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How to fill the inner gaps of each part and segment to different parts

I wanted to fill the inner gaps and segment these three points either. I couldn't use morphology methods because like erosion because it makes inner gaps larger. Actually I was thinking of geometry methods but I didn't have any idea about how to discriminate inner and boundary gaps. image description My output image should be something like this. image description Thanks

How to fill the inner gaps of each part and segment to different parts

I wanted to fill the inner gaps and segment these three points either. I couldn't use morphology methods because like erosion because it makes inner gaps larger. Actually I was thinking of geometry methods but I didn't have any idea about how to discriminate inner and boundary gaps. image descriptionimage description

My output image should be something like this. image descriptionthis.

image description Thanks