Recent years have witnessed the emergence of new image smoothing techniques which have provided new insights and raised new questions about the nature of this well-studied problem. Specifically, these models separate a given image into its structure and texture layers by utilizing non-gradient based definitions for edges or special measures that distinguish edges from oscillations. In this study, we propose an alternative yet simple image smoothing approach which depends on covariance matrices of simple image features, aka the region covariances. The use of second order statistics as a patch descriptor allows us to implicitly capture local structure and texture information and makes our approach particularly effective for structure extraction from texture. Our experimental results have shown that the proposed approach leads to better image decompositions as compared to the state-of-the-art methods and preserves prominent edges and shading well. Moreover, we also demonstrate the applicability of our approach on some image editing and manipulation tasks such as image abstraction, texture and detail enhancement, image composition, inverse halftoning and seam carving.