Alternatives to Hough transform for detecting a grid-like structure
An alternative to the Hough Transform would be the Radon Transform (1, 2). A rough description of an algorithm to detect a grid-like structure could look like this:

1. Perform Radon Transform from 0 to 180 degrees.
2. Find the two highest maxima in the angle bins.
3. For the two angles with maximal amplitude find the local maxima within the bin.
4. You can use the constraint that the maxima should have even spacing to deal with outliers.


EDIT:

Here is a small matlab snippet to illustrate step 1-3:

im = imread('grid.png');
[R, xp] = radon(im, 0:180);
imagesc(0:180, xp, R)




plot(max(R)) % the two maxima are at 65 &amp; 117 degrees




plot(R(:, 65))




plot(R(:,117))




To answer your question from the comments: It appears to me from the one example image that you provided, that this method is more robust against small defects in the detected grid. Skeletons will rarely yield straight lines which might be a disadvantage for the subsequent Hough Transform.