Ghost free image using blur and noise estimation

International Journal of Computer Graphics & Animation (IJCGA) Vol.4, No.3, July 2014
DOI : 10.5121/ijcga.2014.4301 1
GHOST-FREE IMAGE USING BLUR AND NOISE
ESTIMATION
Ji-Hye Kim1
, Rae-Hong Park1
,and SoonKeun Chang2
1
Department of Electronic Engineering, School of Engineering, Sogang University
35 Baekbeom-ro (Sinsu-dong), Mapo-gu, Seoul 121-742, Korea
2
Samsung Electronics Co., Ltd., Suwon, Gyeonggi-do 443-742, Korea
ABSTRACT
This paper presents an efficient image enhancement method by fusion of two different exposure images in
low-light condition. We use two degraded images with different exposures: one is a long-exposure image
that preserves the brightness but contains blur and the other is a short-exposure image that contains a lot of
noise but preserves object boundaries. The weight map used for image fusion without artifacts of blur and
noise is computed using blur and noise estimation. To get a blur map, edges in a long-exposure image are
detected at multiple scales and the amount of blur is estimated at detected edges. Also, we can get a noise
map by noise estimation using a denoised short-exposure image. Ghost effect between two successive
images is avoided according to the moving object map that is generated by a sigmoid comparison function
based on the ratio of two input images. We can get result images by fusion of two degraded images using
the weight maps. The proposed method can be extended to high dynamic range imaging without using
information of a camera response function or generating a radiance map. Experimental results with various
sets of images show the effectiveness of the proposed method in enhancing details and removing ghost
artifacts.
KEYWORDS
Image fusion, Blur estimation, Noise estimation, Motion detection, High dynamic range image, Exposure
1. INTRODUCTION
Digital camera users want to take good pictures without constraints of time and space, however,
hand-held camera users are still suffering from many kinds of distortions such as blur and noise
artifacts. Especially, images captured in low-light condition have dark regions, thus we have a
difficult in figuring out what appears in them. To overcome the lack of lightness, a user can take
an image with high International Organization for Standardization (ISO) setting, however, the
image will contain lots of noise. Another method is to control the exposure time, however, blur
degrades the image quality by camera shaking during taking a picture.
If a user takes pictures, then light comes into the camera through the lens. During sensing using
image sensors such as charge-coupled device (CCD) or complementary metal-oxide
semiconductor (CMOS), the amount of light determines the quality of an image, which is
specified according to the shutter speed and the aperture [1].
In this paper, we use multiple images that are taken with different exposures to reduce the
distortion in dim-light condition. During taking photos, the amount of light is a very important
factor that determines the quality of photos, in which the amount of light is controlled, for
example, according to the shutter speed. With long-exposure time, we get a blurry image by

2
camera shaking, however, brightness of an image is preserved. On the other hand, with short-
exposure time, we get a dark and noisy image according to sensor characteristics or ISO setting,
however, it is free from blurring. To get a crisp and clear image with adequate brightness and
clear boundaries, we propose a fusion method of multi-exposure images that are degraded by blur
and noise.
The rest of the paper is organized as follows. In Section 2, related image fusion methods are
described. In Section 3, we propose a ghost-free image fusion method that uses blur and noise
estimation. Experimental results and comparison of the proposed algorithm with previous work
are shown in Section 4. Finally, conclusions are given in Section 5.
2. PREVIOUS WORK
Various image enhancement methods in low-light condition using different exposure images have
been proposed. First, a single image is used to produce an acceptable image in low light. For
reducing noise in a short-exposure image, total variation [2] is used as a regularization term in
denoising, which is an ill-posed problem. Another denoising methods use a multi-resolution
bilateral filter [3] and a motion-adaptive spatio-temporal filter [4]. However, these methods are
not acceptable, because they do not have enough brightness and color information. Also for
removing motion blur in a long-exposure image, many studies have been done [5]. First, they
estimate the point spread function (PSF) and perform deconvolution to reconstruct the image [6-
8]. Fergus et al.’s method [6] uses a maximum a priori (MAP) method and Shan et al.’s method
[7] uses an ensemble learning method to get a clear output image. Yuan et al.’s method [8] uses
two input images: long- and short-exposure images. It is good to reduce the ringing artifacts,
which is one of the difficult problems in deblurring. However, the deblurring methods that consist
of estimation of the PSF and deconvolution method require lots of iterations and thus have a
drawback of heavy computation.
Second, fusion methods of multi-exposure images have been proposed to obtain the acceptable
output image in dim light and they reduce the computation time with simple processing. These
fusion methods are also used in high dynamic range (HDR) because they give better result
without any information about the camera response function (CRF) and radiance map [9-13].
Raman and Chaudhuri [9] proposed a weighted sum of intensity differences between input images
and bilateral filtered results. This fusion method of multi-exposure images shows good
performance in preserving details and weak edges, however, noise in the short-exposure image is
emphasized in the output image. Zhang and Cham [10] used gradient direction and magnitude as
weights. Also, Martens et al. [11] proposed a weighted sum method using three quality
measurements (contrast, saturation, and well-exposedness). Especially, Tico and Pulli [12] and
Tico et al. [13] proposed fusion methods of two different exposure images: long- and short-
exposure images. These methods perform fusion of luminance in the wavelet domain and then
chrominance fusion is followed based on luminance fusion. These methods contain the weight
that considers noise, thus they give better result in view of noise reduction. However, they do not
reduce blurred edges in a long-exposure image, thus the fused image still suffers from blurring
artifacts.
2.1. Bilateral filtering based compositing method
Raman and Chaudhuri’s method [9] combines multi-exposure images with weights from bilateral
filtering [14]. The bilateral filter is a non-linear filter which smoothes flat regions while
preserving edge regions. It uses two Gaussian weights: one is a range weight considering the

