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 ??

[I,J] = find(binaryimg>max(binaryimg(:))/2);
IJ = [I,J];
[~,idx] = min(IJ*[1 1; -1 1; 1 -1; -1 -1].');
Corners = IJ(idx,:);

Answer 1

[Matt J]

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.

[ahmet ilhan]

Thank you for your answer Matt J. Your answer is very clear.

[ahmet ilhan]

Matt J. Can you give me any paper or link about this algorithm ?

[Matt J]

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).

[Matt J]

Incidentally, I have made a File Exchange submission which generalizes the method to any convex polygon:

https://www.mathworks.com/matlabcentral/fileexchange/74181-find-vertices-in-image-of-convex-polygon

Answer 2

[jim as]

An algorithm addressing this problem that you have raised is escribed in https://arxiv.org/abs/2011.14035

DC