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### 指导图像滤波（Guided Image Filtering） #### 引言在计算机视觉与图形学领域，图像处理技术是不可或缺的一部分。其中，图像滤波作为一种基础且重要的工具，在图像去噪、边缘检测、特征提取等多个方面发挥着关键作用。本文介绍了一种新的显式图像滤波方法——指导滤波（Guided Filter），该方法由局部线性模型推导而来，能够在考虑指导图像内容的基础上计算滤波输出。 #### 方法概述指导滤波是一种基于局部线性模型的滤波器，它通过考虑一个指导图像的内容来计算滤波结果。这个指导图像可以是输入图像本身，也可以是另一张不同的图像。指导滤波不仅可以用作边缘保持平滑算子，类似于流行的双边滤波器，而且在边缘附近具有更好的行为表现。 #### 主要特点与优势 1. **边缘保持平滑**：指导滤波可以作为边缘保持平滑算子，与双边滤波相比，在边缘附近表现出更佳的行为。 2. **结构传递**：指导滤波能够将指导图像的结构传递到滤波输出中，这使得它能够实现诸如去雾和引导羽化等新应用。 3. **快速算法**：指导滤波具备一种快速且非近似的线性时间算法，不论核大小和强度范围如何，其处理速度都非常快，目前是最快的边缘保持滤波器之一。 4. **广泛应用**：实验表明，指导滤波在多种计算机视觉和图形学应用中既有效又高效，如边缘感知平滑、细节增强、HDR压缩、图像抠图/羽化、去雾、联合上采样等。 #### 相关背景与工作原理传统的线性平移不变（LTI）滤波器，例如均值滤波、高斯滤波、拉普拉斯滤波和Sobel滤波等，广泛应用于图像恢复、模糊/锐化、边缘检测和特征提取等领域。另一种方法是通过求解泊松方程来进行LTI滤波，这种方法被用于HDR压缩、图像拼接、图像抠图和梯度域操作等场合。这些LTI滤波器的核是空间不变的，并且不依赖于图像内容。然而，在很多情况下，人们希望根据给定的指导图像包含的额外信息进行滤波。例如，各向异性扩散的方法利用滤波图像本身的梯度来引导扩散过程。与传统滤波器不同，指导滤波能够利用指导图像的信息来调整滤波过程，从而更好地适应特定应用场景的需求。 #### 应用实例 1. **边缘感知平滑**：指导滤波能够有效地保留图像中的边缘细节，同时去除噪声或不必要的纹理。 2. **细节增强**：通过强调图像中的某些特征，提高图像的整体清晰度和观感。 3. **HDR压缩**：在保持图像细节的同时，压缩动态范围，使图像更适合显示。 4. **图像抠图/羽化**：指导滤波可以帮助精确地分离前景和背景，创建平滑过渡的边缘效果。 5. **去雾**：利用指导滤波可以减少大气散射效应，提高图像的清晰度。 6. **联合上采样**：在放大图像的同时，利用指导图像的信息来保持或增强细节。 #### 结论指导滤波作为一种新颖的图像滤波方法，不仅能够有效地进行边缘保持平滑，还能够通过传递指导图像的结构信息来实现更多高级功能。其具备的快速算法使得它在多种实际应用中表现出色。随着研究的深入和技术的发展，指导滤波有望成为计算机视觉和图形学领域的重要工具之一。

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Guided Image Filtering

Kaiming He, Member, IEEE, Jian Sun, Member , IEEE, and Xiaoou Tang, Fellow, IEEE

Abstract—In this paper, we propose a novel explicit image filter called guided filter. Derived from a local linear model, the guided filter

computes the filtering output by considering the content of a guidance image, which can be the input image itself or another different

image. The guided filter can be used as an edge-preserving smoothing operator like the popular bilateral filter [1], but it has better

behaviors near edges. The guided filter is also a more generic concept beyond smoothing: It can transfer the structures of the guidance

image to the filtering output, enabling new filtering applications like dehazing and guided feathering. Moreover, the guided filter

naturally has a fast and nonapproximate linear time algorithm, regardless of the kernel size and the intensity range. Currently, it is one

of the fastest edge-preserving filters. Experiments show that the guided filter is both effective and efficient in a great variety of

computer vision and computer graphics applications, including edge-aware smoothing, detail enhancement, HDR compression, image

matting/feathering, dehazing, joint upsampling, etc.

Index Terms—Edge-preserving filtering, bilateral filter, linear time filtering

1INTRODUCTION

OST applications in computer vision and computer

graphics involve image filtering to suppress and/or

extract content in images. Simple linear translation-invariant

(LTI) filters with explicit kernels, such as the mean,

Gaussian, Laplacian, and Sobel filters [2], have been widely

used in image restoration, blurring/s harpening, edge

detection, feature extraction, etc. Alternatively, LTI filters

can be implicitly performed by solving a Poisson Equation

as in high dynamic range (HDR) compression [3], image

stitching [4], image matting [5], and gradient domain

manipulation [6]. The filtering kernels are implicitly defined

by the inverse of a homogenous Laplacian matrix.

