0681

Proceedings of the 34th Chinese Control Conference
July 28-30, 2015, Hangzhou, China
A Novel Fast Haze Removal Technique for Single Image Using
Image Pyramid
ZHAO Dong 1,2 , BAI Yong-qiang 1,2
1. Department of Automation, Beijing Institute of Technology, Beijing 100081
2. Key Laboratory of Complex System Intelligent Control and Decision, Ministry of Education, Beijing 100081
E-mail: zhaodong biti@163.com
Abstract: Fast single image dehazing has been a challenging problem in many fields, such as computer vision and real-time
applications. Recently, many dehazing algorithms have been proposed based on the dark channel prior (DCP). However, these
algorithms aim to improve the refinement of the raw transmission map, while ignore the computational complexity of DCP itself.
Therefore, this paper proposes a new technique for fast single image haze removal, which achieves a good tradeoff between
the dehazing performance and the computational complexity. We first decompose the observed haze image into a coarse image
and a detail image using Gaussian-Laplacian pyramid. Then, the coarse image is dehazed by Dark Channel Prior and Guided
filter (GDCP). For the size of the coarse image is 1/4 of the original image, the computational complexity is reduced sufficiently.
However, the recomposed image is blurred, since the detail image is still haze. So, we employ an unsharp filter to sharpen
the blurred recomposed image. Experimental results show that the proposed dehazing technique effectively removes haze, and
significantly reduces the computational complexity by 69.59% on average, compared with traditional GDCP algorithm.
Key Words: single image dehazing, image restoration, dark channel prior, image pyramid, unsharp masking
1 Introduction
Images of outdoor scenes are usually degraded by bad
weather conditions, such as haze and fog. Since the additional
particles affect atmospheric absorption and scattering
of lights, distant objects and scene are less visible. As a result,
the captured images lose the color fidelity and contrast.
Removal of weather effects has caught increasing attention,
such as removals of haze[1–3, 5–7, 9, 10, 12, 13],
fog[4], rain[18, 19] and snow[20] from image. Recently,
single image dehazing algorithms have been developed to
overcome the limitations of multiple-image dehazing approaches.
These dehazing algorithms can be divided into
two major categories: physically based and contrast-based
algorithms[1].
Physically based algorithms recover the hazy images
based on the estimated transmission map. Fattal[2] decomposed
the scene radiance of an image into the albedo and
the shading, and then estimated the scene radiance based on
independent component analysis, assuming that the shading
and the scene transmission are locally uncorrelated. He et
al. [3] estimated object depths in a hazy image based on the
dark channel prior (DCP). The object depth was finally refined
by a computationally expensive alpha-matting strategy
in their work. The key idea of Nishino et al.[4] is to model
the image with a factorial Markov random field in which
the scene albedo and depth are two statistically independent
latent layers and to jointly estimate them.
Contrast-based algorithms, on the other hand, aim to restore
the visibility of a hazy image by properly enhancing
the contrast of an input degraded image. Tan[5] maximized
the contrast of a hazy image, assuming that a haze-free image
has a higher contrast ratio than the hazy image. Tarel
and Hautiere[6] attempted to the atmospheric veil(the map
of blended atmospheric light) through the median filter. Ancuti
and Ancuti[7] introduced a fusion-based strategy that
This work is supported by National Natural Science Foundation (NNS-
F) of China under Grant 61304254.
Fig. 1: Dehazing using image pyramid.
derives from two original haze image inputs by applying a
white balance and a contrast enhancing procedure.
Different than most of the existing techniques, the proposed
dehazing technique combines these two dehazing categories.
In this work, we first decompose the observed haze
image into a coarse image and a detail image using image
pyramid technique, and these two images is dehazed differently.
We employ a physically based algorithm to recover
the coarse image, while the primary composed image
(composed by the dehazed coarse image and the haze detail
image) is dehazed by a contrast-based algorithm. An
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overview diagram of the proposed approach is illustrated in
Fig. 1. Here, we choose an improved dark channel prior
called GDCP and an unsharp filter as the physically based
and contrast-based algorithms, respectively. One of the advantages
of the proposed technique is its speed: since the
size of the coarse image is only 1/4 for the original captured
image, the computational complexity is reduced significantly.
