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Region Discovery?

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Lets say we have a set of coplanar regions defined in 2D space, and all regions form together one big region such that no hollow exists. In other words, a regions is subdivided into smaller ones by drawing random paths.

Is there an algorithm to re-identify/discover regions after reshaping one by either reshaping it's boundary without changing the topology or connectivity, or by removing a path forming a boundary of more than a region?

What's it called if any exist?

Is it an open research area?

What would be the right term to google it up?

Thanks.

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