摘 要 ：目的 针对目前已有的纹理滤波方法存在无法有效保证在滤除纹理的同时保持结构稳定的问题，提出一种正则化权值自适应的相对全变分图像平滑算法。方法 首先，提出一种具有纹理抑制和结构保持的多尺度区间圆形梯度算子，其中引入了定向各向异性结构度量框架，提高了纹理-结构间的区分度。随后，利用高斯混合模型和EM算法实现纹理层和结构层的分离。最后，根据纹理和结构之间的差异性，对相对全变分模型中的正则化项进行自适应设置，使之可以在纹理区域利用大权重的正则化权值进行纹理抑制；在结构区域利用小权重的正则化权值进行结构保持。结果 在视觉层面上，通过测试油画、十字绣、涂鸦、壁画和自然场景类型图像，并与已有的主流纹理滤波方法进行比较，本文算法不仅可以有效地抑制强梯度纹理，并且可以保持弱梯度结构边缘的稳定；在定量度量方面，通过JPG格式图像压缩痕迹去除和高斯噪声图像平滑，并与相对全变分、滚动引导图像滤波、双边纹理滤波、尺度感知纹理滤波和梯度最小化进行关于峰值信噪比(peak signal-to-noise ratio，PSNR)和结构相似度(structural similarity index，SSIM)指标的比较，本文均取得最大值。此外，本文将所生成的滤波结果应用于图像的风格化、细节增强和超像素分割，效果具有一定改进和提升。结论 相较于已有的纹理滤波方法，本文算法在强梯度纹理抑制和精细结构保持方面更具优势，这将为后续图像处理奠定坚实的基础。

Abstract: Objective Texture shows different characteristics on different scales. On a smaller scale, the texture may appear more intricate and detailed; On a larger scale, textures may present larger structures and patterns. Therefore, texture patterns are complex and diverse, and the characteristics presented in various patterns are different. For example, structural texture has clear geometric shape and arrangement, natural texture has randomness and complexity, and abstract texture is a combination of different colors, lines and patterns. In general, the human visual system can distinguish the structure from the disordered texture, but this is a challenge for the computer. Texture filtering is a basic and important tool in the field of computer vision and computer graphics. Its main purpose is to filter out unnecessary texture details and maintain the stability of the core structure. The mainstream texture filtering methods have been mainly divided into two categories: local-based and global-based. However, the existing texture filtering methods have not effectively guaranteed the structural stability while filtering the texture. In order to solve this problem, this paper proposes an adaptive regularization of the weighted relative total variation for image smoothing algorithm. Method The main idea of this algorithm is to obtain a structure measure amplitude image with high texture structure discrimination, and then use the relative total variation model to smooth the image according to the difference between texture and structure. Our method includes three steps to implement texture filtering and structure preservation. Firstly, we propose a multi-scale interval circular gradient operator that can effectively distinguish texture from structure. By inputting the intensity change information of the interval gradient in the horizontal and vertical directions captured by the interval circular gradient operator into the frame of DIRECTIONAL ANISOTROPIC STRUCTURE MEASUREMENT (DASM), a structure measure amplitude image with high contrast is generated. In each iteration, the scale radius of the interval circular gradient operator is constantly adjusted, that is, the scale radius of the interval circular gradient operator decreases with the increase of the number of iterations. On the one hand, it can capture the low-level semantic information of texture structure in a large range at the initial stage of iteration, and suppress the texture more effectively; On the other hand, it can more accurately capture the advanced semantic information of texture structure at the end of iteration to keep the structure stable. Secondly, because the Gaussian Mixture Model has the characteristics of high accuracy in data classification, the texture layer and structure layer of the structure measure amplitude image are separated by using the Gaussian Mixture Model and EM algorithm. And before the separation operation, the morphological erosion operation is performed on the image to refine the structure edge and shrink the structure area, so as to make the separation result more accurate. Finally, the regularization weights are adaptively assigned according to the structure measure amplitude image and the texture structure separation image. A regularization term with high weight is assigned to the texture region for texture suppression; The regularization term with small weight is allocated in the structure area to maintain the stability of fine structure, so as to ensure that the texture is filtered out in a large area to the greatest extent while the integrity of the structure is not destroyed. Result The experiment runs on the Windows platform, and the algorithm is implemented by Opencv and MATLAB. Three main parameters are set, including the maximum scale radius of the multi-scale interval circular gradient operator, the regular term of the texture region and the regular term of the structure region. Maximum scale radius controls how much the texture is suppressed. The larger the regular term of the texture region, the smoother the filtering results can be obtained. The smaller the regular term of the structure region, the better the structure retention ability can be obtained. On the visual level, by testing the images of oil paintings, cross embroideries, graffiti, murals and natural scenes, and comparing with the existing mainstream texture filtering methods, the algorithm in this paper can not only effectively suppress the strong gradient texture, but also maintain the stability of the edge of the weak gradient structure; In terms of quantitative measurement, through the removal of compressed traces of JPG images and the smoothing of Gaussian noise images, and the comparison of peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM) indicators with the relative total variation, rolling guidence filtering, bilateral texture filtering, scale-aware texture filtering, and gradient minimization, this paper achieves the maximum value. Conclusion Compared with the existing texture filtering methods, this algorithm achieves the effect of strong gradient texture suppression and fine structure preservation by using the adaptive allocation of regularization weights, and completes the differentiated filtering operation between texture and structure. Experiments show that the algorithm can maintain the main structure of the image and achieve gradient smoothing. This will provide powerful image preprocessing methods for image stylization, detail enhancement, HDR tone mapping, Superpixel segmentation and other fields sensitive to strong gradient texture.