3
intensity difference between neighboring pixels and the other is a domain weight considering the
spatial distance. Weak edges and details can be detected by the difference between the bilateral
filtered image and the original image. In their method [9], the difference with the bilateral filtered
image is used as a weight to preserve both details and weak edges. Let ),( yxIk
represent k th
input
image and ),( yxI BS
k
denote a bilateral filtered image, then the weight of k th
image at ),( yx is
describe as
 


 K
k
BS
kk
BS
kk
k
yxIyxIC
yxIyxIC
yxW
1
),(),(
),(),(
),(
(1)
where C is a constant and K is the number of input images. The total sum of weights ),( yxWk
is
equal to one. The final output image using (1), ),,( yxIO
is described as
.),(),(),(
1


K
k
kkO yxIyxWyxI (2)
An image with lots of details has a large weight value. The compositing method based bilateral
filter [9] preserves edges well. This method is easy to implement, but it is difficult to separate
signal and noise when an input image is noisy. Also more consideration on ghost artifacts is
required.
2.2. Exposure fusion
Exposure fusion [11] can obtain HDR image using several input images of low dynamic range
without generating a radiance map or information about camera setting. Quality measurements
from each image are used to compute weights for image fusion. Quality measurements consist of
three components: contrast, saturation, and well-exposedness. First, weight for contrast
measurement has a high value in edge and texture regions that are detected by a Laplacian filter.
Among the input images, there are images that include saturation region. To avoid artifacts from
saturation, weight for the saturation is detected by the standard deviation in the RGB color space.
At last, weight for well-exposedness is used by the value how close the normalized intensity of
the input image is to 0.5. With three quality measurements, the weighted sum is used for fusion.
In fusion, input images, which are taken with different exposure times, give some artifacts like
seams. To remove them, a pyramid decomposition method [15] is used, in which Laplacian
pyramid is used for input images whereas Gaussian pyramid is used for weights. Therefore,
exposure fusion suffers from ghost artifacts because this method does not consider motion
between input images. Also, it is not appropriate for input images that contain lots of noise, thus
result of exposure fusion is degraded by noise that is contained in input images.
2.3. Image fusion
The goal of image fusion [12] is to get a proper result image by fusion of blurred and noisy
images that are taken under low-light condition. First, image alignment is performed to remove
the misaligned region between two images because of the finite time interval during image
acquisition. Next, photometric calibration is performed to compensate for the brightness change
between two input images. For photometric calibration, a brightness transfer function, which is
also called compagram, is estimated using a joint histogram function between two input images.

4
Using this function, a short-exposure image is compensated in view of a long-exposure image.
Then, two differently exposed images that are aligned and compensated with compagram [16] are
fused with different weights in luminance and chrominance channels. In the CIE L*a*b* space,
fusion of luminance channel is performed using the difference of long- and short-exposure images
in the wavelet transform domain. The difference )(kD is described as
)()()( kGkGkD SL  (3)
where k represents kth
coefficient, GL denotes a long-exposure image, and GS signifies a short-
exposure image in the wavelet domain. The result wavelet coefficient of luminance fusion )(ˆ kF
is described as
)()()()(ˆ kDkWkGkF S  (4)
where W is a weight. The weight is calculated as
])([)()(
22
kDEkkW  (5)
where ])([
2
kDE represents expectation of the squared difference )(kD and 2
 signifies the
variance. This weight emphasizes the edge region of the short-exposure image and flat regions of
the long-exposure image. On the other hand, weight for chrominance fusion is calculated with
luminance value (0~255) from luminance fusion. The weight of the short-exposure image
),,( yxIS which is the brightness-compensated image, is described as
6
255
)( 






