# Convert binary ROI to polygon

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Jurgen on 22 Apr 2016
Commented: Image Analyst on 23 Apr 2016
I have a binary image with a concave polygon drawn in a paint application. Using find() I get a set of points, but they aren't ordered so all the MATLAB polygon functions choke on them. How do I go about turning my 2D line-mask into a proper polygon variable?
Edit: added example
Edit2: It was drawn with 1px pencil in a continuous motion, then 'cleaned' with bwareaopen(). So each pixel should have at most 2 neighbours.
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### Accepted Answer

Walter Roberson on 22 Apr 2016
Edited: Walter Roberson on 22 Apr 2016
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### More Answers (2)

Alessandro Masullo on 22 Apr 2016
Edited: Alessandro Masullo on 22 Apr 2016
You can use bwboundaries to get the boundaries of a binary image.
If you want to sort them, you can evaluate the centre of your points, the angle between each point and the centre and then sort all the points by the angle.
If you just want a rough estimation of the polygon, instead, you can use the douglas-peucker simplification algorithm (already coded in matlab or from the file exchange)
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Jurgen on 22 Apr 2016
I think the centering trick only works if the reference point is inside the polygon, which in my case is true, but it isn't true for all concave polygons.

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Image Analyst on 22 Apr 2016
bwboundaries() gives you an ordered set of coordinates as you move along the perimeter of your shape. I don't think you should need to do any other kind of sorting. For example, a list of coordinates from bwboundaries can be used in poly2mask() and polyarea(), etc. Here's a snippet from my tutorial:
hold on;
boundaries = bwboundaries(binaryImage);
numberOfBoundaries = size(boundaries, 1);
for k = 1 : numberOfBoundaries
thisBoundary = boundaries{k};
plot(thisBoundary(:,2), thisBoundary(:,1), 'g', 'LineWidth', 2);
end
hold off;
Note that x = thisBoundary(:,2), and y = thisBoundary(:,1) -- perhaps backward from what you might think, but it gives (row, column), which is (y,x), not (x,y).
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Image Analyst on 23 Apr 2016
Yes, to erode, use imerode(). Also look at strel() to see the different shapes you can have for the structuring element.

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