Ha ha, it is like ballroom dancing. I sometimes do the upscale downscale thing when I want to do something sub-pixel; e.g., if I want to apply a guided filter with a radius of 0.5. However, there is no filter window with the radius of 0.5; you can’t slice a pixel in half. Well, you could interpolate the calculation, but that is too much math and coding for me to handle ATM…
Anyway, sharpen (3x) in the upscale and downscale sandwich seems to indicate that it is a fool’s errand. I suspect the 3x has to do with the fact that their re-scaling actually softens the image 2x; therefore, necessitating the repetition.
Does this reasoning apply to any operation where radius is a parameter, like sharpen or low pass, to name a few?
If so, does it mean that, whenever I want to go beyond the 1 pixel threshold, I will have to upscale first?
There are countless approaches to sharpening, as exemplified by the wide variety of sharpening algorithms (see G’MIC for instance) and also by the various ways of applying even the most basic of these algorithms. Some techniques lead to realistic results, are easy to perform, apply to a wide variety of subject matter, and give you a usable preview all throughout the tweaking process. Other techniques are more akin to homeopathic dilutions, where they may appear to work more as a matter of faith and because a man in a robe in a dark room surely must know what he’s doing.
Try this technique for yourself. Is it simple to perform, does it work well on a wide variety of subject matter, are the results realistic, do you have a preview of the final result while tweaking, and is it superior to other techniques which do tick all the boxes?