![](bg2.png)
mental results are shown in In Section 3. Finally, we
conclude the advantage of proposed method and the
future works.
2 HAZE REMOVAL ALGORITHM
Nowadays, the image optical (degradation) model is
mostly be used in single image based haze removal
methods (Fattal, 2008) (Tan, 2008) (He et al., 2009):
Y(x) = I(x)e
−βd(x)
+ A(1− e
−βd(x)
), (1)
where Y(x) is the hazy image, I(x) is the haze-free
image; e
−βd(x)
is the atmosphere attenuation term, β
is the coefficient and d(x) is the distance from object
to imaging plan (here call as the depth); A is the atmo-
sphere light, and x is the position of pixel. Observing
this model and the atmospheric scattering theory, the
first term in the right hand is the diffuse reflectance of
object and second term is the the diffuse reflectance
of depth. For describe the model more simply, the
e
−βd(x)
can use T(x) to instead. So the Eq. ( 1) can be
rewritten as:
Y(x) = I(x)T(x) + A[1− T(x)], (2)
where T(x) is the transmission map and have same
feature with depth map. To estimate the haze-free im-
age I(x), only need get the atmosphere A and trans-
mission map T(x). However, single image haze re-
moval problem is an ill-posed problem so it needs
use some methods to change it to well-posed prob-
lem. Because of the parameters are unknown and can-
not to estimate the original haze-free image by optical
model exactly.
For estimating the A and T(x), the first step is esti-
mate the A and then use it to estimate the transmission
T(x). Recently, He et al. (He et al., 2009) proposed a
new approach by observing the darkest value of R, G,
and B of every pixel and defined it as dark channel.
I
min
(x) = min[R(x),G(x),B(x)], (3)
And then get the statistical by dark values (I
min
(x))
of many hazy images to get the prior which the dark
channel can be defined as the transmission map (re-
flect the depth information) to estimate the haze-free
image. He’s method is new and the dark channel is
novel, this prior is effective but in sometimes, the es-
timation of A and T(x) is not accuracy enough. So in
this paper, we use the dark prior with optical model
and improve the parameters selection.
2.1 Atmosphere Light A Estimation
In some existing works, the atmosphere light A is es-
timate from the hazy image directly, but it usually not
correct. In He’s method (He et al., 2009), the author
use the dark channel as Eq. 3 defined to estimate the
position of A and calculate it from hazy image with
same pixel. However, in some situations the local
white influence it strongly, because the atmosphere
light candidate should lager than white object. In He’s
method, by the some objects influence (such as the
tree), the sky region may become to several separate
regions and small than white object, also maybe the
light intensity is weaker than it too. In this situation,
the atmosphere light A usually select the white object
and influence the estimation.
So to overcome this problem, the first thing is ob-
taining the correct candidate region and then select
the ideal values. Here we use the color barycenter
hexagon (CBH) model (Zhang and Kamata, 2008) to
calculate the gray region (not real gray, only the pixels
which not reflect the color information) for obtaining
the atmosphere. At first, use the CBH model to de-
tect the color pixels and turn them into black [Fig.
1(b)], then use the Eq. 3 to calculate the dark pix-
els [Fig. 1(c)]. After this processing, calculate the
0.1% brighter pixels in the image and use the average
value of these pixels in original image as the atmo-
sphere light A. By this selection, the obtained value
can overcome the multi-light source influence.
2.2 Atmospheric Veil Transmission T(x)
Estimation
Considering the different objects have different dif-
fuse reflection ability, also deferent distance have dif-
ferent diffuse reflection, here assume these two re-
flection are same simply. As the dark prior of He’s
method, here we also use it to estimate the transmis-
sion map. Different with He’s method, in current pa-
per we segment the image at first and then calculate
in every region respectively.
In He’s method, the overlapped patches are used
to calculate the dark pixel to estimate the transmis-
sion. In our research, the segmentation with patches
are not the idea in many times, so the region segmen-
tation based method is studied to solve this. Consid-
ering the hazy image usually captured in city and in-
clude many small details and edge. So the normal
edge detection or region segmentation method hard to
get idea segment ion result. So here the watershed
segmentation which introduced by Beucher and Lan-
tujoul (Beucher and Lantujoul, 1979) is used. How-
ever, usually this method only used for gray image
and can’t used for color image directly. So here we
use the CBH model to convert the RGB image to
get the rang image which can reflect the color and
region information more clear than normal gray im-
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