L
LWS
(6)
and the weight of the aligned long-exposure image ),(
~
yxI L is expressed as
).(1)( LWLW SL  (7)
With an image fusion method [12], a user can get a blur- and noise-free image in low light
without PSF estimation. However, blur of a long-exposure image still remains and affects the
quality of the fused image. To reduce blur and ghost artifacts, a motion-blur-free exposure fusion
method [13] was proposed.
Figure 1 shows performance comparison of existing methods described above. Figure 1(a) shows
input images with different exposures, which were used in [11]. Figure 1(b) shows a result image
obtained by a bilateral filter based method [9] and Figure 1(c) shows a result image by the
exposure fusion method [11].

5
Figure 1. Comparison of existing methods. (a) Multi-exposure input images [11], (b) Bilateral filtering
based compositing method [9], (c) Exposure fusion method [11].
3. PROPOSED IMAGE FUSION METHOD
The proposed method uses input images with different exposure images obtained in low- light
condition. The characteristics of each exposure image are shown in Table 1. A long-exposure
image is obtained with enough brightness and proper color, however distorted by blur artifacts.
Whereas, a short-exposure image is very dark and contains lots of noise, with edges preserved.
By the pixel-wise fusion method with these two images, blur and noise artifacts in input images
degrade the fused image. To reduce degradation in the output image, pixel-wise weights that
reflect the characteristics at pixels of input images are used in fusion. As mentioned in Section 2,
existing methods [9-11] use multi-exposure images that do not contain lots of blur and noise, so
they are not appropriate for low-light condition. If the same weights are used for degraded input
images, the fused image suffers from blur and noise. Therefore, with long- and short-exposure
images, weights that reflect the characteristics of input images are to be used.
Table 1. Characteristics of images with different exposures.
Exposure time Artifacts Brightness Color Detail
Long Blur Enough Preserved Blurred
Short Noise Lack Loss Preserved

6
3.1. Pre-processing
In this paper, we use two different exposure images that are taken successively. Small motion or
camera shaking during time interval can produce misaligned regions between two images, which
are caused by the global motion. Therefore, global registration is required for compensation of the
global motion between two input images. In this paper, to estimate a single motion model and to
compensate for global motion, the gradient method [17] is used. For fast computation, a fast
gradient motion estimation method [18] is used. With the parametric coordinate transformation,
two images can be represented as
 p,, )1()1()2(
iii yxfx 
 p,, )1()1()2(
iii yxgy 
(8)
where  )1()1(
, ii yx and  )2()2(
, ii yx are corresponding pixel positions of ),( yxIL and ),( yxIS images,
respectively, with ),( yxIL
representing a long-exposure image and ),( yxIS
denoting a short-
exposure image. f and g are defining functions. The global motion method [12] estimates the
global motion parameter vector p that minimizes the difference between pixel values of two
images. The global motion parameter vector is calculated as
    


Syx
iiSiiL
ii
yxIyxI
),(
2)2()2()1()1(
)1()1(
,,minarg*
p
p (9)
where i represents position index of pixel. The relation between ),( yxIL and ),( yxIS can be
described as
    
    
j
p j
iiiiiiS
iiiiiiSiiL
p
p
yxyyxxI
yxyyxxIyxI
j 0
)1()1()2()1()1()2(
)1()1()2()1()1()2()1()1(
,,,,,
,,0,,,0),(


 



p
p
pp
(10)
using the value of pixel-wise first-order Taylor expansion at 0p  . (10) is a linearization of
Gauss-Newton nonlinear minimization [19]. Let H be the partial differential equation of ,p with
its elements jiH , expressed, by the derivative chain rule, as
 
       .
,,,,,,
,
)1()1()2(
)2(
)2()2()1()1()2(
)2(
)2()2(
)2()2(
,
i
iii
i
iiS
i
iii
i
iiS
i
iiS
ji
p
yxy
y
yxI
p
yxx
x
yxI
p
yxI
H













pp
(11)
Then, motion parameter vector p can be described using (10) and (11) as
  tIHHHp T1T 

(12)
where tI is described as
     .,...,1
T
nttt III (13)
tI is used as error vector and  itI is represented as
        .,,,,,, )1()1()2()1()1()2()1()1(
iiiiiiSiiLit yxyyxxIyxII pp (14)

