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I am trying to find the corners of the "rectangular" shapes. This code is working very well. But I dont know exactly how it works. Can you explain me ??

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ahmet ilhan
ahmet ilhan on 1 Aug 2018
Commented: Matt J on 6 Feb 2020
[I,J] = find(binaryimg>max(binaryimg(:))/2);
IJ = [I,J];
[~,idx] = min(IJ*[1 1; -1 1; 1 -1; -1 -1].');
Corners = IJ(idx,:);

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Matt J
Matt J on 1 Aug 2018
Edited: Matt J on 14 Apr 2019
Maybe this image will help. The corners of a polyhedron will maximize/minimize the intercept of lines of a certain slope - it's a linear programming principle. In the code shown, the lines used x+y, x-y, -x+y,-x-y are those oriented at 45 degrees to the x,y axes. As long as the rectangle edges are approximately parallel/perpendicular to the x,y axes, its corners will minimize the intercept of one of these lines.

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Matt J
Matt J on 1 Aug 2018
Thank you for your answer Matt J. Your answer is very clear.
You're welcome, but please Accept-click the answer to certify that it addressed your question.
Can you give me any paper or link about this algorithm ?
I don't think you'll find any papers about it. It's a very ad hoc method (but if you find any, I'd be glad to hear).

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