The LTI filtering kernels are spatially invariant and

independent of image content. But usually one may want

to consider additional information from a given guidance

image. The pioneer work of anisotropic diffusion [7] uses the

gradients of the filtering image itself to guide a diffusion

process, avoiding smoothing edges. The wei ghted least

squares (WLS) filter [8] utilizes the filtering input (instead

of intermediate results, as in [7]) as the guidance, and

optimizes a quadratic function, which is equivalent to

anisotropic diffusion with a nontrivial steady state. The

guidance image can also be another image besides the

filt ering input in many applications. Fo r example, in

colorization [9] the chrominance channels should not bleed

across luminance edges; in image matting [10] the alpha

matte should capture the thin structures in a composite

image; in haze removal [11] the depth layer should be

consistent with the scene. In these cases, we regard the

chrominance/alpha/depth layers as the image to be

filtered, and the luminance/composite/scene as the gui-

dance image, respectively. The filtering process in [9], [10],

and [11] is achieved by optimizing a quadratic cost

function weighted by the guidance image. The solution is

give n by solving a larg e sparse mat rix which solel y

depends on the guide. This inhomogeneous matrix im-

plicitly defines a translation-variant filtering kernel. While

these optimization-based approaches [8], [9], [10], [11] often

yield state-of-the-art quality, it comes with the price of

expensive computational time.

Another way to take advantage of the guidance image is

to explicitly build it into the filter kernels. The bilateral

filter, independently proposed in [12], [13], and [1] and

later generalized in [14], is perhaps the most popular one

of such explicit filters. Its output at a pixel is a weighted

average of the nearby pixels, where the weights depend on

the intensity/color similarities in the guidance image. The

guidance image can be the filter input itself [1] or another

image [14]. The bilateral filter can smooth small fluctua-

tions and while preserving edges. Though this filter is

effective in many situations, it may have unwanted gradient

reversal artifacts [15], [16], [8] near edges (discussed in

Section 3.4). The fast implementation of the bilateral filter

is also a challenging problem. Recent techniques [17], [18],

[19], [20], [21] rely on quantization methods to accelerate

but may sacrifice accuracy.

In this paper, we propose a novel explicit image filter

called guided filter. The filtering output is locally a linear

transform of the guidance image. On one hand, the guided

filter has good edge-preserving smoothing properties like the

bilateral filter, but it does not suffer from the gradient

reversal artifacts. On the other hand, the guided filter can be

used beyond smoothing: With the help of the guidance

image, it can make the filtering output more structured and

less smoothed than the input. We demonstrate that the

guided filter performs ve ry well in a great variety of

applications, including image smoothing/enhancement,

HDR compression, flash/no-flash imaging, matting/feath-

ering, dehazing, and joint upsampling. Moreover, the guided

IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, VOL. 35, NO. X, XXXXXXX 2013 1

. K. He and J. Sun are with the Visual Computing Group, Microsoft

Research Asia, Microsoft Building 2, #5 Dan Leng Street, Hai Dian

District, Beijing 100080, China. E-mail: {kahe, jiansun}@microsoft.com.

. X. Tang is with the Department of Information Engineering, Chinese

University of Hong Kong, 809 SHB, Shatin, N.T., Hong Kong.

E-mail: xtang@ie.cuhk.edu.hk.

Manuscript received 13 June 2012; revised 6 Sept. 2012; accepted 16 Sept.

2012; published online 1 Oct. 2012.

Recommended for acceptance by J. Jia.

For information on obtaining reprints of this article, please send e-mail to:

tpami@computer.org, and reference IEEECS Log Number

TPAMI-2012-06-0447.

Digital Object Identifier no. 10.1109/TPAMI.2012.213.

0162-8828/13/$31.00 ß 2013 IEEE Published by the IEEE Computer Society

filter naturally has an OðNÞtime (in the number of pixels N)

nonapproximate algorithm for both gray-scale and high-

dimensional images, regardless of the kernel size and the

intensity range. Typically, our CPU implementation achieves

40 ms per mega-pixel performing gray-scale filtering: To the

best of our knowledge, this is one of the fastest edge-

preserving filters.

A preliminary version of this paper was published in

ECCV ’10 [22]. It is worth mentioning that the guided filter

has witnessed a series of new applications since then. The

guided filter enables a high-quality real-time OðNÞ stereo

matching algorithm [23]. A similar stereo method is

proposed independently in [24]. The guided filter has also

been applied in optical flow estimation [23], interactive

image s egmentation [23], saliency detection [25], and

illumination rendering [26]. We believe that the guided

filter has great potential in computer vision and graphics,

given its simplicity, efficiency, and high-quality. We have

provided a public code to facilitate future studies [27].

2RELATED W ORK

We review edge-preserving filtering techniques in this

section. We categorize them as explicit/implicit weighted-

average filters and nonaverage ones.

