A Q-Ising model application for linear-time image segmentation

TL;DR

This paper introduces a linear-time image segmentation method using a Q-Ising (Potts) model, enabling efficient processing of grayscale images for real-time applications across various domains.

Contribution

It presents a novel energy minimization technique that applies four Potts models directly to images, achieving linear-time segmentation unlike previous exponential-time methods.

Findings

Achieves linear-time segmentation of grayscale images.

Demonstrates effectiveness on photographic, medical, and acoustic images.

Provides a practical approach for real-time image processing.

Abstract

A computational method is presented which efficiently segments digital grayscale images by directly applying the Q-state Ising (or Potts) model. Since the Potts model was first proposed in 1952, physicists have studied lattice models to gain deep insights into magnetism and other disordered systems. For some time, researchers have realized that digital images may be modeled in much the same way as these physical systems (i.e., as a square lattice of numerical values). A major drawback in using Potts model methods for image segmentation is that, with conventional methods, it processes in exponential time. Advances have been made via certain approximations to reduce the segmentation process to power-law time. However, in many applications (such as for sonar imagery), real-time processing requires much greater efficiency. This article contains a description of an energy minimization technique that applies four Potts (Q-Ising) models directly to the image and processes in linear time. The result is analogous to partitioning the system into regions of four classes of magnetism. This direct Potts segmentation technique is demonstrated on photographic, medical, and acoustic images.