  Modeling of textures in natural images is an important task to make a
microscopic model of natural images. Portilla and Simoncelli proposed a
generative texture model, which is based on the mechanism of visual systems in
brains, with a set of texture features and a feature matching. On the other
hand, the texture features, used in Portillas' model, have redundancy between
its components came from typical natural textures. In this paper, we propose a
contracted texture model which provides a dimension reduction for the
Portillas' feature. This model is based on a hierarchical principal components
analysis using known group structure of the feature. In the experiment, we
reveal effective dimensions to describe texture is fewer than the original
description. Moreover, we also demonstrate how well the textures can be
synthesized from the contracted texture representations.
