Fusion of Dehazing and Retinex using Transmission
for Visibility Enhancement
Jaepil Ko
1
Dept. of Computer Engineering, Kumoh Nat’l Institute of Tech., Gumi, Korea
Keywords: Transmission, Dehazing, Dark Channel Prior, Retinex, Image Enhancement.
Abstract: Outdoor images are easily degraded by aerosols such as haze and fog. The existing dehazing methods based
on the atmospheric scattering model improve image contrast and color fidelity at the cost of its brightness.
We propose a visibility enhancement method by combining dehazing and retinex with the transmission. The
proposed method retains both color fidelity and brightness without over saturation.
1 INTRODUCTION
Outdoor images are easily degraded by aerosols,
such as haze, fog and dust, since they scatter and
absorb the light while they are blended with the
ambient light called the airlight. Recently, single
image approach without using any other additional
information has made progress (Fattal, 2008); (He et
al., 2009); (Tan, 2008). He et al. (He et al., 2009)
proposed an interesting dark channel prior assuming
that in any local region of a haze free outdoor image
there is at least one channel of a pixel that is dark.
This prior provides easy approximation of the
transmission as well as effective estimation of the
airlight. However, it improves image contrast and
colour fidelity at the cost of image brightness.
Therefore, this method mandatorily adopts post-
processing, such as gamma correction, a simple
brightening by intensity rescaling, and histogram
equalization for better visibility, but they often cause
oversaturation. The formation of a haze image is
described by the atmospheric scattering model
(Narasimhan and Nayar, 2003) that consists of two
terms: attenuation and airlight. Attenuation describes
the way light gets weakened as it traverses from a
scene point to the observer. Airlight quantifies the
scattered light due to the medium in the atmosphere.
(
)
=
(
)
t
(
)
+1−t
(
)
(1)
where I is the observed haze image, J is the scene
radiance that is the haze free image to restore. A is
the global atmospheric light, t is called the medium
transmission and is the portion of the light that
Figure 1: (a) input image, (b) restored image without post-
processing (clouds appear, but it becomes dark in the
mountains), (c) transmission map (rough depth).
reaches the observer without being scattered, and x
indicates the position of a pixel. This model assumes
that the scene radiance is attenuated exponentially
with the scene depth, so the transmission t can be
expressed as follows:
t
(
)
=e
()
(2)
where d(x) is the depth of the scene point from the
observer and λ is the wavelength of the medium. β is
called the scattering coefficient of the medium. The
goal of dehazing is to restore J by estimating t and A
from a given input image I. From the equation (1),
the attenuation term related to the scene radiance can
be computed by subtracting the airlight term from
the input image. It indicates that the restored image
can lose a small amount of brightness. The restored
images look dark compared to the input images
shown in Figure 1(a) and Figure 1(b).
122
Ko J..
Fusion of Dehazing and Retinex using Transmission for Visibility Enhancement.
DOI: 10.5220/0004284801220125
In Proceedings of the International Conference on Computer Vision Theory and Applications (VISAPP-2013), pages 122-125
ISBN: 978-989-8565-47-1
Copyright
c
2013 SCITEPRESS (Science and Technology Publications, Lda.)
In this paper, we present a new method for both
dehazing and visibility enhancement for a given
single input image. We achieve this goal by
combining the results of dehazing and retinex with
the refined dark channel (or the transmission) (He et
al., 2009) that approximates a rough depth as shown
in Figure 1(c).
2 FUSION OF DEHAZING
AND RETINEX
2.1 Dehazing and Retinex
Instead of taking two methods sequentially, we fuse
both dehazing and the multi-scale retinex (Jobson et
al., 1997) in parallel using the estimated
transmission. The dark channel prior assumes that
every local patch except for sky region in the haze-
free image have at least one color channel near black
(near zero). With the dark channel prior, we can
compute a coarse transmission map t
̃
(
)
of a given
scene when the airlight is already obtained:
t
̃
(
)
=1−
min
c∈{r,g,b}
min
∈Ω
(
)
(
)
(3)
where I
is a color channel of I and
(
)
is a local
patch around .
To refine the coarse transmission map, the dark
channel method adopts the soft matting algorithm
(Levin and Weiss, 2006) which is computationally
too expensive. Instead of using the soft matting, a
cross-bilateral filtering method is adopted by (Zhang
et al., 2010) for the refined transmission mapt
(
)
.
In (He et al., 2009), they can recover the scene
radiance simply by solving the inverse of equation
(1) with a minor constraint. They restrict the
transmission to a low bound t
typically being set to
0.1 to preserve a small certain amount of haze in
very dense haze region. The final scene radiance is
recovered by:
(
)
=
(
)
−
max
(
t
(
)
,t
)
+
(4)
The airlight can also be computed from the dark
channel since the airlight is usually estimated from
the most haze-opaque pixels, and the dark channel
approximates the haze denseness. In (He et al.,
2009), they take the top 0.1% brightest pixels in the
dark channel then select the pixels having the
highest intensity in the input image among them. In
our experiment, we just take the average of the top
0.1% brightest dark channel value for simplicity and
robustness.
