When we don't premultiply we blend the green background with the grey background without first considering the alpha value of the background (0), so you have the green showing up in the composite image.
Does the fringe effect only occur when up/downsampling? That is, do we avoid the fringe entirely by just doing a standard one sample/pixel, even without premultiplying?
Is it true that if we don't premultiply with alpha_a, as in the "B over A non-premultiplied" graph, the upsampled alpha value will have samples that are between 1 and 0 to allow some residual green color. Premultiplication eliminates the fractional alphas in this case to avoid residual greens.
Is there any difference between compositing first and upsampling first? What if we first composite with the new background and then upsample, will there be any difference?
If we don't premultiply, when we do up-sample, the object's color would blend with the background color. And when we apply it to the new background it would carry the original background color. Premultiplying is like getting rid of the background before applying the upsample, so the background color won't be carried over in this case.
I can understand why we get fringing when we don't premultiply, I'm pretty sure it's just because we're passing in the original values, some of which are green and multiplying by a_a and (1-a_b) won't dampen that as much, but I'm uncertain as to why premultiplying changes that. Is it because premultiplying somehow darkens the colors?
Is the pre-multiplication just a way to isolate the image from the background?
For example, if I have a picture without background, ie, the checkerboard thing on photoshop, then we don't need pre-multiply get rid of fringe right?
What are B' and A' here?
What would happen if we did (1-a)B + (a)A?