  The study of topological information of spatial objects has for a long time
been a focus of research in disciplines like computational geometry, spatial
reasoning, cognitive science, and robotics. While the majority of these
researches emphasised the topological relations between spatial objects, this
work studies the internal topological structure of bounded plane regions, which
could consist of multiple pieces and/or have holes and islands to any finite
level. The insufficiency of simple regions (regions homeomorphic to closed
disks) to cope with the variety and complexity of spatial entities and
phenomena has been widely acknowledged. Another significant drawback of simple
regions is that they are not closed under set operations union, intersection,
and difference. This paper considers bounded semi-algebraic regions, which are
closed under set operations and can closely approximate most plane regions
arising in practice.
