  We introduce a class of random fields that can be understood as discrete
versions of multi-colour polygonal fields built on regular linear
tessellations. We focus fir st on consistent polygonal fields, for which we
show Markovianity and solvability by means of a dynamic representation. This
representation forms the basis for new sampling techniques for Gibbsian
modifications of such fields, a class which cove rs lattice based random
fields. A flux based modification is applied to the extracti on of the field
tracks network from a SAR image of a rural area.
