Discrete multi-colour random mosaics with an application to network extraction
We introduce a class of random fields that can be understood as discrete versions of multi-colour polygonal fields built on regular linear tessellations. These models generalise the binary fields introduced by Schreiber and Van Lieshout (2010).
We focus first on consistent polygonal fields, for which we show Markovianity and solvability by means of a dynamic representation. This representation enables us to design new sampling techniques for Gibbsian modifications of such fields, a class of models which includes the classic lattice based random fields that are widely used in image analysis. We then illustrate the applicability of our models by using a flux based modification to extract the field tracks network from a SAR image of a rural area.