Multiscale Gradient Based – Directional CFA Interpolation with Refinement

INTERNATIONAL JOURNAL FOR TRENDS IN ENGINEERING & TECHNOLOGY
VOLUME 4 ISSUE 1 – APRIL 2015 - ISSN: 2349 - 9303
90
Multiscale Gradient Based – Directional CFA
Interpolation with Refinement
Aarthy Poornila.A1
1
Mepco Schlenk Engineering
College,
ECE Department
aarthypoornila@gmail.com
R. Mercy Kingsta2
Assistant Professor
3
Mepco Schlenk Engineering College,
ECE Department
m.kingsta@gmail.com
Abstract—Single sensor digital cameras capture only one color value for every pixel location. The process of
reconstructing a full color image from these incomplete color samples output from an image sensor overlaid with a color
filter array (CFA) is called demosaicing or Color Filter Array (CFA) interpolation. The most commonly used CFA
configuration is the Bayer filter. The proposed demosaicing method makes use of multiscale color gradients to adaptively
combine color difference estimates from horizontal and vertical directions and determine the contribution of each direction
to the green channel interpolation. This method does not require any thresholds and is non iterative. The red and blue
channels are then refined using structural approximation.
Index Terms — Multiscale color gradients, Color Filter Array (CFA) interpolation, demosaicing, directional interpolation.
——————————  ——————————
1. INTRODUCTION
emosaicing algorithm is a digital image process used to
reconstruct a full color image from the incomplete color
samples obtained from an image sensor overlaid with a color filter
array (CFA). Also known as CFA interpolation or color
reconstruction [21] .The reconstructed image is typically accurate in
uniform-colored areas, but has a loss of resolution and has edge
artifacts in non uniform-colored areas.
A color filter array is a mosaic of color filters in front of
the image sensor. The most commonly used CFA configuration is
the Bayer filter shown in Fig 1.1. This has alternating red (R) and
green (G) filters for odd rows and alternating green (G) and blue (B)
filters for even rows. There are twice as many green filters as red or
blue ones, exploiting the human eye's higher sensitivity to green
light.
Figure 1.1: Bayer mosaic of color image
1.1 Existing Algorithms
Nearest neighbor interpolation simply copies an adjacent pixel of
the same color channel (2x2 neighborhood). It is unsuitable for any
application where quality matters, but can be used for generating
previews with given limited computational resources [25].In
bilinear interpolation, the red value of a non-red pixel is computed
as the average of the two or four adjacent red pixels. The blue and
green values are also computed in a similar way. Bilinear
interpolation generates significant artifacts, especially across edges
and other high-frequency content, as it doesn`t take into account the
correlation between the RGB values [22].
Cubic interpolation takes into account more neighbors
than in algorithm no. [22] (e.g., 7x7 neighborhood). Lower weight is
given to pixels which are far from the current pixel.Gradient-
corrected bilinear interpolation assumes that in a
luminance/chrominance decomposition, the chrominance
components don`t vary much across pixels. It exploits the inter-
channel correlations between the different color channels and uses
the gradients among one color channel, to correct the bilinearly
interpolated value [23].
Smooth hue transition interpolation assumes that hue is
smoothly changing across an object’s surface; simple equations for
the missing colours can be obtained by using the ratios between the
known colours and the interpolated green values at each pixel [22].
Problem can occur when the green value is 0, so some simple
normalization methods are proposed [24].In order to prevent flaws
when estimating colours on or around edges, pattern recognition
interpolation [3] describes a way to classify and interpolate three
different patterns (edge, corner and strip) in the green color plane
that are shown in Fig 1.2. The first step in this procedure is to find
the average of the four neighboring green pixels, and classify the
neighbors as either high or low in comparison to this average.
.
D

