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ImageMagick seems like not much more than a "free" implementation of many of Photoshop's features.

Well, I suppose that's one way of looking at it, but that's kind of missing the picture (if you'll pardon the pun). ImageMagick is primarily an image processing/compositing library, with a small set of command-line tools, and an even smaller set of GUI tools, built on top of it. I've used the library as much as I have the command-line tools.

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While doing transformations in Photoshop it will continue to use the original until you apply the transformation as well. It doesn't keep resampling from the intermediate stage. That's why in the example I posted I specifically said to press RETURN to apply the transformation.

But once you start the transformation, can you, say, sharpen the image? Or do you have to either cancel, or apply, the transformation, before you're allowed to sharpen the image? My guess (I don't have Photoshop) is that it's an atomic operation -- you can either do a transformation, or not, but you can't have it in some in-between stage. If you don't hit RETURN, what other option do you have, CANCEL?

In the example I used of "display", resizing the image is not an atomic operation. I can change the image size, then go off and do other operations, then come back and hit apply. Essentially, I'm just deferring hitting RETURN, but that doesn't make the display of my image go back to the original size, either. The scale transformation isn't contained in the linear undo/redo stack with the other operations -- it's on the side until I do hit apply.

I'm not trying to be combative, or say "my software is better" -- I just wanted to show that the answer, unfortunately, isn't just common sense following knowledge of what resampling is, but, where multiple image resize operations are concerned, also dependent on implementation details.