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

1Mepco Schlenk Engineering

College,

ECE Department

[email protected]

R. Mercy Kingsta2

Assistant Professor 3Mepco Schlenk Engineering College,

ECE Department

[email protected]

AbstractSingle 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 objects 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


91

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,

, = , 1 + , + 1

2

+2. , , 2 , + 2

4 (1)

, = 1, + ( + 1, )

2

+2. , 2, ( + 2, )

4 (2)


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Here,

, - Horizontal green color channel estimation at red pixel

, - 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,rH i,j =

gH i,j -R i,j , if G is interpolated

G i,j -rH i,j , if R is interpolated (3)

Cg,rV i,j =

gV i,j -R i,j , if G is interpolated

G i,j -rV i,j , if R is interpolated (4)

, , , ,

, 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 , , , 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

g,r i,j = wV.f.Cg,r

V i-1:i+1,j +wH.Cg,rH i,j-1:j+1 .f'

wC (7)

Here

= +


93

f = [1/4 2/4 1/4]

Where , , 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.

, , = , , . (1

+ . , 2,

+ . , + 2, + . , , 2

+ . , , + 2 . / (8)

Here the four neighbors of the target pixel calculated as

north, south, east and west directions. The weights ( , , , ) 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.

, = , , + , (9)

, = , , + (, ) (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 -g,r

i-3:i+3,j-3:j+3 X Prb (11)

B' i,j =G' i,j -g,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.

1, = 1, 1, 1 + 1, + 1

2

, 1 = , 1 1, 1 + + 1, 1

2

+ 1, = + 1, + 1, 1 + + 1, + 1

2

, + 1 = , + 1 + 1, 1 + + 1, + 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

MAXSNR

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-cross anddeviation Standard

means, local theare and ,,,

22,

2

22

1

22

21

xyyxyx

yxyx

xyyx

where

CC

CCyxSSIM

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

CP

SN

R

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

SS

IM

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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Multiscale Gradient Based – Directional CFA Interpolation with Refinement

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