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Figure 1.2: (a) is a high edge pattern, (b) is a low edge pattern, (c) is a
corner pattern, and (d) is a stripe pattern.
Adaptive color plane interpolation assumes that the color
planes are perfectly correlated in small enough neighborhoods [25].
That is, in a small enough neighborhood, the equations.
G = B + k
G = R + j
are true for constants k, j.
In order to expand the edge detection power
of the adaptive color plane method, it is prudent to consider more
than two directions (i.e., not only the horizontal and vertical
directions). Thus directionally weighted gradient based
interpolation uses information from 4 directions (N, S, W, and E as
shown in Figure1.3)
Figure 1.3: Neighborhood of B pixel
A weight is assigned for each direction, using the known
information about the differences between B and G value [25].
2. PROPOSED SYSTEM DESIGN
2.1. System Description
The first step of the algorithm is to get initial directional
color channel estimates. The quality can be improved by applying
the interpolation over color differences using the advantages of
correlation between the color channels. Now every pixel location
has a true color channel value and two directional estimates. By
taking their difference, the directional color difference estimated.
The next step of the algorithm is to reconstruct the green
image along horizontal and vertical directions. Once the missing
green component is interpolated, the same process is performed for
estimating the next missing green component in a raster scan
manner. After interpolating all missing green components of the
image, the missing red and blue components at green CFA sampling
positions are estimated. Next, the directional color difference
estimates are combined from different directions.
The directional CFA interpolation method is based on
multi scale color gradients. Gradients are useful for extracting
directional data from digital images. In this method, the horizontal
and vertical color difference estimates are blended based on the
ratio of the total absolute values of vertical and horizontal color
difference gradients over a local window. For red & green rows and
columns in the input mosaic image, the directional estimates for the
missing red and green pixel values are estimated by initial
directional color channel estimates.
The color difference gradients calculated are used to find
weights for each direction. In order to avoid repetitive weight
calculations, the directional weights are reused.
Then the artifacts are removed and red and blue channels
are refined by the Structural Approximation method. The modules
of the proposed system framework are illustrated in Fig 2.1.
Fig 2.1 System Framework
2.1.1. Initial Directional Color Channel Estimation
To obtain a full color image, various demosaicing
algorithms can be used to interpolate a set of complete red, green,
and blue values for each point. The directional estimates for the
missing red and green pixel values, for red and green rows and
columns in the input mosaic image, are calculated.
The directional estimates for the missing blue and green
pixel values, for blue and green rows and columns in the input
mosaic image are calculated. Then horizontal and vertical color
channel estimates are calculated for finding directional color
channel estimates.
The directional color channel estimates for the missing
green pixel values are,
𝑔 𝐻
𝑖, 𝑗 =
𝐺 𝑖, 𝑗 − 1 + 𝐺 𝑖, 𝑗 + 1
2
+
2. 𝑅 𝑖, 𝑗 − 𝑅 𝑖, 𝑗 − 2 − 𝑅 𝑖, 𝑗 + 2
4
(1)
𝑔 𝑉
𝑖, 𝑗 =
𝐺 𝑖 − 1, 𝑗 + 𝐺(𝑖 + 1, 𝑗)
2
+
2. 𝑅 𝑖, 𝑗 − 𝑅 𝑖 − 2, 𝑗 − 𝑅(𝑖 + 2, 𝑗)
4
(2)

