发布时间: 2018-10-30 摘要点击次数: 全文下载次数: DOI: 10.11834/jig.180280 2018 | Volume 23 | Number 11 图像处理和编码

 收稿日期: 2018-05-07; 修回日期: 2018-06-20 基金项目: 国家自然科学基金项目（61379075，61472363，U1609215）；浙江省自然科学基金项目（LY14F020004）；国家科技支撑计划项目（2014BAK14B01）；浙江省公益性技术应用研究计划项目（2015C33071）；浙江工商大学青年人才基金项目（QZ13-9）；浙江省智能交通工程技术研究中心开放课题（2015ERCITZJ-KF1） 第一作者简介: 邵欢, 1993年生, 男, 浙江工商大学计算机技术硕士研究生在读, 主要研究方向为图像处理与模式识别。E-mail:shaohuan93@outlook.com. 中图法分类号: TP391.4 文献标识码: A 文章编号: 1006-8961(2018)11-1666-10

# 关键词

Texture filtering by using texture gradient suppression and ${L_0}$ gradient minimization
Shao Huan, Liu Chunxiao
School of Computer Science & Information Engineering, Zhejiang Gongshang University, Hangzhou 310018, China
Supported by: National Natural Science Foundation of China(61379075, 61472363, U1609215); Natural Science Foundation of Zhejiang Province, China(LY14F020004)

# Abstract

Objective Texture is a repetitive pattern with high pixel values. Many natural images and works of art include textures such as cross-stitch and mosaic. In many cases, the visual system of individuals ignores the texture pattern and focuses on the main structure of an image. Texture filtering is a basic tool in the computer graphics and image processing fields; the goal of which is to suppress unnecessary texture details and maintain the salient structure in the image. In recent years, various texture filtering methods, which are mainly divided into global-and local-based filtering methods, have been proposed. Most of the existing texture filtering methods handle the small gradient texture images. However, handling the strong gradient texture and losing part of the structure is difficult. To solve this problem, we propose a texture filtering method by using texture gradient suppression and ${L_0}$ gradient minimization to suppress texture and maintain the structure. Method The main idea of this algorithm is to obtain an input image with strong gradient texture suppression and then attain the smooth filtering results through the traditional texture filtering method, which uses ${L_0}$ gradient minimization. Our method involves three steps to achieve the goal of image filtering. First, we improve the interval gradient operator, which has the capability to distinguish texture and structure pixels. We propose a directional interval gradient operator to increase the gradient amplitude by finding the main direction of the structure. We use a local contrast stretching strategy when calculating the direction interval gradient to improve the recognition capability of the weak gradient structure because the pixel gradient value of the weak structure area becomes smaller than the gradient value of the strong gradient texture. The directional interval gradient affects the texture suppression; thus, selecting a computational scale is particularly important. A scale adaptive strategy, which automatically selects the optimal scale for calculating interval gradient, is proposed. Second, we aim to obtain an input image with texture gradient suppression. In the first step, we obtain the directional interval gradient value, where the structured pixel is larger than the texture pixel. Then, a normalized directional interval gradient amplitude is used as the basis for attenuating the gradient of the original image. Image reconstruction is performed after image gradient suppression to obtain a texture-suppressed image with a gray pixel gradient that is smaller than the structural pixel gradient. In the image reconstruction step, we transform the reconstruction problem into the function optimization problem, and the fast Fourier transform is applied to the frequency domain to solve the problem. Finally, we use the ${L_0}$ gradient minimization algorithm with gradient lifting effect to filter the reconstructed image to remove the texture while preserving the structure because the texture gradient suppression operation causes a certain attenuation of the gradient of the structural pixels and thus results in the loss of the structure. Result We tested different types of pictures, including mosaics, nature, and grasslands, to prove the validity of the proposed method. The experiments are run on the windows platform, and the algorithm is implemented in MATLAB. Three main parameters are set, including the scale of calculating the directional interval gradient, the gradient weight $\lambda$ in the image reconstruction step, and the smooth parameter $\lambda$in the ${L_0}$ gradient minimization. $\lambda$ controls the suppression degree of the strong gradient texture in the reconstructed image. The texture is suppressed better with the increase in $\lambda$. We compare this algorithm against other texture filtering methods, including ${L_0}$ gradient minimization, rolling guidance filtering, interval gradient, co-occurrence filter, and relative total variation method. All methods use the code provided by the author and debug the optimal parameters to obtain the filter result. The field of texture filtering has no reasonable objective evaluation index. Therefore, the subjective evaluation of human eyes is used to compare the effects of different methods. The experimental results can be summarized as follows. In the mosaic image with strong gradient texture information and intractable tiny structures, this algorithm surpasses the effects of other algorithms in a strong gradient texture suppression, and the small gradient structure is also maintained. Our algorithm demonstrates superior image smoothing results in filtering out various scale textures and preserving small gradient structures when processing natural images. Moreover, texture filtering is applied to an image edge detection and detail enhancement, which achieves a favorable effect. Conclusion A texture filtering algorithm that combines texture gradient suppression and ${L_0}$ gradient minimization is proposed as a trade-off between strong gradient texture suppression and structure preservation in current texture filtering methods. This paper main purpose is to suppress the texture gradient of the input image. Thus, the texture and structure pixels obtain different texture filtering operations. The experiments demonstrate that our algorithm can maintain the main structure of the image and achieve smooth gradients. In the field of image recognition, image fusion, and edge detection that are susceptible to strong gradient textures, texture filtering has a significant potential for application.

