We propose a texture learning approach that exploits local organizations of scales and directions. First, linear combinations of Riesz wavelets are learned using kernel support vector machines. The resulting texture signatures are modeling optimal class-wise discriminatory properties. The visualization of the obtained signatures allows verifying the visual relevance of the learned concepts. Second, the local orientations of the signatures are optimized to maximize their responses, which is carried out analytically and can still be expressed as a linear combination of the initial steerable Riesz templates. The global process is iteratively repeated to obtain final rotation-covariant texture signatures. Rapid convergence of class-wise signatures is observed, which demonstrates that the instances are projected into a feature space that leverages the local organizations of scales and directions. Experimental evaluation reveals average classification accuracies in the range of 97% to 98% for the Outex_TC_00010, the Outex_TC_00012, and the Contrib_TC_00000 suites for even orders of the Riesz transform, and suggests high robustness to changes in images orientation and illumination. The proposed framework requires no arbitrary choices of scales and directions and is expected to perform well in a large range of computer vision applications.