Cutset Width and Spacing for Reduced Cutset Coding of Markov Random Fields

TL;DR

This paper analyzes how the thickness and spacing of cutsets affect coding efficiency in Reduced Cutset Coding of Markov random fields, providing theoretical insights and numerical validation.

Contribution

It introduces a detailed analysis of tradeoffs in cutset design for RCC, including redundancy decomposition and an estimation algorithm for reduced MRFs.

Findings

Increasing cutset thickness reduces coding rate for the cutset.

Increasing spacing raises the coding rate of non-cutset pixels, but remains lower than that of the cutset.

Numerical simulations confirm the analytical tradeoffs and redundancy analysis.

Abstract

In this paper we explore tradeoffs, regarding coding performance, between the thickness and spacing of the cutset used in Reduced Cutset Coding (RCC) of a Markov random field image model. Considering MRF models on a square lattice of sites, we show that under a stationarity condition, increasing the thickness of the cutset reduces coding rate for the cutset, increasing the spacing between components of the cutset increases the coding rate of the non-cutset pixels, though the coding rate of the latter is always strictly less than that of the former. We show that the redundancy of RCC can be decomposed into two terms, a correlation redundancy due to coding the components of the cutset independently, and a distribution redundancy due to coding the cutset as a reduced MRF. We provide analysis of these two sources of redundancy. We present results from numerical simulations with a homogeneous Ising model that bear out the analytical results. We also present a consistent estimation algorithm for the moment-matching reduced MRF on the cutset.