Multi-colour random fields with polygonal realisations

TL;DR

This paper introduces a new class of multi-colour polygonal random fields on tessellations, demonstrating their Markovianity, solvability, and applications in image analysis with novel sampling techniques.

Contribution

It presents a novel discrete polygonal field model with Markov properties and dynamic sampling methods, extending lattice-based random fields to polygonal structures.

Findings

Markovianity and solvability of the polygonal fields

Development of new sampling techniques for Gibbsian modifications

Application to extracting field networks from SAR images

Abstract

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.