Another obvious advantage is that, because of employing
both the physically based and contrast-based algorithms, the
proposed dehazing technique can recover a high quality and
contrast image.
The remaining of this paper is organized as follows. In
Section 2, the related techniques and our observations are
briefly reviewed. In Section 3, our fast haze removal technique
for single image is introduced in detail. In Section 4,
we report and discuss the experimental results. Finally, in
Section 5, the conclusion is summarized.
2 Related Work and Obervations
The dark channel prior proposed in [3] can directly estimate
the thickness of the haze. So, the proposed fast haze
removal approach is based on dark channel prior aiming to
recover a high quality haze-free image. By employing other
techniques, we improve the computational speed effectively.
In this section, we first review the haze image model.
Then we introduce the dehazing using the dark channel prior
in detail.
2.1 Haze Image Model
Based on the atmospheric optics and only considering s-
ingle scattering [8], the formation hazy imaging model can
be represented [2, 3, 9] as follows:
I(x) =J(x)t(x)+A(1 − t(x)) (1)
where I(x) is the observed haze image at pixel x, J(x) denotes
the original haze-free image, A is the global atmospheric
light, t(x) ∈ [0, 1] is the medium transmission describing
the portion of the light that is not scattered and
reaches the camera. When the atmosphere is homogenous,
the transmission t(x) can be expressed as:
t(x) =e −βd(x) (2)
where d is the scene depth, β is the attenuation coefficient
due to scattering in the medium. This equation indicates that
the scene radiance is attenuated exponentially with the depth.
So, the haze removal is to restore J by estimating A and t
at each pixel x.
2.2 Dehazing Using the Dark Channel Prior
In order to estimate A and t, He et al.[3] proposed the
dark channel prior based on the observation that at least one
of color channel values (RGB) is close to zero in a haze-free
image. That is, for an arbitrary image J, its dark channel
J dark can be formally defined as [3]:
J dark (x) = min [ min J c (y) ] (3)
y∈Ω(x) c∈{R,G,B}
where c denotes one of the three color channels in the RBG
color space, and J c is a color channel of J, Ω(x) is a local
patch centered at x, y denotes the index for a pixel in Ω(x).
(a) (b) (c)
(d) (e) (f)
Fig. 2: Transmission maps and recovered images. (a)-
(c)are estimated transmission maps using DCP(patch size is
15 × 15),GDSP, and GDCP performed on G 1 (the first level
Gaussian pyramid). (d)-(f)are recovered images using (a)-(c)
respectively.
This statistical observation is called dark channel prior (D-
CP).
The color of the sky in a hazy image I is usually very similar
to the global atmospheric light. So, the brightest pixels
in the veiling luminance are considered to be the atmospheric
light. To estimate atmospheric light, in [3], the author
pick the top 0.1% brightest pixels in the dark channel; then
among these pixels, the pixels with highest intensity in the
input image is selected as the global atmospheric light A. After
estimating A, based on the haze imaging model shown in
equation (1) and the dark channel prior, the raw transmission
map t can be derived as:
t(x) =1− w min [min I c (y)
y∈Ω(x) c A c ] (4)
where w is a constant parameter used to keep a very small
amount of haze for the distant objects, 0

2.3 Observations
Although the dark channel prior (DCP) can directly estimate
the thickness of the haze and recover a high quality
haze-free image, it have some limitations in dealing with natural
image. The mainly defect of DCP concerned in this paper
is its computational complexity. As we discussed above,
since the transmission is not always constant in a patch, the
raw transmission map need to be refined by a soft matting
method. However, this matting method is computationally
expensive. So, a lot of improvements[10–13] for dehazing
based on DCP were proposed in recent years. These works
are focus on simplifying the refinement of the raw transmission
map, however, they ignore the cost of DCP itself.
