Abstract: It is ubiquitous that meaningful structures are formed by or appear over textured surfaces. Extracting them under the complication of texture patterns, which could be regular, near-regular, or irregular, is very challenging, but of great practical importance. We propose new inherent variation and relative total variation measures, which capture the essential difference of these two types of visual forms, and develop an efficient optimization system to extract main structures. The new variation measures are validated on millions of sample patches. Our approach finds a number of new applications to manipulate, render, and reuse the immense number of "structure with texture" images and drawings that were traditionally difficult to be edited properly.