Part One: Introduction and Basic Concepts
Noise is a common problem in digital image processing. It can be caused by interference during the capture, transmission, or storage of the image. In order to improve the quality of the image, denoising is usually required. In this article, we will explore the use of MRF (Markov Random Field, Markov Random Field) and Ising model with simulated annealing technology to denoise binary images.
1.1 MRF（Markov Random Field）
Markov random field (MRF) is a probabilistic model widely used in image processing, computer vision and medical image processing. It is based on the concept of a neighborhood system, where the value of a pixel depends on the values of its neighbors. In image denoising, we can use MRF to capture local structure and continuity in the image.
1.2 Ising model
The Ising model was originally proposed to describe the statistical behavior of magnetic materials. However, this model was quickly used to describe a variety of physical and non-physical systems, including binary image denoising. In the Ising model, we consider a regular grid of points, with a rotation on each grid point, and these rotations can take the value of +1 or -1. This matches the pixel values in a binary image, where a pixel can be black (e.g., have a value of 1) or white (e.g., have a value of -1).
1.3 Simulated annealing
Simulated annealing is a stochastic optimization technique inspired by the solid annealing process. In this method, the system starts at a high temperature and gradually cools down until it reaches a stable low-energy state. In the context of binary image denoising, we can use simulated annealing to find image configurations that minimize noise.