7
As a result, aligned ),(
~
yxIL can be calculated using .p Moreover, the fast gradient method [18]
uses multi-scale structure for better performance and the pixel subset selection [20] for speed. In
the pixel subset selection method, motion is estimated by dividing the region into several sub-
regions and by using the gradient value which is upper 10% in each region.
After alignment, the short-exposure image should be corrected to compensate for low light
according to the long-exposure image. As a histogram matching method for color correction of
the short-exposure image, a cumulative histogram [21] is used in this paper. The histogram of the
long-exposure image is calculated as







1
0
1
0
)),(
~
,(
1
)(
H
x
W
y
LL yxIv
HW
vh 
(15)
where W is width and H is depth of an image. The function  is described as


 

otherwise,0
if,1
),(
ba
ba
(16)
where v is pixel intensity between 0 and 255. LI
~
is an aligned long-exposure image. The
mapping function M between the short-exposure image SI and the pixel value to be
compensated is used in calibration for color correction. The cumulative histogram of LC can be
calculated as
.)()(
0



v
i
LL ihvC
(17)
Also, the cumulative histogram of ,SI )(vCS is calculated in the same method. With the
cumulative histogram, the mapping function is described as
).1()()(with)(  uCuCuCuvM LSL
(18)
If the mapping function in (18) is applied to the image, luminance value of SI smaller than
threshold is clipped and mapped into the first active bin. The result image is unnatural, and the
first and last bins in lower boundary and upper boundary, respectively, should be modified. The
highest value of the reference image is applied to the clipped interval value. Lower interval is (0,
…, M(0)) and upper interval is (M(255), …, 255). Using each interval value, the center of mass is
used by the mapping function. The center of mass value for lower interval ls and that for upper
interval us are described as






)0(
0
)0(
0
)(
)(
M
i
L
M
i
L
l
ih
ihi
s
(19)
.
)(
)(
255
)255(
255
)255(






Mi
L
Mi
L
u
ih
ihi
s
(20)

8
With (19) and (20), the mapping function can be described as
lsM )0( and .)255( usM  (21)
Using the mapping function ,M the color-corrected short-exposure image, ),( yxIS
 can be
calculated as
)).,((),( yxIMyxI SS  (22)
3.2. Proposed image fusion method
In this paper, the proposed method uses a weighted sum based fusion method and weights are
obtained by estimating blurriness and noisiness of input images. Aligned long-exposure image LI
~
and color-corrected short-exposure image SI are used as input images. LI
~
contains blur artifacts
around edges whereas SI contains lots of noise which is amplified after color correction. These
artifacts from two input images affect the final fused image. Also, if there is motion during the
time taking two input images, the fused image contains ghost artifacts. Therefore, proper weights
are required to effectively reduce artifacts in input images and motion detection between two
input images is needed to reduce ghost artifacts. To explain the proposed fusion method, first,
image fusion is reviewed and then blur and noise estimation methods are described. At last, a
motion detection method used in the proposed method is presented.
The final output of the proposed fusion method is obtained using two weights: blur weights WL
and noise weight WS. WL is applied to the long-exposure image whereas WS to the short-exposure
image. However, if motion occurs, the fused image is degraded with ghost artifacts. Therefore,
the motion map is used to remove the ghost artifact. The output image ),( yxIO is calculated as


 

otherwise,
1if,,
F
MDS
O
I
MI
I (23)
where MM is the binary motion map obtained from moving object detection. When the value of
the motion map is one, the denoised image is the output image without fusing processing,
otherwise, the fused image FI is used. When motion occurs, fusion processing of images
degrades the output image, thus fusing is performed at pixels with no motion. The fused image,
OI is computed as
.otherwise),,(
~
),(),(),(
),(and),(
1),(
1),(
),,(
~
),(),(),(
),,(
~
),,(
),(
,
,














yxIyxWyxIyxW
TyxBTyxN
yxS
yxM
yxIyxWyxIyxW
yxI
yxI
yxI
LLDSS
BNLLSS
S
DS
O (24)
where the subscript L represents a long-exposure image and the subscript S denotes a short-
exposure image. ),( yxIS
 is the color-corrected short-exposure image and ),(, yxI DS
 is the
denoised short-exposure image. Also, ),(
~
yxIL
is the aligned long-exposure image. B is blur
measurement and N is noise measurement. TB and TN are threshold values for blur and noise
estimation, respectively. In experiments, TB and TN are set to 0.1 and 0.2, respectively. ),( yxMM
is
the binary motion map to reduce the ghost artifacts between two images. If motion occurs, the
value of MM is 1, otherwise, 0. With the motion map, if motion occurs, result of image fusion uses
only ),,(, yxI DS which is the denoised image with the existing denoising method [4]. When motion
does not occur, the weighted sum of long- and short-exposure images is used. Note that they
smooth not only noise but also high-frequency component, thus details are not preserved. To