We observed an improved dehazing algorithm based on dark
channel prior, in which the raw transmission map is refined
by a guided image filter[14] (in this paper, we call this algorithm
the GDCP). It should be noted that in our observations
on the GDCP, the guidance of the guided filter is the grayscale
of the input haze image. Although, comparing with the
results which guided by the color haze image, this simplified
guided filter may lose some edges information, its result
is effective enough for our application and computing faster.
Table 1 shows our observations on the computational time of
the guided filter and dark channel. We find that, almost 94%
runtime is costed on computing the dark channel. It indicates
that, although the GDCP improves the transmission map refinement
for cutting down the computational complexity effectively,
how to improve the computational complexity of
DCP becomes a prominent issue.
Table 1: Computational Time
Images Total Guided DCP (s)
Time(s) Filtering(s) (DCP/Total time%)
Fig. 1 9.538 0.079 9.136 (95.785%)
Fig. 2 11.004 0.091 10.534 (95.729%)
Fig. 5 8.933 0.089 8.386 (93.877%)
Fig. 6(a) 13.519 0.113 12.884 (95.303%)
Fig. 7(b) 11.247 0.092 10.507 (93.420%)
The other defect is that the image contrast after DCP
method become lower[10]. Considering the second term of
equation (1), we know that the 1 − t(x) presents the density
of haze. When different intensity of foreground irradiance
passing though same thickness haze(in a same patch of dark
channel), they have the same degree of attenuation. Thus,
the haze-free image J recovered by DCP have low contrast
(see Fig.2 (e)).
3 Proposed Algorithm
In this work, we assume that an arbitrary observed image
is composed by the coarse and the detail components. The
detail component generally presents higher gradient in the
observed image. So we also assume that for a haze image,
the haze removal degree of the coarse component should be
deeper than the detail one. That is, in the proposed dehazing
algorithm, the haze removal operators are different for
the coarse and detail components. Based on these assumptions
and considering what we observed in subsection 2.3
that the contrast of image recovered by DCP becomes lower,
it is reasonable to decompose a haze image into coarse and
Fig. 3: Decompose by using Gaussian-Laplacian pyramid.
detail images before haze removal. Thus, the detail information
can be preserved and these two components are dehazed
differently.
In fact, these two components of an image can be decomposed
into a coarse image and a detail image by using image
pyramid technique. Here, we choose Gaussian-Laplacian
pyramid proposed by Burt[15] which is an efficient nonorthogonal
pyramid representation of image. Thus, the
coarse image is the first level of Gaussian pyramid G 1 , and
the detail image is the zeroth level of Laplacian pyramid L 0 .
We employ GDCP algorithm to remove haze from the coarse
image, while for the haze of detail image, we remove it by
employing an unsharp masking sharpening technique performed
at the primary recomposed image.
3.1 Haze Removal for the Coarse Image
As we discussed above, we first decompose the haze image
into a coarse image and a detail image using Gaussian-
Laplacian pyramid. The first problem is to conform the level
number N (N =0, 1, 2,...) of the image pyramid. Noting
that, only the highest frequency information presents higher
contrast in the haze areas; and the more levels are chosen,
the more complex the algorithm is. So, N =1is more reasonable.
The decomposition of observed haze image is illustrated
in Fig. 3. In this proposed strategy, the observed haze image
(G 0 ) is firstly decomposed into a coarse image (G 1 , the
first level of Gaussian pyramid) and a detail image (L 0 , the
zeroth level of Laplacian pyramid) by Gaussian-Laplacian
pyramid. Here, the original image G 0 is blurred by Gaussian
filter firstly, then the coarse image G 1 is gained by downsample
this blurred image. The detail image L 0 is the difference
between blurred G 0 and the prediction of G 0 which is
obtained by up-sampling and Gaussian blur filtering for G 1 .
After this decomposition, we performed the GDCP haze
removal algorithm on the coarse image G 1 . Noting that, the
size of the coarse image is only 1/4 of the original image.
