithm used to scale, but at least I used the same algorithm in both cases here (EWA LanczosSharp). To give another example with different artifacts, here's the same with a Gaussian filter, which is blurry but doesn't have other artifacts like the ringing that Lanczos produces: direct and in steps. Quite a difference. Note that in either case, the aspect ratio is also distorted by resizing multiple times because every step has to round the size to full pixels. Of course scaling an image 60 times is going to end up a lot worse than 2 or 3, but I'm just trying to demonstrate that something is lost each time.
post #1891289: resized in linear colorspace and resized in sRGB (the default for the vast majority of software). Small bright points come out much dimmer than they're supposed to be. In images without many small bright points, the effect is less noticeable but still results in a darkening and slight blurring of edges, for example. The visual attractiveness of that effect can be debated, but it is unquestionably a less accurate reproduction of the original. Make sure you view the example images with 100% zoom (and look at the original at 100% as well), because even your browser most likely does it wrong, as does Danbooru's 850px sample. You might be amazed as you click zoom or view original and new stars appear.
Wow, I spent a lot longer on this than I intended to.
In addition to that though, the waifu2x tag is quite peculiar... Does it always do resizes? I think I've seen some posts tagged waifu2x where all that happens is the jpg gets converted to png like with post #2573016 and post #2573019
waifu2x can try to remove jpeg artifacts with or without scaling.
