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},