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I couldn't test the next ideas, but (at least some of them) they should work. Probably you'll have to experiment a bit to find the right parameters.

First, I suggest to do a gamma adjustment as preprocessing; it should darken the grey lines to make them more visible:

out = in ^ gamma

where in is normalized between 0..1 and gamma>1.

To detect the lines, you can use a Sobel filter and get the regions where abs(Gx) is high and Gy=0 (for vertical lines) and abs(Gy) is high and Gx=0 (for horizontal lines).

Another possibility is to create some convolution kernels that respond to the horizontal and vertical lines. For example:

-1 -1 5 -1 -1
-1 -1 5 -1 -1
-1 -1 5 -1 -1

and

-1 -1 -1
-1 -1 -1
 5  5  5
-1 -1 -1
-1 -1 -1

You can make them 3x3, 5x5 and so on. They should highlight the lines.