9
preserve details, SI rather than DSI ,
 is used in fusion process, when blur and noise estimates are
both smaller than threshold values. If either blur or noise estimate is larger than threshold value,
SI produces a fused image with lots of noise remained. ),( yxWS
has a smaller value in noisy
region of SI to suppress the noise in the result image. Whereas ),( yxWL
has a smaller value in
the blur region of ).,(
~
yxIL
Each weight is determined depending on the amount of blur and noise in the images and has the
value between 0 and 1. The normalized blur measurement is computed as
minmax
min),(
),(
BB
ByxB
yxB



(25)
where minB represents the minimum value of ),( yxB and maxB denotes the maximum value.
Also the normalized noise measurement is expressed as
minmax
min),(
),(
NN
NyxN
yxN



(26)
where minN represents the minimum value of ),( yxN and maxN denotes the maximum value.
With each normalized measurement of blur and noise, we can get the weight for image fusion.
First of all, the weight of the long-exposure image ),( yxWL
is calculated as
),(),(
),(
),(
yxByxN
yxN
yxWL




(27)
where ),( yxN denotes the noise measurement whereas ),( yxB represents the blur measurement.
Also,  is used to scale the parameter value. Then, the weight for the short-exposure image is
calculated as
.
),(),(
),(
),(
yxByxN
yxB
yxWS



(28)
Figure 2 shows the block diagram of the proposed image fusion method. There are four steps for
fusing two degraded images. The first step is global registration to compensate for global motion
that affects all the pixels in the whole image with a single motion model applied to a long-
exposure image. Then, color correction is performed to adjust brightness of the short-exposure
image. Compensated input images by two pre-processing steps are fused using appropriate
weights. These weights are based on two measurements: blur and noise estimation. Blur and noise
measurements are computed by estimating the amount of blurriness and noisiness from the long-
exposure image and short-exposure image, respectively. Also the motion map is used to remove
ghost artifacts. Finally, computing the weighted sum of the long-exposure image, short-exposure
image, and denoised short-exposure image, we can get the output image with acceptable
brightness and details, with blur and noise artifacts significantly reduced.
The long-exposure image contains blur and produces blur artifacts in the fused image, especially
around edges. To get the clear fused image, we estimate the amount of blur and apply this
quantity to compute weights used for fusing a set of input images. A small blur weight is applied
to ),(
~
yxIL
when pixel is degraded by blur. For the same reason, a large weight is applied to SI ,
therefore, pixel with blur is reduced in the result image.
Generally, blur artifacts occur around the boundary region of an object rather than in flat region
[22]. Therefore, existing methods detect edges first, and then estimate the amount of blurriness at

10
detected edges [22,23]. In the long-exposure image, it is difficult to detect accurately edges by
existing edge detection methods, in which edges are detected at wrong locations or represented as
discontinuous line. Elder and Zucker [22] proposed an edge detection method with blurred
images. Then, edges are detected by the reliability of the filter response that is obtained using
threshold at each scale. For selecting the threshold value, prior knowledge such as noise
characteristics of sensor is needed. Threshold values, c1 and c2 in the first- and second-derivative
Gaussian filters, respectively, are calculated as
2
1
11
22
ln2
)(



pns
c


(29)
3
2
1
22
34
)(2
)(


 pn erfs
c


(30)
where sn represents the noise level of sensor and p denotes the false positive tolerance.
The minimum reliable scale is decided when the filter response at each pixel is larger than
the threshold value. Elder and Zucker’s method [22] detects edges where gradient has
nonzero value at selected scale and the value of the second-derivative satisfies the zero
crossing condition.
Figure 2. Block diagram of the proposed image fusion method.

