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Image demosaicking for Bayer-patterned CFA images using improved linear
interpolation
Conference Paper · April 2017
DOI: 10.1109/ICIST.2017.7926804
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Image Demosaicking for Bayer-patterned CFA
Images Using Improved Linear Interpolation
Dongyan Wang, Gang Yu, Xiao Zhou and Chengyou Wang*
School of Mechanical, Electrical and Information Engineering
Shandong University
Weihai 264209, China
{wdy, 201400800150}@mail.sdu.edu.cn, {zhouxiao, wangchengyou}@sdu.edu.cn
green light, the number of green pixels is twice as many as the
number of red or blue pixels. Such distribution makes it more
comfortable for human eyes. To get a full-color image, an
appropriate interpolation method called CFA interpolation is
adopted to recover the other two color components by neighbor
pixels at each point. The process of getting a full-color image
by CFA interpolation is also known as demosaicking [2].
Abstract—With the development of digital imaging technique,
the demosaicking algorithm becomes a hot spot in the field of
image processing. An efficient interpolation method with good
visual quality and less calculation amount is urgently needed. In
this paper, an improved linear interpolation for demosaicking of
Bayer-patterned color filter array (CFA) images is proposed.
Compared with bilinear interpolation, the proposed scheme gives
full consideration to brightness information and edge
information of the image. Since different color components need
to be interpolated, different size linear filters with different gain
parameters are designed. We correct the bilinear interpolation
by a correction value to estimate the unknown color.
Experimental results show that the improved scheme achieves
better performance than other two methods both in subjective
assessment and objective assessment. It incurs much fewer false
colors in high-frequency regions. The zipper effect is also
weakened to some extent. Besides, the improved scheme reduces
the computational complexity. Due to good real-time adaptability,
it is easily implemented in hardware.
Fig. 1. Color filter array (CFA).
Keywords—image demosaicking; image interpolation; Bayerpatterned color filter array (CFA); bilinear interpolation
R11 G12 R13 G14 R15 G16 R17 G18
G21 B22 G23 B24 G25 B26 G27 B28
I. INTRODUCTION
R31 G32 R33 G34 R35 G36 R37 G38
Recently, single charge coupled device (CCD) is widely
used as a sensor in most consumer digital products such as
digital camera, digital video camera, and mobile phone.
However, the image sensor itself doesn’t consider the colors
during the process of photoelectric conversion. Therefore, a
layer of color filter array (CFA) is covered on their surface to
get color information. This process is shown in Fig. 1, from
which we can see that there is only one of three primary colors
at each pixel.
G41 B42 G43 B44 G45 B46 G47 B48
R51 G52 R53 G54 R55 G56 R57 G58
G61 B62 G63 B64 G65 B66 G67 B68
R71 G72 R73 G74 R75 G76 R77 G78
G81 B82 G83 B84 G85 B86 G87 B88
Fig. 2. Bayer-patterned CFA image with size of 8×8.
In the past 20 years, the demosaicking algorithm has
always been a hot spot in the field of image processing.
Generally, the demosaicking algorithm is divided into two
categories [3]. One is that the full-color image is reconstructed
without considering the correlations among the three color
planes of color image. These demosaicking algorithms include
nearest neighbor interpolation, bilinear interpolation [4], cubic
convolution interpolation [5], etc. In this scheme, the
unavailable color components are interpolated by the same
color components around. Although this method is easy to
achieve and has good effect in smooth areas, it brings obvious
distortion in high frequency especially at the boundary. To
overcome the defects of the first method, another interpolation
algorithm has been proposed which takes the correlations
Generally, the CFA is arranged as checkerboard format.
According to different arrangement modes and different
proportion of color components, there are various structures in
CFA. The most widely used mode is Bayer mosaic pattern [1].
