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Receptive Fields within the Combinatorial Pyramid Framework

Luc Brun &
Walter Kropatsch.
A hierarchical structure is a stack of successively
reduced image representations. Each basic element of a
hierarchical structure is the father of a set of
elements in the level below. The transitive closure of
this father-child relationship associates to each
element of the hierarchy a set of basic elements in
the base level image representation. Such a set,
called a receptive field, defines the embedding of one
element of the hierarchy on the original image. Using
the father-child relationship, global properties of a
receptive field May be computed in O(log(m))
parallel processing steps where m is the diameter of
the receptive field. Combinatorial pyramids are
defined as a stack of successively reduced
combinatorial maps, each combinatorial map being
defined by two permutations acting on a set of half
edges named darts. The basic element of a
combinatorial pyramid is thus the dart. This paper
defines the receptive field of each dart within a
combinatorial pyramid and studies the main properties
of these sets.