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An anisotropy-based image smoothing method is proposed to remove image details from various images. Image details appear as the textures in the image. After removing them, the remaining part is known as image structure. To effectively distinguish image structures and textures, the authors present an anisotropy-based measurement which depicts the anisotropy degree of local gradients for each edge pixel. The pixels with larger anisotropy are more likely to be the ones on structural edges. Then, the anisotropy-based measurement is embedded in a regularised objective function. To achieve the image smoothing, the objective function is finally optimised by training a deep network. Visual results demonstrate that the proposed method is powerful to keep the edges in the smoothed images sharp and eliminate trivial details simultaneously.