Natural Image Modelling using Mixture Models with compression as an application

This thesis mainly focuses on the problem of finding good generative models of natural images. Two main approaches are used to cope with the high dimensional problem of natural images density estimation. The first approach concentrates on developing models for small natural image patches. Mixture of elliptically contoured distributions are used and its performance is compared to some hierarchical models. The result shows that mixture models outperform the other approaches. This result is further corroborated by developing a compression algorithm that outperforms existing algorithms both quantitatively based on PSNR comparison and qualitatively. The second approach is a “2D homogeneous infinite state-space Markov Chain (IMC)” approach that explicitely makes use of the stationarity property of natural images. The model used in this document is IMC approach with a conditional density similar to the conditional form of mixture of elliptically contoured distributions. It is shown both theoretically and experimentally that using conditional models leads to better image models, i.e. higher likelihood. The success of the proposed approaches lies in the features of natural images that can be captured by them. These features are mainly contrast information and orientation information. The success of the conditional model in generating realistic textures shows the importance of those features.