author = {Luc Brun and Walter Kropatsch}, title = {Receptive Fields within the Combinatorial Pyramid Framework}, journal = {Graphical Models}, year = 2003, pages= {23-42}, volume= 65, 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 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.", url = {article:=https://brunl01.users.greyc.fr/ARTICLES/recep_field.pdf}, theme = {hierarchical}