Texture–based computerized analysis of high–resolution computed tomography images from patients with interstitial lung diseases is introduced to assist radiologists in image interpretation. The cornerstone of our approach is to learn lung texture signatures using a linear combination of N–th order Riesz templates at multiple scales. The weights of the linear combination are derived from one–versus–all support vector machines. Steerability and multiscale properties of Riesz wavelets allow for scale and rotation covariance of the texture descriptors with infinitesimal precision. Orientations are normalized among texture instances by locally aligning the Riesz templates, which is carried out analytically. The proposed approach is compared with state–of–the–art texture attributes and shows significant improvement in classification performance with an average area under receiver operating characteristic curves of 0.94 for five lung tissue classes. The derived lung texture signatures illustrate optimal class–wise discriminative properties.