A Bayesian Factorised Covariance Model for Image Analysis

Abstract

This paper presents a specialised Bayesian model for analysing the covariance of data that are observed in the form of matrices, which is particularly suitable for images. Compared to existing general-purpose covariance learning techniques, we exploit the fact that the variables are organised as an array with two sets of ordered indexes, which induces innate relationship between the variables. Specifically, we adopt a factorised structure for the covariance matrix. The covariance of two variables is represented by the product of the covariance of the two corresponding rows and that of the two columns. The factors, i.e. the row-wise and column-wise covariance matrices are estimated by Bayesian inference with sparse priors. Empirical study has been conducted on image analysis. The model first learns correlations between the rows and columns in an image plane. Then the correlations between individual pixels can be inferred by their locations. This scheme utilises the structural information of an image, and benefits the analysis when the data are damaged or insufficient.