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.