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Implicit encoding of 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 importance of
every pixel. Any reduced combinatorial maps of the pyramid maybe
directly retrieved from this encoding if needed.