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Keywords:

  • consistent polygonal field;
  • dynamic representation;
  • linear network extraction;
  • Markov properties;
  • random field

Abstract

We introduce a class of random fields that can be understood as discrete versions of multicolour polygonal fields built on regular linear tessellations. We focus first on a subclass of consistent polygonal fields, for which we show Markovianity and solvability by means of a dynamic representation. This representation is used to design new sampling techniques for Gibbsian modifications of such fields, a class which covers lattice-based random fields. A flux-based modification is applied to the extraction of the field tracks network from a Synthetic Aperture Radar image of a rural area.