how to postprocess photographed book

Sometimes you photo some book in the library. The effect usually looks like that:

The light is never equal on all picture - some parts are brighter, some parts are darker. This is bad if you plan to OCR it or convert to djvu. Here I will describe how to postprocess such photo in GIMP, so it is equally light in all parts.

I open this photo in Gimp. Then I do a second copy of a layer. Now I have two layers with two copies of the same image.

Then I blur the upper layer with gaussian blur, with a large radius, e.g. 100 pixels.

The effect looks like that:

As you can see, the blured image shows us what parts of the image are dark and what parts are bright.

Now I change the mode of this upper (blured) layer to divide.

This causes the bottom layer to be divided by the upper one. The result looks like that:

Now I flatten image.

I correct levels a little bit and have something like that:

great!

Post scriptum: you can do the same using imagemagick:

$ convert input.png -resize 4% -resize 2125x2716 blur.png ; 
$ convert input.png blur.png -fx '(u/(v+0.001))' -threshold 80% output.png