92
Here,
𝑔 𝐻
𝑖, 𝑗 - Horizontal green color channel estimation at red
pixel
𝑔 𝑉
𝑖, 𝑗 - Vertical green color channel estimation at red
pixel
The color channel estimates are calculated from the Bayer
pattern. Here H and V denotes horizontal and vertical directions and
(i,j) denotes the pixel location.
2.1.2. Directional Color Difference Estimation
The quality can be improved by applying the interpolation
over color differences to take advantage of the correlation between
the color channels. This is an important technique employed in the
reconstruction of full color images, obtained by interpolation along
horizontal and vertical direction. Every pixel coordinate has a true
color channel value and two directional estimates. By taking their
difference directional color difference estimated.
Cg,r
H
i,j =
gH
i,j -R i,j , if G is interpolated
G i,j -rH
i,j , if R is interpolated
(3)
Cg,r
V
i,j =
gV
i,j -R i,j , if G is interpolated
G i,j -rV
i,j , if R is interpolated
(4)
𝐶𝑔,𝑟
𝐻
𝑖, 𝑗 , 𝐶𝑔,𝑟
𝑉
𝑖, 𝑗 are the horizontal and vertical difference
estimates between green and red channels.
2.1.3. Multiscale Gradient Calculation
A full-color image is usually composed of three color
planes. Three separate sensors are required for a camera to measure
an image. To reduce the cost, many cameras use a single sensor
overlaid with a color filter array. The most commonly used CFA
nowadays is the Bayer CFA. In a single sensor digital camera, only
one color is measured at each pixel and the other two missing color
values are estimated. This estimation process is known as color
demosaicing.
The Bayer pattern is comprised of blue and green and red
and green rows and columns as shown in Fig 2.2. To obtain a full-
color image, various demosaicing algorithms can be used to
interpolate a set of complete red, green, and blue values for each
point.For red and green rows and columns in the input mosaic
image, the directional estimates for the missing red and green pixel
values are calculated
.
Fig 2.2 Bayer pattern
The quality can be improved by applying the interpolation
over color differences to take advantage of the correlation between
the color channels. This is an important technique employs the
reconstruction of full color images, obtained by interpolation along
horizontal and vertical direction. For every pixel coordinate has a
true color channel value and two directional estimates.
The multi scale gradient equation determine the difference
between the available color channel values one pixel (instead of two
pixels) away from the target pixel, then do the same operation in
terms of the other channel by using its closest samples, and then
take the difference between these two as shown in Fig 2.3. Observe
that the first part of this equation is the green channel gradient, and
the second part is the red channel gradient at twice the scale
normalized by the distance between their operands.
Fig 2.3: Multiscale Gradient Equation
The Multiscale gradient equations for red and green rows and
column values are,
MH
i,j =
G i,j+1 -G i,j-1
2
-
R i,j+2 -R i,j-2
N1
+
G i,j+3 -G i,j-3
N2
-
R i,j+4 -R i,j-4
N3
(5)
MV
i,j =
G i+1,j -G i-1,j
2
-
R i+2,j -R i-2,j
N1
+
G i+3,j -G i-3,j
N2
-
R i+4,j -R i-4,j
N3
(6)
Where 𝑀 𝐻
𝑖, 𝑗 , 𝑀 𝑉
𝑖, 𝑗 denotes the multiscale gradient
equation at each pixel coordinates in horizontal and vertical
direction and N denotes Normalizers.The normalizer values are
N1=2, N2=4, N3=6
The color difference gradient is calculated by taking the
difference between the available color channel values that are two
pixels away from the target pixel. The same operation is done for
other color channels by using simple averaging, and then finding the
difference between these two operations
2.1.4. Initial Green Channel Interpolation
The next step of the algorithm is to reconstruct the green
image along horizontal and vertical directions. Initial green channel
interpolation section concentrates on estimating missing green
pixels from known green and red pixel values using the green-red
row of Bayer pattern. The same technique is used in estimating
missing green pixels from known green and blue pixels. For this,
directional color difference estimates around every green pixel to be
interpolated has to be estimated. Multiscale gradient a smaller scale
is more desirable because it allows the local color dynamics to be
captured at a better resolution. The available color channels are
replaced at this scale, but still performing the same operations. The
interpolated green channel is
δg,r i,j =
wV.f.Cg,r
V
i-1:i+1,j +wH.Cg,r
H
i,j-1:j+1 .f'
wC
(7)
Here
𝑤 𝐶 = 𝑤 𝑉 + 𝑤 𝐻

