THIS is exactly the sort of insight I wish I would get when I click one of those "one weird trick" links!
They're a bit obscure if you don't know how they work, basically Grain Extract subtracts the layers and adds 128, so you get sort of a fake 8-bit signed integer. Grain Merge does the opposite (add two layers, subtract 128).
I haven't tried to divide-by-blur (but I'm going to :) ). Grain Extract on the other hand, allows to subtract-with-blur, which is more like what I'd do if I were to code such an algorithm myself (the operation is roughly what the Unsharp Mask filter does, but you get a bit more control). Still I'm curious to see how divide-by-blur differs in its results.
Check this Flickr-post which has a nice explanation of using Grain Extract (used for a different purpose here, it's really a very interesting and versatile trick, only discovered it last week myself):
https://www.flickr.com/groups/48637250@N00/discuss/721576192...
Subtraction would be fine if the data were logarithmic: that is to say, if the intensity information we are operating on represents decibels. We figure out the low frequency signal's "floor" over each area of the image, and simply subtract those decibels.
Division is better on the assumption that the intensity values of the pixels are linear. Division of linear samples is subtraction, in the decibel scale.
The right way is somewhere in between, because in RGB displays, pixels are put through some gamma curve. They are neither linear nor logarithmic.
[1] https://fstoppers.com/post-production/ultimate-guide-frequen...
By the way, here is a useful trick: blurred layer in Divide mode, plus vary the opacity. You can reduce the amount of contrast between light and dark areas in an image without completely leveling it. Works well with low opacity levels (just a slight blend of the Divide mode layer). If you have a picture with areas that are too dark and too bright, a touch of this can help. High radii tend to work well, with blends of up to 20% or so.
For me, this does what I want Retinex to do! Only better, with intuitive control parameters and predictable results.
Look at the picture of the little girl peering out of the back window of a truck on NASA's Retinex page, as enhanced by Retinex:
http://dragon.larc.nasa.gov/retinex/pao/news/
Now my version:
http://www.kylheku.com/~kaz/nasa-image-girl-truck.png
The reflection in the glass is brought out in a less cheesy way that you might not guess is the result of processing, if you don't already know.
I did a decompose of the image to the LAB color space (Colors/Components/Decompose...). Then I used a blur radius of 200 pixels on a copy of the L layer. Put into Divide mode and blended at a bit over 30%, and recomposed from LAB back to the original RGB image.
(That's a simplification; of course I had to struggle with Gimp to preserve the ID of the L layer, which is destroyed by a straight "merge layer down" after which the recompose operation fails with an error. I in fact made two copies of the L layer, and did the processing and merge operation between those two copies. Then I did a select all to copy the resulting layer to the clipboard and pasted that into the original L layer to replace it.)
Here is my very quick and dirty manual job of the same example page:
http://www.kylheku.com/~kaz/dewarp.png
Literally less than five minutes.
First I cropped the image. Then duplicated the layer. Blurred the top layer (Gaussian, 50 radius). Then flipped to Divide mode and merged the visible layers. This leveled the lightness quite well, almost completely eliminating the shadow over he right side of the page and all other lighting differences. There is a hint of the edge of the shadow still present because it is such a sharp contrast; but that can be eliminated in an adjustment of the intensity curves. In such cases it may be helpful to experiment with smaller blur radii, too.
I then did a perspective transform in the lateral direction, squeezing the left side top-bottom and expanding the right, resulting in the warp now being approximately horizontal. (The perspective transform is not just for adding a perspective effect; it is also useful reversing perspective!)
Finally, I used the Curve Bend (with its horrible interactive interface and awful preview) to warp in a compensating way. Basically, the idea is to draw an upper and lower curve which is the opposite of the curve on the page. I made two attempts, keeping the results of the second.
If the preview of this tool wasn't a ridiculous, inscrutable thumbnail, it would be possible to do an excellent job in one attempt, probably close to perfect.
Because the page is evenly light thanks to the divide-by-blurred layer trick, it will nicely threshold to black and white, or a narrow grayscale range.