Guided Image Filtering & Fast Guided Filter

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

OST applications in computer vision and computer

graphics involve image filtering to suppress and/or

extract content in images. Simple linear translation-invariant

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

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

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

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

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

less smoothed than the input. We demonstrate that the

guided filter performs ve ry well in a great variety of

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

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

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

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

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

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

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

process, which involves a guidance image I, an filtering

input image p, and an output image q. Both I and p are

given beforehand according to the application, and they can

be identical. The filtering output at a pixel i is expressed as

a weighted average:

(Fig. 1 (left)). The bilateral filtering kernel W

is given by

1

where x is the pixel coordinate and K

parameter to ensure that

optimize a quadratic function and solve a linear system in

this form:

Now we define the guided filter. The key assumption of the

guided filter is a local linear model between the guidance I

and the filtering output q. We assume that q is a linear

transform of I in a window !

centered at the pixel k:

local linear model ensures that q has an edge only if I has an

useful in image super-resolution [50], image matting [10],

and dehazing [11].

constraints from the filtering input p. We model the output q

as the input p subtracting some unwanted components n

we minimize the following cost function in the window !

:

will investigate its i ntuitive meaning in Section 3.2.

Equation (6) is the linear ridge regression model [51], [52]

and its solution is given by

Fig. 1. Illustrations of the bilateral filtering process (left) and the guided filtering process (right).

Here, 



of p in !

can compute the filtering output q

/

methods.

the filtering input p. We can see that the guided filter

behaves as an edge-preserving smoothing operator (Fig. 2).

The edge-preserving filtering property of the guided

filter can be explained intuitively as following. Consider the

within !

Case 2: “Flat patch.” If the image I is almost constant in

, we have 

in (10) to get the output, we have that if a pixel is in the

middle of a “flat patch” area, its value becomes the average

More specifically, the criterion of a “flat patch” or a “high

variance” one is given by the parameter . The patches with

variance (

in the bilateral filter (2): Both determine “what is an

edge/a high variance patch that should be preserved.”

Further, in a flat region the guided filter becomes a

cascade of two box mean filters whose radius is r. Cascades

of box filters are good approximations of Gaussian filters.

Thus, we empirically set up a “correspondence” between

.

It is often considered as visually insensitive when

It is easy to show that the relationships among I, p, and q,

given by (7), (8), and (10), are in the weighted-average form

as (1). In fact, a

in (7) can be rewritten as a weighted sum of

from (10). We can

prove that the kernel weights is explicitly expressed by

filter kernel is given by W