Bayesian Matting Algorithm

This document discusses the Bayesian matting algorithm and its approach to alpha matte estimation using maximum likelihood criterion. Matting algorithms represent computer vision techniques that extract foreground objects from images for composition onto different backgrounds. The Bayesian theorem serves as the foundation for this algorithm, utilizing prior probabilities and likelihood functions to estimate posterior probabilities. Implementation typically involves defining color distributions for foreground and background regions using Gaussian mixture models (GMMs), where the Expectation-Maximization (EM) algorithm iteratively refines these distributions. The algorithm's applications span diverse fields including image processing, video editing, and virtual reality systems. Alpha mattes quantify pixel opacity levels, typically represented by values ranging from 0 (fully transparent) to 255 (completely opaque). Through maximum likelihood estimation methods, the algorithm computes unknown alpha values based on observed color data from known foreground and background regions. The core computation involves solving for alpha using Bayesian inference: α = argmax P(F,B|α)P(α)/P(F,B), where F and B represent foreground and background color distributions. This probabilistic framework enables more precise alpha matte estimation during image processing, ultimately yielding superior compositing results with accurate transparency handling.