Thanks again Henrik. Lots of ideas to play around with!

Yes, with Mathematica there are almost always other approaches possible. Here is one on the basis of image manipulation (but the result is less convincing):

img0 = Import["https://community.wolfram.com//c/portal/getImageAttachment?filename=shapes.jpg&userId=1703851"];
img = ImagePad[Thinning@Dilation[DeleteSmallComponents[ColorNegate@Binarize[img0], 10], 3], 50];
mcp = MorphologicalComponents[img];
indx = Rest@DeleteDuplicates@Flatten[mcp];
singleImgs = Table[Image[Map[If[# == c, 1, 0] &, mcp, {2}]], {c, indx}];
width = (1 /. ComponentMeasurements[#, "Width"] & /@ singleImgs)/2;
ColorNegate@ImagePad[ImageAdd@MapThread[Closing[#1, #2] &, {singleImgs, width}], -50]

That is a nice problem! Here is one way to separate single candidates for polygons and close them:

img = Import[
   "https://community.wolfram.com//c/portal/getImageAttachment?filename=shapes.jpg&userId=1703851"];
pts = PixelValuePositions[DeleteSmallComponents[Thinning@ColorNegate@Binarize[img], 10], 1];
clusters = FindClusters[pts, Method -> "SpanningTree"];
orders = Last@*FindShortestTour /@ clusters;
polygs = MapThread[Polygon[#1[[#2]]] &, {clusters, orders}];
grph=Graphics[{Orange, EdgeForm[{Thick, Black}], polygs}]

This can be exported as image like so:

Export["ClusterPolygs.png", grph]

Regards -- Henrik

Well, thank you, Rohit! But it is rather Mathematica which makes it really easy and elegant!

Best Regards --Henrik

Ahmed,

I was wondering why there are 8 clusters ...

well, that is strange! This effect seems to be depending on the version of MMA:

• on 13.1 (where the code was originally written) you get 7 clusters;
• on 13.2 you actually get 8 clusters - as you did;

One not really elegant solution is to explicitly input the number of clusters:

clusters = FindClusters[pts, 7, Method -> "SpanningTree"]

Maybe anyone has a better method.

Ahmed,

here is annother idea that might help separating the clusters in a clean way, just replace this line:

pts = PixelValuePositions[
  Thinning@Dilation[DeleteSmallComponents[ColorNegate@Binarize[img], 10], 3], 
  1]

The dilation of the contours (before Thinning again) makes sure that a single contour is really connected. With this I always get:

clusters = FindClusters[pts, Method -> "SpanningTree"];
Length[clusters]
(*   Out:   7   *)

Can you provide some sample images?