In this paper we present a new approach to material classification under unknown viewpoint and illumination. Our texture model is based on the statistical distribution of clustered filter responses. However, unlike previous 3D texton representations, we use rotationally invariant filters and cluster in an extremely low dimensional space. Having built a texton dictionary, we present a novel method of classifying a single image without requiring any a priori knowledge about the viewing or illumination conditions under which it was photographed. We argue that using rotationally invariant filters while clustering in such a low dimensional space improves classification performance and demonstrate this claim with results on all 61 textures in the Columbia-Utrecht database. We then proceed to show how texture models can be further extended by compensating for viewpoint changes using weak isotropy. The new clustering and classification methods are compared to those of Leung and Malik (ICCV 1999), Schmid (CVPR 2001) and Cula and Dana (CVPR 2001), which are the current state-of-the-art approaches.