Fig. 2 shows the Bayer-patterned color filter array image with
size of 8×8. In this mode, the three primary colors are in
staggered arrangement. In other words, within each square of
four pixels, each pixel location records only one color
component. Since human visual system is more sensitive to
This work was supported by the 11th Student Research Training Program
(SRTP) and the 8th Undergraduate Research Apprentice Program (URAP) at
Shandong University (Weihai), China; and the Natural Science Foundation of
Shandong Province, China under Grant No. ZR2015PF004.
978-1-5090-5401-5/17/$31.00 ©2017 IEEE
464
among the three color planes into account. This method
combines image detail analysis and judgment, and achieves
better interpolation performance than the first method. The
second method includes the edge directed interpolation [6],
gradient based algorithm [7], and directional based method [8].
However, these methods are relatively complicated and far
from the requirements of the real-time system.
Experimental results and performance analysis are presented in
Section IV. Conclusions and future work are given finally in
Section V.
II. BILINEAR INTERPOLATION METHOD
Owing to the simple calculation, bilinear interpolation
algorithm is one of the widely used interpolation algorithms.
For the most common used Bayer color filter pattern referring
to Fig. 2, the bilinear interpolation algorithm can be achieved
by (1), which takes R, G at the position (2, 2) and B at the
position (2, 3) for example.
To get a clearer full-color image, many improved
demosaicking algorithms [9-14] have been proposed in recent
years. Malvar et al. [9] proposed a high-quality linear
interpolation for demosaicking of Bayer pattern color images.
In their scheme, at least nine or eleven neighbor pixels in linear
filters are used to reconstruct the missing color. The filter
coefficients of linear filters used in [9] are obtained by Wiener
approach. As we all know, the more neighbor pixels used in
interpolation, the better the reconstructed color image will be.
Therefore, the reconstructed image in [9] has a higher peak
signal-to-noise ratio (PSNR) than that of bilinear interpolation.
But at the same time, the computation is more complex and not
suitable for real-time system. Li et al. [10] proposed a color
difference space demosaicking algorithm based on all phase
DCT/IDCT filters. All phase diamond halfband IDCT filter is
used to reconstruct the green image, and all phase extended
DCT interpolation filter is used to reconstruct the R-G and B-G
images. Experimental results show that it can preserve more
image edge details and has higher computational efficiency
than other adaptive methods. To reduce computational
complexity and improve its real-time property, Luo et al. [11]
proposed an improved demosaicking method based on [9].
Compared with Malvar’s method, it reduces the computational
complexity. However, the PSNR of the interpolation image is
much lower than that of image in [9]. In [12], Chen and Chang
proposed a demosaicking algorithm based on edge property for
color filter arrays. In their scheme, an edge detecting method is
used to generate accurate weights for image interpolation.
Although this method can reduce some color artifacts, the
zipper effects are still remarkable. Shi et al. [13] proposed a
region-adaptive demosaicking algorithm. To improve the
effectiveness of the interpolation algorithm, it firstly divides
the input image into two kinds of regions and then adopts
different interpolation methods for each type. The proposed
interpolation method makes full use of bilinear’s fast execution
speeds in smooth region. It directly extracts and recovers edge
information with weighted values of multidirectional
components in edge regions. Kiku et al. [14] proposed residual
interpolation (RI) as an alternative to color difference
interpolation, which is a widely accepted technique for color
image demosaicking. It performs the interpolation in a residual
domain, where the residuals are differences between observed
and tentatively estimated pixel values. Experimental results
show that it can reduce color artifacts efficiently.
G22 = (G12 + G21 + G23 + G32 ) / 4,
R22 = ( R11 + R13 + R31 + R33 ) / 4,
(1)
B23 = ( B22 + B24 ) / 2.
From (1), we can see that the interpolated value is
computed by the average of the nearest neighbor values with
the same color. The same conclusion can be drawn from Fig. 3,
which are the linear filters used in bilinear interpolation. Given
this characteristic, the bilinear interpolation algorithm achieves
good performance in the smooth region. However, in high
frequency, this algorithm cannot match with the actual
situation which brings serious distortion. Besides, at image
boundaries, it doesn’t consider the directionality of the pixel
values which leads to many color artifacts. Because of this, the
edge regions turn to be jagged, which is called zipper effect
[15].
