MATLAB: Convert binary ROI to polygon

image processingregion of interest

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.