11
In detected edges, the amount of blurriness is estimated using the difference of extreme values of
plus and minus of the second-derivative. It can be described as
  2
2
2
2  dBM (31)
where d is calculated to minimize the least square fitting error at edges. The blur estimation
methods mentioned previously need post-processing in computing the weights in our fusion
method because estimated measure of blurriness is discontinuous. For post-processing, we use
Bae and Durand’s method [24], in which edges are detected and the amount of blur is estimated.
Then, they used two steps. The first step is refinement, in which a cross bilateral filter [25] is used
to remove outliers from estimated blur measurement. Then, propagation [26] is performed for
extending blur measurement from edges to the flat region. This blur measurement is used to
compute the blur weight in image fusion.
Under low-light condition, an image is degraded mostly by noise. Especially, the short- exposure
image after color correction is degraded by magnified noise, which affects the quality of the fused
image. In low-light condition, there are many kinds of noises such as photon noise and dark
current noise. These noises can be modeled by Gaussian or Poisson distribution. In this paper, we
classify noise into two types: Poisson counting noise (PCN) and false color noise (FCN) [5]. We
first detect pixels that are distorted by noise and then estimate the amount of noise at detected
locations. For detection and estimation of noise, we use a noise adaptive spatio temporal filter
proposed by Lee et al. [5]. Also, two types of noises are decided as PCN and FCN according to
motion that is detected by the sum of absolute differences (SAD). This method is for noise
removal for video in low-light condition. Our proposed fusion method uses two images instead of
video that consists of a sequence of temporal frames. Even though input type of the proposed
method is different from that of Lee et al.’s method, noise characteristics in low-light condition
are the same, so we can apply the noise detection algorithm to the compensated short-exposure
image.
According to [5], two types of noises are detected. First, using local statistics PCN is detected in
the short-exposure image that contains lots of low-light noise. Then, PCN noise measurement in
,SI ),( yxNP is calculated as
),(),(),( yxSyxIyxN NSP  (32)
where ),( yxSN represents local statistics. It is described as
  ),(,),(),(median),( srsrIyxIyxS SSN
(33)
where ),( yx is the coordinate of the center pixel and ),( sr represent the coordinates of
neighboring pixels in widow .
Meanwhile, FCN noise is independent of neighboring pixels and it can be detected using statistics
between two sequential images. The local statistics of the short-exposure image is calculated as
  ),(),(),(),( 22
yxyxIyxIyxS SSSS  (34)
where ),( yxIS represents the mean value and ),(2
yxS denotes the variance of the long-
exposure image. With each local statistics, noise measurement of FCN is calculated as

12







otherwise.,),(),(
~
),(),(,),(),(
),(
yxSyxI
yxSyxSyxSyxI
yxN
LL
SLSS
F
(35)
With ),( yxNP
and ),,( yxNF measurement in low light, N is computed as
otherwise),,(
0),(),,(
),(


 

yxN
yxMyxN
yxN
F
P
(36)
where ),( yxM is the motion map which is calculated in terms of the SAD. Noise measurement N
is used as weight in image fusion.
The proposed method uses input images taken consecutively. Motion during time interval
between two successive images reduces the quality of the fused image. Global motion is reduced
by registration processing whereas local motion still produces artifacts in the fused image. There
are many approaches to reducing ghost artifacts [27-28]. In this paper, to reduce ghost artifacts,
the binary motion map is generated by detecting motion between two input images and by
applying it to the fusion process.
To detect moving objects, the proposed method uses Markowski’s method [27], which is a
motion detection method for HDR. This method consists of three steps. First, the initial motion
map is described as
)),(),,(
~
(),( yxIyxIFyxM SLM
 (37)
where F is a de-ghosting comparison function. The function F is computed as
  
























 



bgrc
cL
cS
cS
cL
SL
yxI
yxI
yxI
yxI
yxIyxIF
,,
2035.1
),(
~
),(
,
),(
),(
~
maxexp1
1
),(),,(
~ (38)
where c represents three color channels in the RGB color space. The comparison function is a
sigmoid function that compares two images. Then, the normalized motion map is computed as
n
M
MM
MyxM
yxM 








minmax
min),(
),(
(39)
where Mmin (Mmax) represents minimum (maximum) value of the initial motion map. Artifacts
such as seams near the detected motion region by the normalized ),( yxM can occur after images
with different exposures are fused. For smoothing and reducing artifacts, three morphology
operations are sequentially used: dilation, erosion, and conversion [27], after which a more
accurate motion map is obtained.
Figure 3(a) shows blur measurement, Figure 3(b) shows noise measurement, and Figure 3(c)
shows motion map. With blur and noise measurements, the weight of the short-exposure image,
),( yxWS is illustrated in Figure 3(d) and the weight of the long-exposure image, ),( yxWL is
shown in Figure 3(e).

13
(a) (b)
(c)
(d)
(e)
Figure 3. Results of each step of the proposed image fusion method. (a) Blur
measurement  ),( yxB , (b) Noise measurement  ),( yxN , (c) Motion map  ),( yxM , (d)
Weight of the short-exposure image )),(( yxWS
, (e) Weight of the long-exposure image
)),(( yxWL
.
4. EXPERIMENTAL RESULTS AND DISCUSSIONS
Figure 4 shows two test image sets used in our experiments, which are used in the existing image
fusion method [12] and their size is 1024×1024. Figure 4(a) is a short-exposure image in low-
light condition, which is degraded with lots of noise in flat region, however, preserves details. In
contrast, Figure 4(b) is a long-exposure image which is degraded with blur artifacts in edges and
saturated in window of the right side of an image. Also, in bottom left of Figure 4(b), there are

