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Combinatorial Pyramids

Luc Brun &
Walter Kropatsch.
An irregular pyramid consists of a stack of successively
reduced graphs. Each smaller graph is deduced from the preceding one
by the contraction or the removal of a set of edges. Using a fixed
decimation ratio we need approximately O(log(image size)) graphs to
encode the whole pyramid. A combinatorial map encodes a planar graph
thanks to two permutations encoding the edges and their orientation
around the vertices. We present in this article an encoding of a
combinatorial pyramid which allows to fold the whole pyramid in the
base level layer and provides at the same time a measure of the
relevance of every pixel. This encoding is used to retreive any
reduced combinatorial map of the pyramid from its base and to
compute the borders of the partition encoded by the combinatorial
maps.