This paper presents a novel edge/structure-preserving image smoothing via relativity-of-Gaussian. As a simple local regularization, it performs the local analysis of scale features and globally optimizes its results into a piecewise smooth. The central idea to ensure proper texture smoothing is based on cross-scale relative that captures the weak textures from the most prominent edges/structures. Our method outperforms the previous methods in removing the detail information while preserving main image content.