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Part of important structural edges in the image is smoothed due to the small gradients, while the others are preserved with greater gradients. Therefore, the authors propose a two‐stage image smoothing method based on edge‐patch histogram equalisation and patch decomposition. The authors' purpose is to increase the gradient of important structural edges while reducing the gradient of the texture region. Therefore, they divide the image into edge‐patches where the structural edges are concentrated or non‐edge‐patches where the texture details are concentrated by image segmentation. The edge‐patch needs to be equalised by the histograms for increasing the gradient of the edge pixels. All patches are decomposed to extract the smooth component for reducing the gradient of pixels. The smooth component of each patch is smoothed via L0 gradient minimisation. In order to ensure the continuity of the patch boundaries, the edge‐patch is inversely equalised. Finally, the whole image is smoothed via L0 gradient minimisation for removing residual textures and seams. Experimental results demonstrate that the proposed method is more competitive in maintaining important structural edges and removing texture details than the state‐of‐the‐art approaches. The proposed method can be applied to many areas of image processing. [ABSTRACT FROM AUTHOR]