Separation of multiplicative image components by Bayesian Independent Component Analysis

The ability to decompose superimposed images to their basic components has a fundamental importance in machine vision applications. Segmentation Algorithms consider an image composed of several regions each with a particular gray level, texture or color and try to extract those regions which are not covering each other. However, in this paper, we propose a method for decomposing an image to its superimposed components. Taking prior assumptions into account requires Bayesian framework which is well adapted to this application. Also, a profound mathematical theory called Variational Method is used here which makes us capable of calculating intractable integrals and marginal posteriors. In this paper, situations where superimposed images are to be recovered are discussed and a thorough framework is suggested which is basically founded on the ground of Blind Source Separation (BSS) and Independent Component Analysis (ICA). The main idea of this paper is exerted on some synthetic images to verify its applicability.