Since the scene radiance is usually darker than
the airlight, the recovered image looks dim with a
higher dynamic range as shown in Figure 1(b).
Therefore, the existing methods usually adopt post
processing such as gamma correction, simple
brightening by intensity rescaling, and histogram
equalization for better visibility under the risk of
over saturation.
Retinex is a theory of color vision that explains
how the human visual system extracts reliable
information from the world despite of illumination
changes. Retinex assumes that the image is the
product of the illumination and surface
reflectance . The goal of the retinex is to
decompose the image into the reflectance image and
the illumination image. One approach first proposed
by Land (Land, 1986), assumes that the illumination
value for a pixel is a weighted average of its
surroundings, whose weights are given by a
Gaussian function. The retinex output is given by:
log
(
)
=log
(
)
−log
G
(
,σ
)
∗()
(5)
where “∗” denotes the convolution operation, and
G
(
x,σ
)
=Ke
‖
‖
/
where σ is the scale and K is
selected such that
∬
G
(
x,σ
)
dx=1. This model is
extended by simply taking the weighted sum of the
retinex outputs with different scales of the Gaussian
function. This technique is called the multi-scale
retinex (Jobson et al., 1997). The multi-scale retinex
output is given by:
()= ω
∙
(
log
(
)
−log
G
(
,σ
)
∗()
)
(6)
where N is the number of scales, and ω
is the
weight typically set to 1/N for most applications.
The number of scales is usually set to three scales;
small, intermediate, and large. This technique
significantly enhances the dark region of images
usually caused by backlight, which can be achieved
by controlling the scale parameter.
2.2 Transmission-based Fusion
The dehazed images often lose their brightness while
achieving better contrast and color fidelity.
Therefore, the conventional dehazing methods
require post-processing that increases the brightness.
The retinex algorithm can just be applied as post-
processing. However, the images needed to be
dehazed have been captured under low lightness, so
the sequential combination of dehazing and retinex
can make input images be oversaturated with strong
FusionofDehazingandRetinexusingTransmissionforVisibilityEnhancement
123
noise. We take advantages of dehazing and retinex
by combining their results in parallel. The dehazing
algorithm has more strength in the pixels at a long
distance under the strong influence of haze while the
retinex algorithm has strength in the pixels at a
relative near distance. This approach requires a
depth map. We propose to use the transmission t
(
)
the airlight normalized dark channel that effectively
approximates the depth of an input image. The
proposed method is simply formulated as follow:
(
)
=(1−αt
(
)
)
(
)
+αt
(
)
()
(7)
where α is the combining weight. In our experiment,
we usually get visually better results with α=0.8 for
higher weight to the dehazing.
Figure 2: From left to right, dehazing without post-
processing, transmission, retinex, and the final result of
combining (a) and (c) using (b).
Figure 2 demonstrates the effectiveness of the
proposed method. In Figure 2(a) the dehazing has
strength in the sky region by recovering the shape
and color of the clouds at the cost of losing much
brightness. In Figure 2(b) the transmission map
achieves reasonable depth estimation of the scene;
close object looks bright and distance object looks
dark. In Figure 2(c) the retinex achieves a good
brightness in the shadow regions of the mountain;
however, it fails to recover the sky region. In Figure
2(d) our proposed fusion method takes both
advantages of dehazing and retinex.
3 EXPERIMENTS
In Figure 3, we compare the proposed method with
respect to post-processing. Our method generates
more natural scenery compared to the others that
suffer from oversaturation in the middle of the
mountain and sky regions. Gamma correction
increases brightness of the mountain region but not
sufficient. Intensity rescaling fails to recover the
correct color in both sky and mountain regions.
Figure 4 compares He’s method, retinex, and the
Figure 3: He’s result with a: gamma correction, b:
intensity rescaling and c: the proposed method.
proposed method. Our proposed method achieved
better visibility in the region of the tree and the
boundary of the lake while revealing the building
covered by a dense fog in background like (b).
Meanwhile the retinex has no effect on removing
dense haze at all in this image.
Figure 4: Visual comparison results. (a) input image, (b)
dehazing, (c) retinex, and (d) the proposed method.
4 CONCLUSIONS
In this paper, we proposed to use the transmission
map; rough estimation of scene depth, for combining
both results of dehazing and retinex to retain the
advantages of them. The experimental results
demonstrated that our method generated more
natural scenery with a proper visibility
ACKNOWLEDGMENTS
This work (Grants No.C0033001) was supported by
Business for Cooperative R&D between Industry,
Academy, and Research Institute funded Korea
Small and Medium Business Administration in 2012.
VISAPP2013-InternationalConferenceonComputerVisionTheoryandApplications
124
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