Objective

2

Texture shows different characteristics on different scales. On a smaller scale， the texture may appear more intricate and detailed， but on a larger scale， texture may present large structures and patterns. Therefore， texture patterns are complex and diverse and show various characteristics across patterns. For example， structural texture has clear geometric shape and arrangement， natural texture has randomness and complexity， and abstract texture presents a combination of different colors， lines， and patterns. While the human visual system can effectively distinguish an ordered structure from a disordered one， computers are generally unable to do so. Texture filtering is a basic and important tool in the fields of computer vision and computer graphics whose main purpose is to filter out unnecessary texture details and maintain the stability of the core structure. The mainstream texture filtering methods are mainly divided into local- and global-based methods. However， the existing texture filtering methods do not effectively guarantee the structural stability while filtering the texture. To address this problem， we propose an adaptive regularization of the weighted relative total variation for image smoothing algorithm.

Method

2

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 this image according to the difference between the texture and structure. Our method implements texture filtering and structure preservation in three steps. First， 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）， we generate a structure measure amplitude image with high contrast. In each iteration， we constantly adjust the scale radius of the interval circular gradient operator， where the scale radius of the interval circular gradient operator decreases as the number of iterations increases. On the one hand， this approach can capture the low-level semantic information of the texture structure in a large range at the initial stage of iteration and suppress the texture effectively. On the other hand， this approach can accurately capture the advanced semantic information of the texture structure at the end of the iteration to keep the structure stable. Second， given the high accuracy of the Gaussian mixture model in data classification， we separate the texture and structure layers of the structure measure amplitude image by using this model along with the EM algorithm. Before the separation operation， we conduct a morphological erosion operation on the image to refine the structure edge and shrink the structure area so as to improve the accuracy of the separation result. Finally， we adaptively assign regularization weights according to the structure measure amplitude image and the texture structure separation image. We assign a regularization term with high weight to the texture region for texture suppression， and we allocate a regularization term with a small weight in the structure area to maintain the stability of the fine structure and to ensure that the texture is filtered out in a large area to the greatest extent while maintaining the integrity of the structure.

Result

2

We ran our experiment on the Windows platform and implement our algorithm using Opencv and MATLAB. We defined three main parameters， 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 texture is suppressed. A larger regular term of the texture region corresponds to smoother filtering results， while a smaller regular term of the structure region corresponds to a better structure retention ability. 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， our proposed algorithm not only effectively suppresses the strong gradient texture but also maintains the stability of the edge of the weak gradient structure. In terms of quantitative measurement， by removing compressed traces of JPG images and smoothing Gaussian noise images， our proposed algorithm obtains the maximum peak signal-to-noise ratio （PSNR） and structural similarity index （SSIM） compared with the relative total variation， rolling guidance filtering， bilateral texture filtering， scale-aware texture filtering， and

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Conclusion

2

Compared with the existing texture filtering methods， the proposed algorithm achieves strong gradient texture suppression and fine structure preservation by using the adaptive allocation of regularization weights and completes the differentiated filtering operation between the texture and structure. Experiments show that our algorithm can maintain the main structure of the image and achieve gradient smoothing. This algorithm can be used to design powerful image preprocessing methods for image stylization， detail enhancement， HDR tone mapping， superpixel segmentation， and other fields sensitive to strong gradient texture.