93
f = [1/4 2/4 1/4]
Where 𝛿𝑔,𝑟 𝑖, 𝑗 indicates initial green channel interpolation at red
pixel locations.
2.1.5. Green Channel Update
After interpolating all missing green components of the
image, the missing red and blue components at green CFA sampling
positions are estimated. After the directional color difference
estimates are combined as explained in the previous section, the
green channel can be directly calculated and then the other channels
are completed. However, it is possible to improve the green channel
results by updating the initial color difference estimates. Consider
the closest four neighbors to the target pixel with each one having
its own weight.
𝛾𝑔,𝑟 𝑖, 𝑗 = 𝛿𝑔,𝑟 𝑖, 𝑗 . (1 − 𝑤
+ 𝑤 𝑁. 𝛿𝑔,𝑟 𝑖 − 2, 𝑗
+ 𝑤𝑆. 𝛿𝑔,𝑟 𝑖 + 2, 𝑗 +𝑤 𝐸. 𝛿𝑔,𝑟 𝑖, 𝑗 − 2
+ 𝑤 𝑁. 𝛿𝑔,𝑟 𝑖, 𝑗 + 2 . 𝑤
/𝑤 𝑇 (8)
Here the four neighbors of the target pixel calculated as
north, south, east and west directions. The weights (𝑤 𝑁, 𝑤𝑆, 𝑤 𝐸, 𝑤 𝑊)
are calculated by finding the total multiscale color gradients over a
local window. Once the missing green component is interpolated,
the same process is performed for estimating the next missing green
component in a raster scan manner. Once the color difference
estimate is finalized, we add it to the available target pixel to obtain
the estimated green channel value.
𝐺′ 𝑖,𝑗
= 𝛾𝑔,𝑟 𝑖, 𝑗 + 𝑅 𝑖, 𝑗 (9)
𝐺′ 𝑖, 𝑗 = 𝛾𝑔,𝑟 𝑖, 𝑗 + 𝐵(𝑖, 𝑗) (10)
2.1.6. Red and Blue Channel Interpolation
After the green channel has been reconstructed, interpolate
the red and blue components. The most common approach for red
and blue estimation consists of interpolation of the color differences
R-G, B-G instead of R and G directly. Finally, the missing blue
(red) components at the red (blue) sampling positions are
interpolated. For red and blue channel interpolation, first complete
the missing diagonal samples i.e. red pixel values at blue locations
and blue pixel values at red locations. These pixels are interpolated
using the 7 by 7 filter proposed.
Referring to the estimation of the red component (the same
strategy is applied for the blue one), thus all the green positions are
interpolated. Therefore, we choose to perform an interpolation using
the estimated red samples in the green location.
R'
i,j =G'
i,j -γg,r
i-3:i+3,j-3:j+3 X Prb (11)
B'
i,j =G'
i,j -γg,b
i-3:i+3,j-3:j+3 X Prb (12)
With the completion of red and blue pixel values at green
coordinates the full color image is to be generated.
2.1.7. Red and Blue Channel Refinement
The final step of the proposed method is to refine the
interpolated red and blue values. The equations for doing such
refinements by using Structural Approximation method [11] are
given below.
Let Q (k, l) be either red or blue sample as shown in Fig 2.4. Let
D (k, l) = G (k, l) – Q (k, l). (13)
Fig 2.4 Reference Bayer pattern
.
Here, G is a green sample, and P and Q represent either
red or blue sample respectively. If P is red, then Q is blue, and vice
versa.
𝑄 𝑖 − 1, 𝑗 = 𝐺 𝑖 − 1, 𝑗 −
𝐷 𝑖 − 1, 𝑗 − 1 + 𝐷 𝑖 − 1, 𝑗 + 1
2
𝑄 𝑖, 𝑗 − 1 = 𝐺 𝑖, 𝑗 − 1 −
𝐷 𝑖 − 1, 𝑗 − 1 + 𝐷 𝑖 + 1, 𝑗 − 1
2
𝑄 𝑖 + 1, 𝑗 = 𝐺 𝑖 + 1, 𝑗 −
𝐷 𝑖 + 1, 𝑗 − 1 + 𝐷 𝑖 + 1, 𝑗 + 1
2
𝑄 𝑖, 𝑗 + 1 = 𝐺 𝑖, 𝑗 + 1 −
𝐷 𝑖 + 1, 𝑗 − 1 + 𝐷 𝑖 + 1, 𝑗 + 1
2
The final interpolation after the above refinements is given by the
following equation,
Q i,j =G i,j -
D i-1,j +D i,j-1 +D i+1,j +D i,j+1
4
(14)
. The end of this equation can be seen that the proposed method
produce superior image quality than other demosaicing algorithms
2.2. Special Features
This method produces better results in terms of image
quality. It does not require any thresholds as it does not make any
hard decisions. It is non iterative. Features of gradients at different
scales are used. This is applied in digital camera.
3. RESULTS
A set of twenty four images from Kodak test set shown in
Fig 3.1 is used for the experimental verification of the proposed
algorithm. These images are captured using a single sensor digital
camera that uses a Color Filter Array (CFA) in which the color
filters are arranged in Bayer pattern. The sensor alignment of this

