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Inside and Outside within Combinatorial Pyramids

Luc Brun &
Walter Kropatsch.
Irregular pyramids are made of a stack of
successively reduced graphs embedded in the
plane. Such pyramids are often used within the
segmentation and the connected component analysis
frameworks to detect meaningful objects together
with their spatial and topological
relationships. The graphs reduced in the pyramid
May be region adjacency graphs, dual graphs or
combinatorial maps. Using any of these graphs each
vertex of a reduced graph encodes a region of the
image. Using simple graphs one edge between two
vertices encodes the existence of a common boundary
between two regions. Using dual graphs and
combinatorial maps, each connected boundary segment
between two regions is associated to one
edge. Moreover, special edges called loops May be
used to differentiate a special type of adjacency
where one region surrounds the other. We show in
this article that the loop information does not
allow to distinguish inside and outside of the loop
by local computations. We provide a method based on
the combinatorial pyramid framework which uses the
orientation explicitly encoded by combinatorial
maps to determine inside and outside with local
calculus.