@INPROCEEDINGS{brun-02-2,


AUTHOR = {Luc Brun and Walter Kropatsch},
TITLE = {Receptive Fields within the Combinatorial Pyramid Framework},
BOOKTITLE = {Discrete Geometry for Computer Imagery},
PAGES = {92-101},
YEAR = 2002,
EDITOR = {Achille Braquelaire and Lachaud, Jacques-Olivier and Anne Vialard},
VOLUME = 2301,
SERIES = {LNCS},
ADDRESS = {Bordeaux},
theme = {hierarchical},
MONTH = {April},
PUBLISHER = {Springer-Verlag},
NOTE = {ISBN 3-540-43380-5, ISSN 0302-9743},
ABSTRACT = {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.},
url = {article:=https://brunl01.users.greyc.fr/ARTICLES/dgci2002.pdf},

 }