2.1 Explicit Weighted-Average Filters

The bilateral filter [1] is perhaps the simplest and most

intuitive one among explicit weighted-average filters. It

computes the filtering output at each pixel as the average of

neighboring pixels, weighted by the Gaussian of both

spatial and intensity distance. The bilateral filter smooths

the image while preserving edges. It has been widely used

in noise reduction [28], HDR compression [15], multiscale

detail decomposition [29], and image abstraction [30]. It is

generalized to the joint bilateral filter in [14], where the

weights are computed from another guidance image rather

than the filtering input. The joint bilateral filter is

particularly favored when the image to be filtered is not

reliable to provide edge information, e.g., when it is very

noisy or is an intermediate result, such as in flash/no-flash

denoising [14], image upsamling [31], image deconvolution

[32], stereo matching [33], etc.

The bilateral filter has limitations despite its popularity. It

has been noticed in [15], [16], and [8] that the bilateral filter

may suffer from “gradient reversal” artifacts. The reason is

that when a pixel (often on an edge) has few similar pixels

around it, the Gaussian weighted average is unstable. In this

case, the results may exhibit unwanted profiles around

edges, usually observed in detail enhancement or HDR

compression.

Another issue concerning the bilateral filter is the

efficiency. A brute-force implementation is OðNr

Þtime with

kernel radius r. Durand and Dorsey [15] propose a piece-wise

linear model and enable FFT-based filtering. Paris and

Durand [17] formulate the gray-scale bilateral filter as a 3D

filter in a space-range domain, and downsample this domain

to speed up if the Nyquist condition is approximately true. In

the case of box spatial kernels, Weiss [34] proposes an

OðN log rÞ time method based on distributive histograms, and

Porikli [18] proposes the first OðNÞ time method using

integral histograms. We point out that constructing the

histograms is essentially performing a 2D spatial filter in

the space-range domain with a 1D range filter followed.

Under this viewpoint, both [34] and [18] sample the signal

along the range domain but do not reconstruct it. Yang [19]

proposes another OðNÞ time method which interpolates

along the range domain to allow more aggressive subsam-

pling. All of the above methods are linearly complex w.r.t. the

number of the sampled intensities (e.g., number of linear

pieces or histogram bins). They require coarse sampling to

achieve satisfactory speed, but at the expense of quality

degradation if the Nyquist condition is severely broken.

The space-range domain is generalized to h igher

dimension for color-weighted bilateral filtering [35]. The

expensive cost due to the high dimensionality can be

reduced by the Gaussian kd-trees [20], the Permutohedral

Lattices [21], or the Adaptive Manifolds [36]. But the

performance of these methods is not competitive for gray-

scale bilateral filters because they spend much extra time

preparing the data structures.

Given the limitations of the bilateral filter, people began

to investigate new designs of fast edge-preserving filters.

The OðNÞ time Edge-Avoiding Wavelets (EAW) [37] are

wavelets with explicit image-adaptive weights. But the

kernels of the wavelets are sparsely distributed in the image

plane, with constrained kernel sizes (to powers of two),

which may limit the applications. Recently, Gastal and

Oliveira [38] propose another OðNÞ time filter known as the

Domain Transform filter. The key idea is to iteratively and

separably apply 1D edge-aware filters. The OðNÞ time

complexity is achieved by integral images or recursive

filtering. We will compare with this filter in this paper.

2.2 Implicit Weighted-Average Filters

A series of approaches optimize a quadratic cost function

and solve a linear system, which is equivalent to implicitly

filtering an image by an inverse matrix. In image segmenta-

tion [39] and colorization [9], the affinities of this matrix are

Gaus sian function s of the color similarities. In image

matting, a matting Laplacian matrix [10] is designed to

enforce the alpha matte as a local linear transform of the

image colors. This matrix is also applied in haze removal

[11]. The weighted least squares filter in [8] adjusts the

matrix affinities according to the image gradients and

produces halo-free edge-preserving smoothing.

Although these optimization-based approaches often

generate high quality results, solving the linear system is

time-consuming. Direct solvers like Gaussian Elimination

are not practical due to the memory-demanding “filled in”

problem [40], [41]. Iterative solvers like the Jacobi method,

Successive Over-Relaxation (SOR), and Conjugate Gradi-

ents [40] are too slow t o converge. Though caref ully

designed preconditioners [41] greatly reduce the iteration

number, the computational cost is still high. The multigrid

method [42] is proven OðNÞ time complex for homogeneous

Poisson equations, but its quality degrades when the matrix

becomes more inhomogeneous. Empirically, the implicit

weighted-average filters take at least a few seconds to

process a one megapixel image either by preconditioning

[41] or by multigrid [8].

2 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, VOL. 35, NO. X, XXXXXXX 2013

1. In the literature, “OðNÞ/linear time” algorithms are sometimes

referred to as “O(1)/constant time” (per pixel). We are particula rly

interested in the complexity of filtering the entire image, and we will us e

the way of “OðNÞ time” throughout this paper.

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