VISIBILITY RESTORATION FROM SINGLE IMAGE BASED

OPTICAL MODEL

Qieshi Zhang

†‡

and Sei-ichiro Kamata

†

Graduate School of Information, Production and Systems, Waseda University, Tokyo, Japan

‡

Japan Society for the Promotion of Science (JSPS) Research Fellow, Japan

Keywords:

Haze Removal, Single Image, Optical Model, Color Barycenter Hexagon (CBH) Model, Watershed.

Abstract:

In this paper, we propose a segmentation based method to estimate the haze-free image by the optical model. In

this work, we estimate the atmospheric light by color barycenter hexagon (CBH) model and use the watershed

to segment the image to calculate transmission map by dark pixels with single image. Firstly, non-color

region is segmented by CBH model and calculate the atmospheric light. Then, use the watershed with rang

component of CBH model to segment the color image into several sub-regions, and estimate the transmission

map. Finally, use the optical model with the parameters to restore the haze-free image. The experimental

results show that our method is more effective and able to get better results than other compared single image

based methods.

1 INTRODUCTION

Image taken in the outdoors scenes usually inﬂuenced

by many nature elements, such as, haze, smoke, fog,

rain, snow and other atmosphere factors. Among of

them, the atmosphere quality, haze is the most com-

mon problem in our daily life.So the haze removal

problem needs be studied and obtain the more clear

image for keeping the image quality in practical ap-

plication.

For solving this problem, one kinds of ap-

proach is multi-image which captured in same scene

with different haze level (Narasimhan and Nayar,

2000) (Narasimhan and Nayar, 2002) (Narasimhan

and Nayar, 2003). These methods are use the multi-

image to estimate the depth information. However,

if the condition difference is little or hard to obtain

the several images, the results will not accuracy. But,

in many practical conditions, it’s hardly to obtain the

multi-image in same scene, especially the real-time

application. So this condition limits the development

and the practical application. Considering this short

come, more and more researchers aim to do the re-

search in single image for solving this. However,

to obtain the depth information from single image is

very difﬁcult.

Short recently, some single image based haze

removal methods have been developed (Fattal,

2008) (Tan, 2008) (Kratz and Nishino, 2009) (He

et al., 2009). For single image, the depth information

can’t be calculated directly, so the estimation based

methods are used. To solve this, the main framework

is the optical model which widely be used. Fattal (Fat-

tal, 2008) uses the Independent Component Analysis

(ICA) to estimate the transmission map, but it hardly

to obtain ideal results in heavy hazy condition. Also,

if the ICA assumption not correctly enough, it will

get wrong result. Tan (Tan, 2008) calculates the max-

imization of local contrast to enhance the image, and

use Markov Random Field (MRF) for haze removing.

But this method didn’t consider the atmospheric light,

so usually it leads to over-enhanced of some regions,

specially the sky region. By analyzing many haze-

free images, He et al. (He et al., 2009)propose a dark

channel prior. The priors show that the haze-free im-

age is close to black, and for hazy image become to

bright. So its can be used to estimate the transmission

map and the atmospheric light. However, for local

bright or multi-light source it hard to obtain ideal re-

sults.

Considering the advantage and disadvantage of

existing single image based methods, this paper pro-

posed estimate the parameters by segmentation in

CBH component.

The remainder of this paper as follows: In Section

2, the optical model is be introduced at ﬁrst. Then,

atmospheric light and transmission estimation are de-

scribed. The compression and discussion of experi-

213

Zhang Q. and Kamata S..

VISIBILITY RESTORATION FROM SINGLE IMAGE BASED OPTICAL MODEL.

DOI: 10.5220/0003877902130216

In Proceedings of the International Conference on Computer Vision Theory and Applications (VISAPP-2012), pages 213-216

ISBN: 978-989-8565-03-7

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

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

−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.

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-

VISAPP 2012 - International Conference on Computer Vision Theory and Applications

214

(a) Hazy image (b) Non-color region (c) Dark pixel (d) Segmented image (e) Our result

Figure 1: Atmosphere light estimation

age. After this, use the watershed method to segment

the image to get several region [Fig. 1(d)]. If the

area of region lager than 200 pixels, segment it into

s = area/200 sub-regions equally, otherwise ignore

it. Then, calculate the local minimum of every re-

gion with min(R,G,B) to obtain the rough transmis-

sion map T

(x). For obtaining more accuracy trans-

mission, the soft matting (Levin et al., 2006) as He

described is used to optimal T

(x) to show more de-

tails transmission T(x).

2.3 Recovering the Haze-free Image

With the atmospheric veil transmission T(x) and the

atmosphere light A, the haze-fee image can be calcu-

lated by Eq. 2. Considering in sometimes, the value

of estimated T(x) is close to zero, direct use it may

let the recovered pixel become to inﬁnite. So use

the minimum transmission value T

to limit the lower

bound same as He’s method (He et al., 2009). Finally,

the recovered haze-free image I(x) can be calculated

by following equation:

I(x) =

Y(x) − A+ AT(x)

max[T(x),T

]

, (4)

here T

set as 0.1. After the recovering, for obtaining

more natural vision effect, the contract enhancement

method (Zhang and Kamata, 2012) is used.

3 EXPERIMENTAL AND

DISCUSSION

For comparing the results with other methods, some

widely compared images are tested. In the experi-

mental part, the previous works (Fattal, 2008) (Tan,

2008) (He et al., 2009) and histogram equalization

(HE) are compared.

In Figs. 2 and 3, two natural images are com-

pared with existing single image based methods. In

(a) Hazy image (b) HE

(e) He’s result (f) Our result

Figure 2: Result comparison 1.

VISIBILITY RESTORATION FROM SINGLE IMAGE BASED OPTICAL MODEL

215

(a) Hazy image (b) HE

(e) He’s result (f) Our result

Figure 3: Result comparison 2.

the 5 compared methods, HE makes the near region

become darker and the far region brighter, but the

haze removal effect is not good in far distance region.

The effect of Fattal’s methods (Fattal, 2008) is a little

weak, only the near region have good effect. Tan’s

method (Tan, 2008) is the worst, too many details and

the color information are missing because of the local

contrast enhancement lost the global constraint. So

the air region become to blue and the saturation of

buildings become too deep. He’s method (He et al.,

2009) can get good effect, but the air region is not nat-

ural than HE, and the long distance become to dark.

Compared with other methods, the proposed method

makes the whole image become to clear, keeps the

details and seems more natural.

4 CONCLUSIONS AND FUTURE

WORKS

In this paper, a segment ion and CBH model based at-

mospheric light and transmission estimation method

is proposed. The presented method use the color re-

gion segmentation to estimate transmission more ac-

curacy and can restore more details for vision.

However, how to segment the image to get more

accuracy transmission and without use the soft mat-

ting need be studied.

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