94
single sensor digital camera is of the pattern GRBG as shown in Fig
2.2.
Fig: 3.1 Kodak Image Test Set
One of the 24 images of the Kodak image test set is taken as the
input for demosaicing process is shown in the Fig 3.2.
Fig: 3.2 Input Kodak Image
Mosaic Image is a picture that has been divided into
(usually equal sized) rectangular sections, each of which gives a
single color value red or green or blue based on the Bayer pattern as
shown in Fig 3.3.
Fig: 3.3 Mosaic Image
The horizontal estimate for the missing red and green pixel
values of the red and green rows and columns in the input mosaic
image and the horizontal estimate for the missing blue and green
pixel values of the blue and green rows and columns in the input
mosaic image are calculated.
Fig: 3.4 Horizontal color channel estimation
The vertical estimate for the missing red and green pixel
values of the red and green rows and columns in the input mosaic
image and the vertical estimate for the missing blue and green pixel
values of the blue and green rows and columns in the input mosaic
image are calculated.

95
Fig: 3.5 Vertical color channel estimation
Fig: 3.6 Horizontal color difference
The image quality can be improved by applying the
interpolation over color differences. This is an important technique
employs the reconstruction of full color images, obtained by
interpolation along horizontal and vertical directions as in Fig 3.6
and Fig 3.7.
Fig: 3.7 Vertical color difference
Initial green channel interpolation concentrates on
estimating missing green pixels from known green and red pixel
values using the green and red row of Bayer pattern and missing
green pixels from known green and blue pixel values using the
green and blue row of Bayer pattern as shown in Fig 3.8.
Fig: 3.8 Initial Green channel Interpolation
Fig: 3.9 Green channel update
The green channel results are improved by updating the
initial color difference estimates as shown in Fig 3.9. Here the four
neighbors of the target pixel calculated as north, south, east and
west directions.
Fig: 3.10 Before Refinement
After the green channel has been reconstructed, the red and blue
components are interpolated. The most common approach for red
and blue estimation consists in interpolation of the color differences.
Now the image can be reconstructed with these interpolated color
channel values as shown in Fig 3.10.
.

96
Fig: 3.11 Red plane Refinement
After interpolating the red and blue channels, the red channel is further
refined using structural approximation method as shown in Fig 3.11.
Fig: 3.12 Blue Plane Refinement
After interpolating the red and blue channels, the blue channel
is further refined using structural approximation method as shown in
Fig 3.12.
Fig: 3.13 Reconstructed image
The above fig 3.13 is the reconstruction of the whole
image. After the interpolation red and blue channel refinement takes
place by using structural approximation method. Here we conclude
that the proposed method out performs the other methods through
the tests in terms of PSNR.
4. Image Quality Metrics
Objective measures of quality require a reference image
that is distortion-free to be used for comparison with the image
whose quality is to be measured. The dimensions of the reference
image and the dimensions of the degraded image must be identical.
Quality of the images can be measured in terms of:
4.1. PSNR
The peak signal-to-noise ratio is a measure of quality that
is determined by first calculating the mean squared error (MSE) and
then dividing the maximum range of the data type by the MSE. This
measure is simple to calculate but sometimes doesn't align well with
perceived quality by humans. For example, the PSNR for a blurred
image compared to an unblurred image is quite high, even though
the perceived quality is low.
)(log.10)(log.20
log.10
1010
2
10
MSEMAXSNR
MSE
MAX
SNR
I
I










4.2. SSIM
The Structural Similarity (SSIM) Index measure of quality
works by measuring the structural similarity that compares local
patterns of pixel intensities that have been normalized for luminance
and contrast. This quality metric is based on the principle that the
human visual system is good for extracting information based on
structure.
 
