Simulated Annealing

This article introduces the combination of Bayesian methods and Markov Random Fields (MRF) through an image segmentation example. By introducing ‘Homogeneity Prior’ and ‘Gibbs Sampling’, it demonstrates how to use MRF to solve image denoising and segmentation problems, and compares the results of traditional Maximum Likelihood, MRF Simulated Annealing, and the Simple Relaxation (ICM) method commonly used in industry. [Read More]

This article introduces the core concepts of Markov Random Fields (MRF), extending from Markov Chains in time series to MRFs on spatial lattices. It defines local dependencies through ’neighborhoods’ and ‘cliques,’ and details how the Hammersley-Clifford theorem connects MRFs with Gibbs distributions. Finally, it demonstrates a Python implementation of image denoising using MRF combined with Simulated Annealing and Gibbs Sampling. [Read More]

When optimization problems are trapped in the maze of local optima, deterministic algorithms are often helpless. This article takes you into the world of stochastic optimization, exploring how to transform the problem of finding minimum energy into finding maximum probability. We will delve into the physical intuition and mathematical principles of the Simulated Annealing algorithm, demonstrate its elegant mechanism of ‘high-temperature exploration, low-temperature locking’ through dynamic visualization, and derive the Pincus Theorem in detail, mathematically proving why the annealing algorithm can find the global optimal solution. [Read More]