# Key words

texture filtering; ${L_0}$ gradient minimization; strong gradient texture; structure preserving; texture suppression

# 1.1 区间梯度计算

 ${u_p} = {g_{\rm{r}}}\left( {{R_p}} \right) - {g_{\rm{l}}}\left( {{L_p}} \right)$ (1)

 ${v_p} = {g_{\rm{r}}}\left( {\phi \left( {{R_p}} \right)} \right) - {g_{\rm{l}}}\left( {\phi \left( {{L_p}} \right)} \right)$ (4)

 ${\beta _p} = \arctan \left( {\frac{{{u_{p \cdot y}}}}{{{u_{p \cdot x}}}}} \right)$ (5)

${\beta _p}$为像素$p$的结构主方向，在此方向下计算得到${v_{p \cdot x}}$${v_{p \cdot y}}，最后图像的方向性区间梯度幅值为v = \sqrt {v_{p \cdot x}^2 + v_{p \cdot y}^2} 图 2(b)展示了改进的方向性区间梯度幅值图，但是该算子因为块计算的本质无法有效识别弱梯度结构区域的像素，因此本文提出一种局部对比度拉伸策略，即  A = \left[ {W - \min \left( W \right)} \right]/\left[ {\max \left( W \right) - \min \left( W \right)} \right] (6) 式中，W为计算v时局部窗口的像素块；A$$W$局部对比度拉伸后的块内像素；上述所有操作符均按照像素操作。图 2(c)为局部对比度拉伸后得到的区间梯度幅值，对比发现，经过拉伸后得到的区间梯度能对弱梯度结构区域的像素有效地识别。

 $k = round\left[ {\frac{{\sum\limits_{i = 2}^{m - 2} {\left( {\left| {{D_{i - 1}} - {D_i}} \right| + \left| {{D_i} - {D_{i + 1}}} \right|} \right)} }}{{m - 2}}} \right]$ (7)

# 1.2 纹理平滑抑制

 ${G_p} = {v_p} \cdot \nabla {I_p}$ (8)

 $\mathop {\min }\limits_J E\left( J \right) = \mathop {\min }\limits_J \sum {{{\left( {J - I} \right)}^2}} + \eta {\left( {\nabla J - G} \right)^2}$ (9)

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