Repeated editing methods

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I was wondering - for things like the unsharpen mask and noise removal tools, is it better to run the process once over a shot - increasing the amounts to point where you get the most return for minimal loss for each; or is it better to run the program a few times on low settings and build up to a point where you get the best results?
 
Gonna run a test or two, but I'm banking on one-shot in theory. I'll post up an example.

Edit: I was right. I'll post up the example. Hold tight just a sec.
 
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One-shot is the way to go. My theory is as follows. It isn't 100% scientific in terms of PS lexicon but I'm positive it's correct even if I can't explain it in a manner that's exactly technically precise:
-Unsharp mask increases contrast differentially by density in order to create sharper edges.
-If you sharpen a given area at 200% the edges become 200% sharper than the original.
Corrolary:
-If you sharpen a given area at 100%, the edges become 100% sharper than the original.
-If you sharpen that image at 100% the edges become 100% sharper.

This functions in an exponential manner (though I don't believe it's ^2 (squared)), not a linear one. If you sharpen something at 50% and then sharpen again at 50%, it doesn't become 100% sharper than the original. Instead, it becomes 100%-200% sharper (likely closer to 200%, though I can't quantify precisely on theory and visual data alone).

The results can be seen in the following linked image, which is a 100% crop of a photo of mine, which is a scan of a Kodak Portra 160NC 645 negative. The results appear to be independent of the pixel radius. Sharpening twice at 50% percent always produces a more contrasty and artifacted image than sharpening once at 100%, so on and so forth.


Comparison
 
Ahh thanks so much for that Alpha :)
Learning that its an exponential graph does explain why it would be the case.
 
Sure. And I should add that the only reason the original looks soft is because that 100% crop is from an image that's about 28.5 x 38.5 inches at that dpi. God I love medium format.
 
This is right for unsharp mask, but it depends on the process. For instance sharpening by layering high pass filters together via overlays is often repeated for a more severe effect, but it can also be stuffed up. e.g. Duplicate the image twice apply high pass to each layer and then over lay them and you end up with an increased sharpening levels. But if you high pass once, then take the result and high pass that again you end up with what is in the above example by Alpha.

This also has a downside. Sharpening creates an outline of pixels. Of opposing colours from neutral grey around the area. Suppose you sharpen twice at 100% the second time around you're sharpening the outline of the first which inverts the sharpening and creates a harsh transition.

Here's a visual example:

Many photoshop filters can be qualified by comparing a gradient to neutral grey. The top one shows the original gradient.
The second line shows the gradient with a large radius 15px sharpened at 500%. Note the dark areas have a smooth white counterpart.
The third line shows the gradient with a large radius 15px sharpened twice at 250%.

Untitled-1-1.jpg


From the bottom it can be seen the smooth white outline now has an additional black outline, and this double sharpening is often what contributes to the halo effect seen usually in poor processing.
 

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