(eng): Tensor fields (TF) are a special kind of multidimensional data, in which a tensor is given for each point in space. Often, it is a 3 × 3 array in each voxel. To detect the patterns of interest in the field, special matching methods must be developed. We propose a method for the description and matching of TF patterns under an unknown affine transformation of the field. Transformations of TFs act not only in the spatial coordinates but also on the field values, which makes the detection more challenging. To measure the similarity between the template and the field patch, we propose original invariants with respect to affine transformations designed from moments. Their performance is demonstrated by experiments on real data from diffusion tensor imaging.