How can I simplify the polygon?

The polygon above is got after I shrank a rectangle. However, The meaningless branches are not desired. How can I remove them and split it into polygons that are independent to each other?

[Tony Carl]

For illustration, the data of the polygon and an example figure is shown below, plotted by code:

plot(data(:,1),data(:,2),'bo-');

[Tony Carl]

The data pack of the polygon.

Answer 1

[Ahmet Cecen]

Well purely speculating, assuming you have a binary image with those lines:

FilledPolygons  = imfill(PolygonImage,'holes');
OnlyPolygonsFilled = FilledPolygons - PolygonImage;
OnlyPolygonEdges = edge(OnlyPolygonsFilled);

[Tony Carl]

Thanks a lot, when converted to an 0-1 image, it can really be much helpful for solving the problem. Is there any way to match the boundary points with the set of points on original polygon? As the algorithm of main body are based on the original data.

[Ahmet Cecen]

You will need to clarify a bit more. Maybe show your actual data etc.

[Tony Carl]

An example figure and its relevant data are appended below the question.