Natural Images, Gaussian Mixtures and Dead Leaves Supplementary Material

"Natural Images, Gaussian Mixtures and Dead Leaves"

Yair Weiss School of Computer Science and Engineering Hebrew University of Jerusalem Israel yweiss@cs . huj i. ac . i l Simple Gaussian Mixture Models (GMMs) learned from pixels of natural image patches have been recently shown to be surprisingly strong performers in modeling the statistics of natural images. Here we provide an in depth analysis of this simple yet rich model. We show that such ...

The Transparent Dead Leaves Model

This paper introduces the transparent dead leaves (TDL) random field, a new germ-grain model in which the grains are combined according to a transparency principle. Informally, this model may be seen as the superposition of infinitely many semi-transparent objects. It is therefore of interest in view of the modeling of natural images. Properties of this new model are established and a simulatio...

The Infinite Mixture of Infinite Gaussian Mixtures for Clustering Data Sets with Multi-mode and Rare Clusters Supplementary Material

Mixtures of Conditional Gaussian Scale Mixtures Applied to Multiscale Image Representations

We present a probabilistic model for natural images that is based on mixtures of Gaussian scale mixtures and a simple multiscale representation. We show that it is able to generate images with interesting higher-order correlations when trained on natural images or samples from an occlusion-based model. More importantly, our multiscale model allows for a principled evaluation. While it is easy t...

The Dead Leaves Model : a General Tessellation Modeling Occlusion

In this article, we study a particular example of general random tessellation, the dead leaves model. This model, first studied by the Mathematical Morphology school, is defined as a sequential superimposition of random closed sets, and provides the natural tool to study the occlusion phenomenon, essential ingredient in the formation of visual images. We generalize results from G. Matheron, and...