结构张量引导的自适应WLS滤波器

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"基于StructureTensor的WLS滤波器，用于自适应平滑" 这篇研究论文主要探讨了在图像处理领域中的一种改进的自适应平滑技术，即基于StructureTensor的加权最小二乘（WLS）滤波器，旨在更好地保留边缘信息的同时增强对局部纹理的平滑效果。Weighted Least Squares (WLS)滤波器是一种广泛使用的边缘保持平滑技术，其权重高度依赖于图像梯度。然而，这使得WLS滤波器在处理梯度较大的局部纹理时面临挑战。作者Zhendong Zhang和Cheolkon Jung来自西安电子科技大学电子工程学院，他们提出了一种新的结构张量引导的WLS（ST-WLS）滤波器。结构张量被引入到WLS滤波器中，目的是提取图像的局部结构信息，并利用这些信息指导平滑过程。结构张量可以用来衡量像素的各向同性，即像素周围的纹理均匀性。在ST-WLS滤波器中，不仅考虑像素的各向同性，还结合了梯度信息来计算平滑权重。这样做的好处是，它能够更准确地识别和处理各向同性纹理，同时保持图像中物体边界的清晰度和结构完整性。实验结果显示，ST-WLS滤波器在平滑各种纹理，特别是各向同性纹理方面表现出强大的能力。与其他方法相比，它更有效地平衡了平滑与边缘保持之间的关系，显著提高了图像处理的质量。通过这种方式，该滤波器为自适应平滑提供了一个更加精确和有效的解决方案，尤其适用于处理具有复杂纹理的图像。关键词：自适应平滑，各向同性纹理，结构张量，图像结构

Structure Tensor-Based WLS Filter for Adaptive

Smoothing

Zhendong Zhang and Cheolkon Jung

School of Electronic Engineering, Xidian University, Xi’an 710071, China

zhengzk@xidian.edu.cn

Abstract—The weighted least s

quares (WLS) filter is a well-

known edge preserving smoothing technique, but its weights

highly depend on the image gradients. Thus, it is hard to

smooth local textures with large gradients by WLS filter. In

this paper, we propose a structure tensor-based WLS (ST-

WLS) filter to enhance the smoothing ability of WLS filter

while successfully keeping object boundaries. We introduce

structure tensor into WLS filter to extract local structures in

an image and use them to guide the smoothing process.

Specifically, we use structure tensor to measure isotropy of

pixels. Then, we calculate the smoothing weights for pixels

based on both their isotropy and gradients. Experimental

results demonstrate that ST-WLS filter has strong ability of

smoothing textures, especially for isotropic textures, while

preserving boundaries and structures of objects.

Index Terms

—

Adaptive smoothing, isotropic textures,

structure tensor, structure preserving, WLS filter.

NTRODUCTION

Many applications in computer vision need adaptive

smoothing filters to suppress or extract content of images.

Up to the present, many outstanding results in adaptive

smoothing have been achieved by researchers [1]-[11]. They

are classified into two main groups. The first group, called

edge-preserving filter, aims at smoothing images while

preserving their edges, e.g. anisotropic diffusion filter [1],

total variation-based filter [2], bilateral filter [3, 4], WLS

filter [5], L

smoothing filter [6], and guided image filter

[7]. These filters often use gradient magnitudes of images as

an edge indicator. Due to their local contrast-based edge

definition, these filters are hard to extract textures from the

main structures. The second group of adaptive smoothing

filters, called structure-preserving filter, aims at extracting

textures from structures. This group has been popularly

investigated in recent years [8-11]. These filters commonly

use local descriptors as a structure indicator, e.g. local

histogram [8], local extrema [9], relative total variation [10]

and region covariance [11]. Although these two kinds of

filters aim at solving different problems, there is no absolute

boundary to classify them. Structure-preserving filters are

effective in preserving edges of an image because edges are

regarded as parts of structures, i.e. according to the

definition of edges and structures, while edge-preserving

filters smooth textures whose gradients are small. WLS

filter achieves smoothing in an image by finding the

minimum of weighted square errors using a global

optimization model, and its weights for smoothing only

depend on the image gradients. In this paper, we propose

ST-WLS filter for adaptive smoothing. ST-WLS filter is

based on WLS filter, but different from WLS filter because

we assume that edges are regarded as a set of pixels with

both strong anisotropy and large gradients. That is, we

compute smoothing weights for ST-WLS filter using both

gradients and anisotropy of pixels which is measured by

structure tensor. If a pixel has strong anisotropy and large

gradient, its smoothing weight becomes small, and vice

versa. Experimental results demonstrate that ST-WLS filter

has a strong smoothing ability of local textures, especially

for isotropic textures, than WLS filter, while keeping its

boundary-preserving property.

II.

WLS

ILTER

Given an in

put image g, WLS filter seek a new image u,

which is close to g, while smoothing the whole image

except for pixels with large gradients in g. It finds the

minimum of the following equation:

( ) () ()

ug ag ag



∂∂





−+ +



∂∂





(1)

where the subscript p denotes the location of a pixel. The

first term minimizes the difference between u and g. The

second term achieves smoothness by minimizing the partial

derivatives of u.

is a parameter which controls the balance

between two terms. a

and a

are spatially varying weights

for smoothing which depend on g. The larger the gradient is,

the smaller a

and a

are. We compute a

and a

as follows:

,xp

−



∂



∂



y, p

−



∂



∂



(2)

where l is the log-luminance channel of g; the exponent α

(typically between 1.2 and 2) determines the sensitivity to

the gradients of g; ε (typically 0.0001) is a small constant

that prevents division by zero in the constant areas of g.

III.

TRUCTURE

ENSOR

Structure tens

or is a tensor that extracts structural

information at a pixel. It has been commonly applied to

image and video processing [12], [13]. We obtain structure

tensor using spatial information for simplicity.

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