The paper presents a novel method for extracting meaningful structures from textured surfaces, addressing the challenge of distinguishing between structures and textures, which can be regular, near-regular, or irregular. The authors propose new variation measures, including inherent variation and relative total variation (RTV), to capture the essential differences between these visual forms. They develop an efficient optimization system to extract the main structures, which is validated on millions of sample patches. The method is effective in various applications such as structural edge detection, vectorization, seamless cloning, and structure-only image composition. The approach does not assume specific regularity or symmetry of texture patterns and can handle non-uniform and anisotropic textures. The paper also discusses the limitations of the method, such as its inability to distinguish between similar textures and structures, and provides a detailed analysis of the numerical solution and parameter adjustment. The effectiveness of the method is demonstrated through comparisons with other techniques and applications, showing its potential for practical use in image editing and rendering.The paper presents a novel method for extracting meaningful structures from textured surfaces, addressing the challenge of distinguishing between structures and textures, which can be regular, near-regular, or irregular. The authors propose new variation measures, including inherent variation and relative total variation (RTV), to capture the essential differences between these visual forms. They develop an efficient optimization system to extract the main structures, which is validated on millions of sample patches. The method is effective in various applications such as structural edge detection, vectorization, seamless cloning, and structure-only image composition. The approach does not assume specific regularity or symmetry of texture patterns and can handle non-uniform and anisotropic textures. The paper also discusses the limitations of the method, such as its inability to distinguish between similar textures and structures, and provides a detailed analysis of the numerical solution and parameter adjustment. The effectiveness of the method is demonstrated through comparisons with other techniques and applications, showing its potential for practical use in image editing and rendering.