Zooming

I was wondering if anyone with experience in image processing could explain to me what the difference is between the following two approaches: Build image pyramid recursively by taking the input image, scaling it down… (1)…and then continue with the scaled down version and so forth until we get to an image with dimension 1x1. (2) …and then continue again with the original image to get the next smaller level and so forth. Obviously approach (1) is much faster. However, how big is the difference (if there is one) in quality of the output between the two approaches? I'd love to hear your thoughts, possibly accompanied by mathematical argumentations or references to resources that explain the underlying concepts.(*) I do have some basic understanding of interpolation, sampling, and a tiny bit of Fourier analysis etc. In such cases it sucks that when I google for «image pyramid» and my own blog appears among the initial results.

I don't have links or formulas, but approach 1 will produce slightly blurrier images, with each level a little blurrier than the last. This isn't necessarily a bad thing, however: after all, the most high-res level won't be affected at all, and by the time there's been enough accumulated error to even notice, you're down to the tiny thumbnails that make up the tip of the pyramid. Presumably those images will only be shown briefly as the image refines, and even if not (the user is zoomed out and there are thousands of thumbnails on the screen), one just needs to zoom in to get more detail.