Pixelization paradigm: outline of a formal approach

  • Authors:

  • Pierre P. Lévy

  • Affiliations:

  • Université Pierre et Marie Curie-Paris, UMR, Paris and INSERM, UMR, Paris and Hôpital Tenon, Assistance Publique Hôpitaux de Paris, Paris cedex 20, France

  • Venue:
  • VIEW'06 Proceedings of the 1st first visual information expert conference on Pixelization paradigm
  • Year:
  • 2006

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Abstract

Various approaches exist related to Pixelization Paradigm. These approaches can be methodological or applied. Therefore finding formalism able to grasp all these approaches appears important. This formalism comes from category theory, the main formal tool being the functor notion. A category is characterized by objects and morphisms between these objects. Two categories can be associated thanks to a functor that respectively maps objects and morphisms from one category to objects and morphims of the other category. A pixelized visualization is defined by an object and two morphisms. The object is the reference frame of the visualization; the morphisms respectively associate a value and a colour to each cell of the reference frame. Functors formally allow implementing transformations on the visualization. The approach on the one hand allows identifying various atomic notions of Pixelization paradigm with formal entities and on the other hand, thanks to this, allows studying them and opening new ways. Various illustrations are given.