1/4
1/4
1/4
1/4
1/4
1/4
1/4
1/4
(a)
(b)
1/4
1/2
1/4
1/2
(d)
1/2
1/4
1/2
1/4
1/4
1/2
1/4
(e)
1/2
(c)
1/4
1/2
1/2
(f)
(g)
1/4
(h)
Fig. 3. Linear filters used in bilinear interpolation: (a) Interpolating G at R
locations; (b) Interpolating G at B locations; (c) Interpolating R at G locations
in R row, B column; (d) Interpolating R at G locations in B row, R column; (e)
Interpolating R at B locations; (f) Interpolating B at G locations in B row, R
column; (g) Interpolating B at G locations in R row, B column; (h)
Interpolating B at R locations.
III. THE PROPOSED ALGORITHM
It is well known that the bilinear interpolation algorithm
can cause zipper effect at image edges. If we retrieve the R, G,
and B channels of the reconstructed full-color image, it could
be found that the zipper effect in green channel is particularly
evident. This is because that G carries most of luminance
information for human vision, and its sampling rate is twice
than that of R and G. Therefore, if we restore the G channel
more accurately, we can reduce the influence of zipper effect
and get clearer full-color image. In bilinear interpolation
algorithm, the green pixel ĝ at red pixels can be computed by
To solve the above problem and get a clearer full-color
image, an improved linear interpolation with good performance
and fewer calculations is proposed for demosaicking of Bayer
pattern color images. Besides, it can meet the requirements of
real-time image processing due to its simplicity.
The rest of this paper is organized as follows. Section II
introduces the conventional bilinear interpolation method.
Section III gives the proposed interpolation algorithm.
465
gˆ(i, j ) =
∑ g (i + m, j + n) ,
numbers of non-zero filter coefficients as far as possible on the
premise of keeping good interpolation performance. In this
paper, a series of linear filters shown in Fig. 4 are adopted to
reconstruct the unknown pixels. To reduce the computational
complexity and improve the interpolation effects, different
filters are used according to different colors that need to be
restored. Since the neighbor pixels contain more relevant
information about the missing pixel, we utilize the nearest
neighbor pixels as many as possible in interpolation. For
example, we use the filter with the size of 3×3 to interpolate R
values at green pixels, which is shown as Fig. 4(c) and Fig.
4(d).
(2)
4
where ( m, n) = {(0,1), (0, −1), (1, 0), (−1, 0)} , (i, j ) is the
position of red pixel. From (2), we can see that the R value is
not involved when interpolate G value at R location. The
scheme of our improved interpolation algorithm is based on the
truth that the chrominance information is much richer than the
luminance information at image boundaries. In fact, the red
pixel is very useful to get an accurate green value. Therefore,
we compare the red pixel with the average of the red pixels
around it. If the difference value between them is relatively
large, it indicates that this point is at image boundaries. If a
pixel is at the boundaries, the luminance information will have
an obvious jump. Therefore, we can use this difference value to
modify the green value we need. The simplest way is to
multiply the difference value with a constant and plus the green
pixel value obtained by bilinear interpolation algorithm. This
process can be formulated as
gˆ (i, j ) = gˆ b (i, j ) + αΔ R (i, j ),
(3)
-1/8
1
∑ r (i + m, j + n) is the difference
4
value between the red pixel r (i, j ) and the average of the
neighbor red values; ( m, n) = {(0, 2), (0, −2), (2, 0), (−2, 0)} ; α
is a constant called gain parameter and gˆ b (i, j ) is the G value
interpolated by bilinear interpolation algorithm. In other words,
we correct the bilinear interpolation by a correction value to
estimate the unknown color. For interpolating G at blue pixels,
the value can be estimated in the same way with the correction
value Δ B (i, j ) . Similarly, the R at green pixels can be
interpolated by
(4)
rˆ(i, j ) = rˆb (i, j ) + βΔ G (i, j ),
1/4
where Δ R (i, j ) 5 r (i, j ) −
-1/8
-1/8
1/4
1/4
1/2
1/4
-1/8
-1/8
1/4
1/2
1/4
1/4
-1/8
-1/8
(a)
(b)
(c)
(d)
1/4
-1/8
-3/16
1/4
where rˆb (i, j ) is the red value interpolated by bilinear
interpolation algorithm, rˆ(i, j ) is corrected R value, β is gain
parameter, and Δ G (i, j ) is the difference value like Δ R (i, j ) .
