The existing non-local structure tensors utilize the isotropic nature of the neighborhoods and compare similarity of tensors by the Euclidean distance for tensor field regularization, thus resulting in limited performances in image analysis. In this paper, we present an anisotropic nonlocal tensor regularization method by using a directional projection based atomic decomposition scheme, which offers two advantages: better exploitation of spatial directional information for anisotropically regularizing tensor field, and straightforward employment of the Euclidean distance to compute smoothing weights without extending the original non-local means filter to tensor field. Experimental results show that the proposed anisotropic structure tensor is superior to existing representative nonlinear structure tensors, in terms of corner detection and image denoising.