14
ghost artifacts because of motion of people. However, it has proper color with enough light.
Figure 4(c) is a short-exposure image with noise artifacts in flat region whereas Figure 4(d) is a
long-exposure image with blurred edges. Figure 4(c) has sharp edges and Figure 4(d) has proper
color with enough light.
In experiments, two methods are used to compare the performance of the proposed method. The
exposure fusion method [11] explained in Section 2.1 and the image fusion method [12] described
in Section 2.3 are used. Figures 5(a)-5(d) are result images of image enhancement methods in
low-light condition. Figure 5(a) shows a color-corrected result of the short-exposure image based
on color of the long-exposure image. The color-corrected result image in low light is noisy
because noise is also boosted along with an image signal. Figure 5(b) is a result of the exposure
fusion method [11] that uses multi-exposure images, in which blur and noise artifacts of input
images affect the result image. Figure 5(c) is a result of the image fusion method [12], which uses
two images: long- and short-exposure images. The image fusion method [12] computes weights
Figure 4. Test image set with different exposures. (a), (c) Short-exposure images, (b),
(d) Long-exposure images.

15
according to the amount of noise to give small weight in noisy region. However, blur artifacts
from the long-exposure image still remain. Result of the proposed method is shown in Figure 5(d)
and blur artifacts near edges and noise in flat region are reduced. Also, the proposed method
reduces ghost artifacts. Figure 6 shows more details on result images.
Figure 6 shows enlarged subimages enclosed by the red box in Figure 5. The subimage enclosed
by the red rectangle shows preserved details in the image. The subimage enclosed by the blue
rectangle in Figure 6 shows enhanced performance of removing ghost artifacts caused by a
moving object or people in the image. Figure 6(a) shows result images of color correction of the
short-exposure image. The subimage enclosed by the red rectangle in Figure 6(a) shows a sharp
image that is degraded with lots of noise because noise boosting of the short-exposure image

16
.
Figure 5. Result images with Figures 4(a) and 4(b). (a) Color-corrected short-exposure
image, (b) Result image of the exposure fusion method [11], (c) Result image of the
image fusion method [12], (d) Result image of the proposed method.
Figure 6. Enlarged images of Figures 5(a)-(d). (a) Color-corrected short-exposure image,
(b) Result image of the exposure fusion method [11], (c) Result image of the image
fusion method [12], (d) Result image of the proposed method.

17
appears with a gain in terms of color correction. Figure 6(b) shows the result of the exposure
fusion method [11]. The subimage enclosed by the blue rectangle shows ghost artifacts because
this method uses the weighted sum of multi-exposure images without considering ghost artifacts.
The subimage enclosed by the red rectangle shows degraded details. It is because blur and noise
artifacts in input images affect the result image directly. Figure 6(c) shows the result of the image
fusion method [12] and ghost artifacts are almost removed in the subimage enclosed by the blue
rectangle, but still blur artifacts in edges and noise in flat and low-light regions are shown in the
subimage enclosed by the blue rectangle. Also, the subimage enclosed by the red rectangle shows
blurred edges. Figure 6(d) shows the result of the proposed method. Ghost artifacts are removed
in the subimage enclosed by the blue rectangle and details of people are preserved. Even though
noise is still shown in the subimage enclosed by the blue rectangle, the proposed method shows
better performance in view of details in edges and noise in flat region.
Figure 7. Results images with Figures 4(c) and 4(d). (a) Color-corrected short-exposure
image, (b) Result image of the exposure fusion method [11], (c) Result image of the image
fusion method [12], (d) Result image of the proposed method.
Figure 7 shows results of three enhancement methods in low-light condition and input images are
from Figures 4(c) and 4(d). Figure 7(a) shows a color-corrected image which uses only a short-
exposure image with details preserved, however, the image is distorted by the noise of low-light
condition. Figure 7(b) shows better result of the exposure fusion method [11] than other method,
with blur artifacts in low-light condition. Figure 7(c) shows the result of the image fusion method
[12]. The image fusion method gives denoised result, however, blur artifacts are still remain.
Figure 7(d) shows the result of the proposed method with the reduced noise and details preserved.
Figure 8 shows enlarged images of Figure 7. Figure 8(a) shows preserved detail, but distorted by
lots of noise. Especially, flat region in the subimage enclosed by the red rectangle is distorted