The R value at blue pixels is obtained by (5) with the gain
parameter γ .
rˆ(i, j ) = rˆb (i, j ) + γΔ B (i, j ).
(5)
-3/16
1/4
3/4
1/4
-3/16
1/4
-3/16
(f)
(e)
-3/16
Similarly, the B values at green pixels and red pixels can be
estimated by the same way.
1/4
To make the reconstructed full-color image more similar to
the real image, we need to choose appropriate values for the
three gain parameters ( α , β , and γ ). In [9], three optimal
parameters are obtained by a Wiener approach. It is indicated
that when α = 1/ 2 , β = 5 / 8 , and γ = 3 / 4 , the errors
between the interpolated image and the original image reach to
the minimum. In the proposed scheme, we use these gain
parameters to design a series of linear filters. But the solution is
not unique. Theoretically, the bigger the size of the filter is, the
better the interpolation effect is. It is noticeable that more
pixels will be used in interpolation by using the filter with a
bigger size. However, it also increases the computational
complexity at the same time, which is not suitable for the realtime system. A good way to solve this problem is to reduce the
-3/16
1/4
3/4
1/4
-3/16
1/4
-3/16
(g)
(h)
Fig. 4. Linear filters used in this paper: (a) Interpolating G at R locations; (b)
Interpolating G at B locations; (c) Interpolating R at G locations in R row, B
column; (d) Interpolating R at G locations in B row, R column; (e)
Interpolating R at B locations; (f) Interpolating B at G locations in B row, R
column; (g) Interpolating B at G locations in R row, B column; (h)
Interpolating B at R locations.
466
the CPSNR can reflect the interpolation effects more
comprehensively.
IV. EXPERIMENTAL RESULTS AND PERFORMANCE ANALYSIS
An interpolated color image with good quality is the
ultimate goal of a demosaicking algorithm. In this section, we
use PSNR and composite peak signal-to-noise ratio (CPSNR)
[16] to test the interpolation performance of the improved
method. The comparisons among the improved algorithm and
other two demosaicking algorithms are also presented.
B. Experimental Results and Performance Analysis
In this section, we give the experimental results of the
proposed interpolation algorithm. 24 Kodak test images [17]
shown in Fig. 5 are selected to test the interpolation effects,
which are either 768×512 or 512×768 in size. According to the
characteristics of the interpolation filters, the boundary
extension is needed. In this paper, we adopt symmetric
boundary extension. In addition, all experiments in this paper
are conducted with MATLAB R2012a.
A. Evaluation Criteria
The PSNR and CPSNR are two image quality evaluation
indexes adopted in most interpolation algorithms. The PSNR is
used to assess the visual quality of each color channel. Taking
the red channel for example, the PSNR can be defined as
Table I shows the comparisons of PSNR and CPSNR
among bilinear interpolation, Luo’s method [11], and the
proposed algorithm. From Table I, we can see that the
improved interpolation algorithm has about 3-5 dB
improvement in each color channel and almost 5 dB
improvement in CPSNR. These results are consistent with
theoretical analysis described above. Since the proposed
algorithm takes the correlations among the three color planes
into account, it is obvious that the proposed method achieves
better performance than bilinear interpolation. It can be
observed that the improved method outperforms the latter with
higher PSNR and CPSNR. The reason is that the proposed
method uses more nearest neighbor pixels during interpolation
process. To evaluate the subjective effect of the reconstructed
color image, the demosaicking results of a cropped region from
Fig. 5(s) are shown in Fig. 6. From Fig. 6, we can see that the
three interpolation methods have similar performance in
smooth regions like sky area. Compared with other two
interpolation methods, the improved algorithm incurs fewer
false colors in high-frequency regions. The color artifact is also
weakened to a certain extent.