  
  
covariance-crossanddeviationStandard
means,localtheareand,,,
22
,
2
22
1
22
21
xyyxyx
yxyx
xyyx
where
CC
CC
yxSSIM






4.1.1. Performance Comparison in terms of CPSNR
The performance of proposed method in terms of CPSNR
compared with the Local Polynomial Approximation (LPA),
Gradient Based Threshold Free demosaicing (GBTF) and Multiscale
Gradient Based Demosaicing (MGBD). Finally the proposed
method gives more performance than the existing methods.

97
Table 4.1.1: Comparison of CPSNR Error Measure for Different
Demosaicing Methods on the BAYER PATTERN
Fig: 4.1.1. Performance comparisons after refinement
4.2.1. Performance Comparison in terms of SSIM
The performance of proposed method in terms of SSIM
compared with the Multiscale Gradient Based Demosaicing
(MGBD). Finally the proposed method gives more performance
than the existing method.
Table 4.2.1: Comparison of SSIM before and after refinement
Fig: 4.2.1. Performance comparisons after refinement
5. CONCLUSION AND FUTURE WORK
0
10
20
30
40
50
60
1
4
7
10
13
16
19
22
Avg
CPSNR
Image Number
Performance Measure in terms of CPSNR
LPA
GBTF
MGBD
Proposed
0.8
0.85
0.9
0.95
1
1
4
7
10
13
16
19
22
Avg
SSIM
Image Number
Performance in terms of SSIM
MGBD
Proposed
No LPA GBTF MGBD Proposed
1 40.46 36.19 39.87 40.61
2 41.33 41.99 41.77 46.18
3 43.47 43.66 43.72 47.86
4 40.86 42.38 41.13 45.86
5 37.54 37.86 39.05 42.47
6 40.93 37.74 41.38 42.87
7 43.02 43.16 43.51 47.89
8 37.13 34.94 37.56 39.99
9 43.49 42.01 43.96 47.89
10 42.67 42.67 43.20 47.72
11 40.53 39.09 41.36 43.62
12 43.98 42.43 44.45 48.26
13 36.09 35.22 36.00 37.72
14 36.97 39.19 37.97 42.29
15 40.09 41.86 40.30 45.00
16 43.99 40.12 44.86 46.33
17 41.80 42.43 42.32 46.76
18 37.42 38.97 38.22 41.97
19 41.51 38.42 42.17 44.71
20 41.44 41.86 42.16 45.96
21 39.63 38.76 40.31 42.44
22 38.49 40.15 39.05 43.68
23 43.89 44.08 44.02 47.46
24 35.37 38.32 35.69 41.38
Avg 40.50 40.15 41.00 44.46
No MGBD Proposed
1 0.9186 0.9523
2 0.9227 0.9711
3 0.9110 0.9595
4 0.9135 0.9616
5 0.9352 0.9621
6 0.8887 0.9586
7 0.9204 0.9615
8 0.9249 0.9540
9 0.9116 0.9488
10 0.9169 0.9529
11 0.8917 0.9526
12 0.8801 0.9600
13 0.9167 0.9473
14 0.9255 0.9579
15 0.9288 0.9668
16 0.9142 0.9544
17 0.9422 0.9589
18 0.9368 0.9638
19 0.9182 0.9553
20 0.9201 0.9523
21 0.9193 0.9561
22 0.9250 0.9571
23 0.9267 0.9635
24 0.9297 0.9550
Avg 0.9183 0.9576

98
The proposed demosaicing method uses Multiscale color
gradients to adaptively combine color difference estimates from
different directions and then the red and blue channels are refined
using Structural Approximation method. The proposed solution
does not require any thresholds since it does not make any hard
decisions. It is non-iterative. The relationship between color
gradients at different scales can be used to develop a high quality
CFA interpolation. This method is easy to implement. Experimental
results show the effectiveness of proposed method as it clearly
outperforms the other available algorithms by a margin in terms of
CPSNR and SSIM. Further research efforts can focus on improving
the results and applying the multi scale gradients idea to other image
processing problems.
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