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I have an image which is composed of multiple 'angles' which form a grid shape:

enter image description here

After some searching, Hough seemed like a good fit, because it isn't troubled by breaks in lines. However, the problem I have is that my lines are 'fat', and any edge detection I run (Canny in this case), picks out the edges of the line, and not the middle:

enter image description here

This means that the Hough transform ends up picking out one (or both) of the 'sides' of my grid lines, and not the middle.

enter image description here

Given that I know what I'm looking for (this grid-like shape, always in roughly the same orientation), is there a better way to perform the 'edge detection' part to give me the centre lines, or should I be looking at a totally different method?

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  • $\begingroup$ For context, this grid will be compared to a nominal grid to perform Tsai camera calibration. $\endgroup$
    – Benjol
    May 21, 2012 at 10:02
  • $\begingroup$ "edge detection I run, picks out the edges of the line" Yes, because edge detection converts edges to ridges, and your image is already ridges. An edge is a boundary between light and dark. $\endgroup$
    – endolith
    Oct 5, 2012 at 17:46

2 Answers 2

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The Hough Transform would indeed help in picking up the Grid in this case. To "thin" the lines, you might want to consider the operation of Skeletonization

That would produce an image like this one: Skeletonization Output

Due to the way that skeletonization works, it will still produce some lines that will seem irrelevant to the grid but these lines towards "erroneous" directions are not that many (at least in the given image) to confuse the line detection of the Hough Transform too much and it will clearly pick the two main sets of lines at distinct directions. (Here is how the HT output looks like: ) enter image description here

If you are using MATLAB, you might want to check this help page

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  • $\begingroup$ Thanks! This helps a lot. Haven't got my MATLAB licence yet, but I tried it out using AForge's SimpleSkeletonization, and it works better... Though still not perfect. I'll be revisiting this subject later when I get some real data to test it on. $\endgroup$
    – Benjol
    May 21, 2012 at 14:03
  • $\begingroup$ You might want to try thresholding your original image first at some threshold that seems to be producing "optimal" fat grid lines. What i mean by optimal is that they are at least connected. That could improve the performance of the skeletonization but you would have an extra parameter to determine (the threshold). Maybe it's also worth looking into how to improve the image acquisition as well. $\endgroup$
    – A_A
    May 21, 2012 at 14:11
  • $\begingroup$ yes, as I said, when I have the real data to play with, it'll be worth my time to fine tune the system. One major doubt I have about Hough in general is that the discretization of theta is going to work against the sub-pixel precision we need. (That, and I'm not completely convinced that lens aberrations won't mean that the lines could be curved, no straight...) $\endgroup$
    – Benjol
    May 22, 2012 at 5:57
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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)

Result of the Radon Transform

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

Maxima over all angles

plot(R(:, 65))

Maxima at 65 degrees

plot(R(:,117))

Maxima at 117 degrees

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.

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  • $\begingroup$ Thanks, could you tell me in a few words what advantage you would expect the Radon Transform to give me, compared to the Hough Transform? $\endgroup$
    – Benjol
    May 25, 2012 at 5:34
  • $\begingroup$ @benjol, I updated my answer. $\endgroup$
    – bjoernz
    May 25, 2012 at 7:02
  • $\begingroup$ Very nice, thanks a lot. Once IT give me access to Matlab I'll be giving it a try! $\endgroup$
    – Benjol
    May 25, 2012 at 7:29
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    $\begingroup$ @Benjol: See What's the difference between the Hough and Radon transforms? $\endgroup$
    – endolith
    Oct 5, 2012 at 17:42

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