Receptive Fields within the Combinatorial Pyramid Framework

  • Luc Brun
  • Walter G. Kropatsch
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2301)


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 study the main properties of these sets.


Receptive Field Construction Scheme Double Edge Contraction Operation Adjacency Relationship 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Luc Brun
    • 1
  • Walter G. Kropatsch
    • 2
  1. 1.Laboratoire d’Études et de Recherche en Informatique (EA 2618)Université de ReimsFrance
  2. 2.Institute for Computer-aided Automation Pattern Recognition and Image Processing GroupVienna Univ. of TechnologyAustria

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