This paper proposes a new method for extracting meaningful structures from textured surfaces. The method introduces two novel variation measures: inherent variation and relative total variation (RTV), which capture the essential differences between textures and structures. These measures are used to develop an efficient optimization system for structure extraction. The new variation measures are validated on millions of sample patches and have been applied to various tasks, including manipulating, rendering, and reusing "structure with texture" images and drawings that were traditionally difficult to edit properly. The method uses a combination of windowed total variation and windowed inherent variation to distinguish between textures and structures. The RTV measure is particularly effective in penalizing textures less than structures, allowing for their decomposition. The method is robust and can handle non-uniform and anisotropic textures in a unified framework. The optimization process involves decomposing the original non-convex problem into linear systems, which can be solved efficiently. The method has been tested on various examples, including natural scenes, mosaics, and artistic works. It has shown superior performance in structure extraction compared to existing methods, especially in handling complex textures and preserving meaningful edges. The method is also effective in applications such as image vectorization, edge detection, and image composition. It can enhance texture layers to improve contrast and create different visual impressions. The method is also useful for content-aware image resizing, where it helps preserve important features while removing less important details. The method does not require prior knowledge of texture patterns and can handle a wide range of textures and structures. However, it may struggle with textures and structures that are visually similar in scale or appearance. The method is particularly effective in scenarios where the lighting is not very complex and there is no strong perspective distortion. The method has been shown to be effective in various applications, including structure extraction, edge simplification, and texture enhancement. The method is also useful for image composition, where it helps remove conflicting details and textures between source and target images. The method has been validated on a large dataset and has shown promising results in various tasks.This paper proposes a new method for extracting meaningful structures from textured surfaces. The method introduces two novel variation measures: inherent variation and relative total variation (RTV), which capture the essential differences between textures and structures. These measures are used to develop an efficient optimization system for structure extraction. The new variation measures are validated on millions of sample patches and have been applied to various tasks, including manipulating, rendering, and reusing "structure with texture" images and drawings that were traditionally difficult to edit properly. The method uses a combination of windowed total variation and windowed inherent variation to distinguish between textures and structures. The RTV measure is particularly effective in penalizing textures less than structures, allowing for their decomposition. The method is robust and can handle non-uniform and anisotropic textures in a unified framework. The optimization process involves decomposing the original non-convex problem into linear systems, which can be solved efficiently. The method has been tested on various examples, including natural scenes, mosaics, and artistic works. It has shown superior performance in structure extraction compared to existing methods, especially in handling complex textures and preserving meaningful edges. The method is also effective in applications such as image vectorization, edge detection, and image composition. It can enhance texture layers to improve contrast and create different visual impressions. The method is also useful for content-aware image resizing, where it helps preserve important features while removing less important details. The method does not require prior knowledge of texture patterns and can handle a wide range of textures and structures. However, it may struggle with textures and structures that are visually similar in scale or appearance. The method is particularly effective in scenarios where the lighting is not very complex and there is no strong perspective distortion. The method has been shown to be effective in various applications, including structure extraction, edge simplification, and texture enhancement. The method is also useful for image composition, where it helps remove conflicting details and textures between source and target images. The method has been validated on a large dataset and has shown promising results in various tasks.