So, the dehazing runtime is speeded up greatly.
However, as a statistical prior, the pixel is a crucial element
which has a great effect on the estimation accuracy.
That means, perform GDCP on the original size and on
down-sample size would be different, which mainly repre-
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senting in the estimation of atmospheric light A. From Table
2 (the G 0 and G 1 columns are the results estimated from the
original image G 0 and the coarse image G 1 , respectively),
we find that the value estimated at G 1 is lager than that estimated
at G 0 , which is caused by Gaussian blurring when the
original image is decomposed. Therefore, improvements on
estimating atmospheric light is required.
3.2 Estimating Atmospheric Light A
In subsection 2.2, we introduced an estimating method
proposed in [3]. If we pick the top 0.1% brightest pixels
from the dark channel prior of the coarse image G 1 , the atmospheric
light would be estimated form the pixels in the G 1
with highest intensity. Noting that, the G 1 is down-passed
from the Gaussian blurred original image, the selected highest
intensity in the coarse image G 1 is not equal to the coordinates
intensity in the original image G 0 . Therefore, instead
of G 1 , we select the corresponding pixels with highest intensity
in the original image G 0 as the atmospheric light.
For example, the selected top 0.1% brightest pixels in dark
channel of the coarse image G 1 are p dark
g 1
(i, j)(where i, j are
the position of the selected pixels). Then, among these pixels,
we select the pixels p g0 (2 × i, 2 × j) with highest intensity
in the input haze image G 0 as the atmospheric light. We find
that, estimating by this improvement is more accurately, see
Table 2 and 3.
(a) (b) (c)
Fig. 4: An exmpel of unsharp filter.
Table 2: The Estimation of A (I)
Images G 0 G 1
Fig. 1 [0.808, 0.830, 0.841] [0.793, 0.807, 0.808]
Fig. 2 [0.694, 0.713, 0.716] [0.678, 0.648, 0.641]
Fig. 5 [0.836, 0.836, 0.844] [0.837, 0.836, 0.844]
Fig. 6(a) [0.773, 0.769, 0.772] [0.773, 0.772, 0.773]
Fig. 7(b) [0.836, 0.836, 0.844] [0.778, 0.766, 0.780]
Table 3: The Estimation of A (II)
Images Improvement results
Fig. 1 [0.801, 0.822, 0.825]
Fig. 2 [0.703, 0.694, 0.699]
Fig. 5 [0.836, 0.832, 0.843]
Fig. 6(a) [0.774, 0.770, 0.769]
Fig. 7(b) [0.812, 0.813, 0.849]
3.3 Haze Removal for the Detail Image
The primary haze removal image is recomposed by the dehazed
coarse image and the detail image. However, this recomposed
image is blurring. To address this issue, we tested
several more recent edge preserving techniques (e.g. Self-
Adapted Sharpening[16] and WLS[17]), but we did not obtain
significant improvement, since the blurring phenomenon
is generated by the still haze detail component while the
coarse component is dehazed, which means that the haze is
uneven in the primary recomposed image. Thus, the uneven
haze at detail component should be ’dispersed’ at first by certain
technique, then enhance the image sharpness. By these
operators, the slight haze is distributed across the whole image
and the edge is sharpened.
To achieve these two operators, we employ an Unsharp
Filter, and performed it at the dimension L ∗ of the Lab color
space of the primary recomposed image. This unsharp
Fig. 5: Detail image haze removal using the unsharp sharpening
filter. In left column, image above is the primary recomposed
image, while the blow image is the results obtained
by unsharp sharpening the above one. Images in right
column are details of the left one marked by yellow rectangle.
masking sharpening process is equates to disperse the haze
at detail edge to the whole image at first, and then enhance
the sharpness.
denote the sharpening filter. Our sharpening
filter is constructed by a high-pass filter and a Gaussian blur
filter linearly:
Let F sharp
n×n
F sharp
n×n = μFn×n blur + νF high
n×n (6)
where, Fn×n blur presents a n × n Gaussian blur filter (with n =
5, δ =1in this paper); F high
n×n presents a n × n high-pass
filter (with the center pixel value is 1, and other pixels are
0). In fact, the Fn×n blur is used to blur the primary recomposed
image, thus the haze in detail image is distributed cross the
whole image.