⎡
⎤
⎢
⎥
2
M
N
255
×
×
⎥ (dB), (6)
PSNR = 10 log10 ⎢ M N
2 ⎥
⎢
R
i
j
R
i
j
(
,
)
(
,
)
−
]⎥
out
⎢ ∑∑ [ in
⎣ i =1 j =1
⎦
where M × N is the size of the full-color image, Rin (i, j ) and
Rout (i, j ) are pixel values at the position (i, j ) of the original
red channel and the reconstructed red channel respectively.
Generally, the bigger the PSNR is, the better the quality of the
restored image is. An image whose PSNR is 30 dB or greater is
considered as an image with good quality.
The CPSNR is used to assess overall quality of the
reconstructed image. For a full-color image with size of
M × N , the CPSNR can be expressed as
⎡
⎤
⎢
⎥
2
×
×
×
3
M
N
255
⎥ (dB), (7)
CPSNR = 10log10 ⎢ 3 M N
2⎥
⎢
⎢ ∑∑∑[ I in (i, j, k ) − I out (i, j, k )] ⎥
⎣ k =1 i =1 j =1
⎦
where I in is the original color image, I out is the reconstructed
image, and k (k = 1, 2,3) is color plane. Compared with PSNR,
Finally, we would like to point out that the proposed
algorithm is also applied to other test images, and similar
results can be obtained.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
(l)
(m)
(n)
(o)
(p)
(q)
(r)
(s)
(t)
(u)
(v)
(w)
(x)
Fig. 5. Kodak test images.
467
further improve the accuracy of the interpolation and enhance
the image quality.
V. CONCLUSION
In this paper, an improved linear interpolation for
demosaicking of Bayer-patterned CFA images is proposed.
According to different colors needed to be interpolated,
different size linear filters with different gain parameters are
designed. Experimental results show that the improved scheme
achieves better performance than other two methods both in
subjective assessment and objective assessment. Besides, the
improved scheme reduces the computational complexity. Due
to good real-time adaptability, it can be easily implemented in
hardware. But it is easy to find that there are still color artifacts
in the reconstructed full-color image. For further work, we will
ACKNOWLEDGMENT
Dongyan Wang and Gang Yu thank the Image Processing
and Computer Vision (IPCV) research group at Shandong
University (Weihai) for giving them the opportunity to do
some research in their college years. The authors thank Heng
Zhang, Yunpeng Zhang, Zhi Zhang, and Ke Yu for their help
in revising this paper. The authors also thank the anonymous
reviewers for their valuable comments to improve the
presentation of the paper.
COMPARISONS OF PSNR AND CPSNR AMONG BILINEAR INTERPOLATION, LUO’S METHOD [11], AND THE PROPOSED ALGORITHM TO KODAK
IMAGES WITH SIZE OF 512×768 OR 768×512 IN PNG FORMAT
TABLE I.
