# Tolerance on image detection

I am trying to pick straight lines out of a photographic image to track deflections of a structure under loading.

The idea is to mark certain structural elements with straight lines, as they deflect I can then extract the vectors from the image, find the centre point and measure how much the vector has displaced and rotated since the previous image.

I have used the second answer to this question to get the bones of a process up and running, code below. Using a generic vector image from web as a test image until my rig is up and running.

i = ColorNegate@Import["http://goo.gl/5R4MAl"]
p = Closing[Binarize@ImageTake[i, 480], 1];
Show[p, Graphics[{Thick, Orange, Line /@ ImageLines[p, Segmented -> True]}]]


This seems to pick out the main vectors quite nicely.

Whilst the length of results returned is 9 which is what I expected, on closer inspection there are additional points that are very close together. I'm guessing that these are rogue parts of the arrowheads being picked up.

foo = ImageLines[p, Segmented -> True]
foo // Length


Gives the length to be 9, which is what I would have expected given there are nine primary lines, but if displayed in matrixform I'm getting additional rogue points.

foo // MatrixForm


I've tried to tinker about with limiting the MaxFeatures->9 and using DeleteSmallComponents with mixed success. I'm struggling to find any helpful guidance too on what t (threshold) and d (distinctness) actually do with regards the image recognition.

What methods exist to extract the primary straight lines from images like the one used in the above example that gives a start and and end co-ordinate of the line that can then be used in subsequent calculations please? I'd also prefer to not set the number of lines I'm expecting Mathematica to discover.

Here is an example returning 9 lines without additional points:

i = Import["http://goo.gl/5R4MAl"];
ii = Closing[Binarize[GradientFilter[ColorNegate@Binarize[i, .55], 2], 0.1], 1];
foo = Select[ImageLines[ii, Segmented -> True], EuclideanDistance @@ #[[1]] > 100 &];
Show[i, Graphics[{Thick, Orange, Line /@ foo}]]


Here are the details for foo:

Length /@ foo
Length@foo

{2, 2, 2, 2, 2, 2, 2, 2, 2}
9


Note that foo = ImageLines[ii, .1, Segmented -> True] produces the exact same lines.

Checking the length of the lines in foo:

EuclideanDistance @@ # & @@@ foo

{164., 163.5, 163., 163.5, 163.5, 163.5, 163.5, 163., 162.}

• Because Segmented-> False is used on the second block of code, doesn't this extend the vectors out to the edge of the image, and this is why the y co-ordinate is always either 0 or 300. Therefore this doesn't give the actual length of the vector but a false measurement instead? Apologies if I'm misunderstanding. Aug 7, 2014 at 10:19
• @ASBOAllstar See, that's why I wanted comments :D It's obviously a mistake. Fixing it now :)
– Öskå
Aug 7, 2014 at 10:29
• @ASBOAllstar Please check the edit.
– Öskå
Aug 7, 2014 at 10:44
• Thanks, essentially the sensitivity has been introduced for anything longer than 100? Aug 7, 2014 at 10:49
• @ASBOAllstar Then you should use foo = ImageLines[ii, .1, Segmented -> True]. Like I said at the end of the answer, it's exactly the same as Select[..., EuclideanDistance..]
– Öskå
Aug 8, 2014 at 19:49