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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 on the original
image. 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 study the main properties of these sets.