Bilinear Interpolation
Test
Images
Luo’s Method [11]
PSNR/dB
Proposed Algorithm
PSNR/dB
PSNR/dB
CPSNR/dB
R
G
B
Fig.5(a)
24.97
29.47
25.30
Fig.5(b)
31.85
35.92
Fig.5(c)
32.63
Fig.5(d)
CPSNR/dB
R
G
B
26.16
28.81
35.54
28.74
31.43
32.65
35.68
40.04
36.61
32.68
33.62
36.80
32.20
36.22
32.20
33.17
Fig.5(e)
25.51
29.18
25.99
Fig.5(f)
26.41
30.88
Fig.5(g)
31.99
Fig.5(h)
CPSNR/dB
R
G
B
30.10
29.44
35.54
29.55
30.75
34.01
35.93
36.03
40.04
34.66
36.38
42.32
35.29
37.26
37.25
42.32
36.31
37.95
35.96
41.43
35.96
37.14
36.46
41.43
36.86
37.74
26.62
30.45
36.68
29.81
31.43
31.40
36.68
31.00
32.38
26.74
27.59
30.32
36.74
29.77
31.36
30.97
36.74
30.66
32.05
35.98
32.02
32.97
36.22
41.83
35.08
36.88
37.27
41.83
36.28
37.88
22.46
27.35
22.72
23.68
26.27
33.12
25.94
27.45
27.08
33.12
26.88
28.24
Fig.5(i)
31.06
35.48
31.33
32.21
34.82
41.41
34.53
36.00
35.61
41.41
35.62
36.84
Fig.5(j)
31.09
35.13
31.18
32.11
35.55
42.00
35.01
36.59
36.38
42.00
36.05
37.43
Fig.5(k)
28.07
32.20
28.40
29.20
32.27
37.94
31.81
33.27
32.87
37.94
32.62
33.89
Fig.5(l)
31.18
36.20
32.05
32.66
35.30
41.96
34.58
36.28
36.06
41.96
35.58
37.08
Fig.5(m)
23.02
26.45
23.12
23.93
27.67
32.68
27.14
28.56
28.13
32.68
27.68
28.99
Fig.5(n)
28.07
31.88
28.21
29.07
32.30
37.36
31.03
32.84
32.96
37.36
31.87
33.50
Fig.5(o)
29.74
34.42
30.40
31.09
33.84
39.40
32.99
34.64
34.62
39.40
33.83
35.35
Fig.5(p)
29.93
34.36
29.70
30.87
33.30
39.79
32.93
34.43
33.88
39.79
33.84
35.10
Fig.5(q)
31.43
34.57
30.76
31.96
35.24
40.47
34.83
36.21
36.04
40.47
35.63
36.90
Fig.5(r)
27.19
30.45
26.94
27.93
31.60
36.24
30.87
32.34
32.19
36.24
31.41
32.83
Fig.5(s)
27.02
31.76
27.13
28.15
30.68
37.23
30.35
31.83
31.42
37.23
31.14
32.52
Fig.5(t)
29.93
33.80
29.75
30.81
33.95
40.07
33.46
34.98
34.60
40.07
34.14
35.57
Fig.5(u)
27.56
31.50
27.53
28.51
31.54
37.45
30.98
32.52
32.27
37.45
31.86
33.24
Fig.5(v)
29.80
33.33
29.33
30.49
33.70
38.51
32.34
34.16
34.21
38.51
33.10
34.73
Fig.5(w)
33.43
37.56
33.62
34.50
37.73
43.06
36.63
38.38
38.32
43.06
37.45
39.01
Fig.5(x)
26.34
29.43
25.33
26.72
30.63
35.43
29.13
31.02
31.29
35.43
29.54
31.46
468
(a)
(b)
(c)
(d)
(e)
Fig. 6. Experimental results: (a) Original color images; (b) Bayer-patterned CFA image; (c) Demosaicking by bilinear interpolation; (d) Demosaicking by Luo’s
method [11]; (e) Demosaicking by the proposed algorithm.
[10] L. Li, Z. X. Hou, C. Y. Wang, and F. He, “Demosaicing algorithm based
on all phase DCT/IDCT interpolation,” Opto-Electronic Engineering,
vol. 35, no. 12, pp. 96-100, Dec. 2008. (in Chinese)
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demosaicing of Bayer pattern images,” Chinese Journal of Optics and
Applied Optics, vol. 3, no. 2, pp. 182-187, Apr. 2010. (in Chinese)
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on edge property for color filter arrays,” Digital Signal Processing, vol.
22, no. 1, pp. 163-169, Jan. 2012.
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with weighted values of multidirectional information,” Journal of
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