To express the sharpening filter as an unsharp filer, we
propose μ = −α while ν = α + β, then the equation (6) is
derived as:
F sharp
n×n
= α(F high
n×n − F blur
n×n)+βF high
n×n (7)
where, F sharp
n×n is an unsharp filter. Parameter α specifies the
linear strength of the sharpening effect. A higher α value
leads to larger increase in the contrast of the sharpened pix-
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(a)
Fig. 6: Comparisons of recovered images with the sky. The
first row is the input haze images. The second is the results
of GDCP performed on original image. The last row is our
results.
(b)
(a)
(b)
Fig. 7: Comparisons of recovered non-sky region images.
The first row is the input haze images. The second is the
results of GDCP performed on original image. The last row
is our results.
els. Parameter β is used to adjust the center pixel value of
F sharp
n×n , which affects the overall L ∗ dimension. Normally,
α =0.9,β =1.
Fig. 4 is an example to illustrate the unsharp filter in detail.
In this figure, (a)-(c) are the local L ∗ dimension of primary
recomposed image, Gaussian blurring image, and sharpening
image. The values marked by red box and yellow box
are the maximum and minimum value for each local L ∗ .We
find that, when the Gaussian blur filter sliding the L ∗ channel,
the value are tend to be flat, which means that the haze in
the detail image is dispersed. While the unsharp filter makes
the L ∗ channel more contrast. Fig. 5 shows the dehazing
result using the unsharp filter in detail.
4 Experimental Results
In our experiments, we evaluate the dehazing effect and
the computational complexity of the proposed algorithm by
comparing with the GDCP performed on original size.
4.1 Dehazing Effect Comparisons
Fig.6 and 7 are our experimental results compared with
traditional GDCP dehazing algorithm. To prove the robustness
of our improvement, we have tested the new operator
on a large dataset of different hazy images.
In Fig.6 we illustrate images with the sky, while the Fig.7
presents the results of non-sky region images. We can find
that, compared with the traditional GDCP, performing GD-
CP on the first level Gaussian pyramid G 1 does not have obvious
impacts on haze removal effect. Since we employ an
unsharp sharpening filter to refine the blurring recomposed
image, our improvements achieve a better perceptual quality
than the traditional GDCP.
4.2 Computational Complexity Evaluations
The proposed improvement combining the GDCP and
Gaussian-Laplacian pyramid skillfully. So, in our computational
complexity evaluations, we evaluate the quality of
this algorithm by objective assessment. The minimum running
time for different images are recorded in Table 4. The
time reported in the paper is from MATLAB implementation
on a PC with Intel(R) Core (TM) i5-3230M CPU @ 2.60
GHz with 8 GB RAM). Compared with the traditional GD-
CP algorithm, the proposed algorithm significantly reduces
the computational complexity by 69.59% on average.
Table 4: Computational Complexity
Our algorithm
Images
Traditional
Compare with
GDCP (s) Time traditional
(s) GDCP(%)
Fig. 1 9.54 2.95 -69.08
Fig. 2 11.01 3.36 -69.48
Fig. 5 8.93 2.76 -69.09
Fig. 6(a) 13.52 3.95 -70.78
Fig. 7(a) 14.48 4.41 -69.54
Average 11.50 3.49 -69.59
5 Conclusions
In this work, we propose a novel fast single image haze removal
technique that dehazing the coarse and detail image d-
ifferently: by using physically and contrast-based algorithms,
respectively. In fact, the proposed technique achieves performing
the haze removal algorithms at a higher image pyramid
successfully, with sufficient low computational complexity
while no obvious influence on dehazing effect. Another
great contribute for this work is that, for almost any
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other existing dehazing algorithms can be employed to recover
the coarse image. In future work we would like to test
our method on videos.
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