yrizoud, that visualization you posted is quite nice. Makes discussing the matter a lot easier!
But, first here's one of mine:
As you can see one of the properties of the upscaling algorithm is that they "rounden" the image. Without upscaling diagonals would appear jagged (due to the low resolution) and the artist relies on the eye of the viewer to reconstruct the image. With the right upscaling algorithm the "real" shape of the depicted thing is approximated. And this improves the quality when rotating, transforming and rescaling the image. A chunk of pixels that is meant to have a certain shape is more likely to end up in that shape after the transformation!
My progress is a lot slower then I hoped for (due to a lot of distractions, not because I don't believe in it's doability) but in my most recent build you can freely transform (left mouse button) and rotate (right mouse button) the image allready, and I think that it allready domonstrates that using an upsaled source image does improve the final quality.
PixelPunch003.rarIt's far from perfect but there's still one step in the transformation process that I didn't adress yet. Sampling. Your illustration and explaination show perfectly what causes the artefacts. Now let's say for every green square you count the number of white and black sub-pixels to make a decision. That would get rid of most of the artefacts except where there are diagonals in the source image that introduce jaggedness because of the low resolution in which case (hopefully) the upscaling will kick in.
P.S.: None of the artworks shown in the screenshots are done by me. But they all have been posted on the forums so I hope it's okay for me to use them in the screenshots.