18
with lots of noise. Figure 8(a) shows the result of the exposure fusion method [11]. In Figure 8(a),
details are preserved with an image distorted in the subimages enclosed by the red and blue
rectangles and low-light noise. In Figure 8(b), the subimages enclosed by the red and blue
rectangles show blur artifacts in the exposure fusion method. In Figure 8(c), the subimage
enclosed by the red rectangle shows blur artifacts and the subimage enclosed by the blue
rectangle shows denoised image in flat region. The result image by the proposed method is shown
in Figure 8(d). In Figure 8(d), the subimage enclosed by the red rectangle shows preserved edges
and the subimage enclosed by the blue rectangle also shows denoised clear result and preserved
edges. Flat region in the subimage enclosed by the blue rectangle shows especially denoised and
preserved edges well.
5. CONCLUSIONS
In this paper, we propose an image fusion method using two differently exposed images in low-
light condition. For fusion based on the weighted sum approach, weights are computed by
estimating the amount of blurriness and noisiness. Blur is measured by detecting edges and
estimating the amount of blurriness at detected edges in the compensated long-exposure image.
Then, outliers of blur measurement are removed by a cross bilateral filter. Meanwhile, noise is
estimated in the color-corrected short-exposure image according to the local statistics using the
adaptive noise method. Next, the motion map is applied to fusion for removing ghost artifacts.
Figure 8. Enlarged image of Figures 7(a)-(d). (a) Color-corrected short-exposure
image, (b) Result image of the exposure fusion method [11], (c) Result image of the
image fusion method [12], (d) Result image of the proposed method.

19
With weights and motion map, the final fused image is computed by the weighted sum of short-
and long-exposure images and denoised short-exposure image. A multi-resolution bilateral filter
[3] is used for denoising a short-exposure image. The denoised image is clear in flat region,
however, with details lost. To preserve details in the fused image, a short-exposure image is used
in region where both amounts of blur and noise are small, i.e., where the blur and noise estimates
are smaller than the threshold values.
We simulate the exposure fusion and image fusion method for experimental comparison of the
proposed method. Experimental results show that the proposed image fusion method using two
different exposure images shows better performance for removing blur and noise artifacts than the
existing methods. For future work, the proposed method is to be extended to deal with multiple
exposure images as in HDR imaging.
ACKNOWLEDGEMENTS
This work was supported in part by Samsung Electronics, Co., Ltd.
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Authors
Ji-Hye Kim received the B.S. degree in electronic engineering from Myong-Ji University in 2005 and M.S.
degree in electronic engineering from Sogang University in 2011. Her current research interests are image
processing and image enhancement. Currently she works at Samsung Electronics Co., Ltd., Korea.
Rae-Hong Park received the B.S. and M.S. degrees in electronics engineering from Seoul National
University, Seoul, Korea, in 1976 and 1979, respectively, and the M.S. and Ph.D. degrees in electrical
engineering from Stanford University, Stanford, CA, in 1981 and 1984, respectively. In 1984, he joined the
faculty of the Department of Electronic Engineering, School of Engineering, Sogang University, Seoul,
Korea, where he is currently a Professor. In 1990, he spent his sabbatical year as a Visiting Associate
Professor with the Computer Vision Laboratory, Center for Automation Research, University of Maryland
at College Park. In 2001 and 2004, he spent sabbatical semesters at Digital Media Research and
Development Center (DTV image/video enhancement), Samsung Electronics Co., Ltd., Suwon, Korea. In
2012, he spent a sabbatical year in Digital Imaging Business (R&D Team) and Visual Display Business
(R&D Office), Samsung Electronics Co., Ltd., Suwon, Korea. His current research interests are video
communication, computer vision, and pattern recognition. He served as Editor for the Korea Institute of
Telematics and Electronics (KITE) Journal of Electronics Engineering from 1995 to 1996. Dr. Park was
the recipient of a 1990 Post-Doctoral Fellowship presented by the Korea Science and Engineering
Foundation (KOSEF), the 1987 Academic Award presented by the KITE, the 2000 Haedong Paper Award
presented by the Institute of Electronics Engineers of Korea (IEEK), the 1997 First Sogang Academic
Award, and the 1999 Professor Achievement Excellence Award presented by Sogang University. He is a
co-recipient of the Best Student Paper Awards of the IEEE Int. Symp. Multimedia (ISM 2006) and the
IEEE Int. Symp. Consumer Electronics (ISCE 2011).
SoonKeun Chang received his B.S. degree in astronomy and space science from KyungHee University,
Korea, in 2000 and M.S. degree in control engineering from Kanazawa University in 2003. He received a
Ph.D. degree in control engineering from Tokyo Institute of Technology (TITech) in 2007. Now he works
at Samsung Electronics Co., Ltd., Korea. His main research interests include computer vision and image
processing.

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