Multiscale Gradient Based – Directional CFA Interpolation with Refinement

INTERNATIONAL JOURNAL FOR TRENDS IN ENGINEERING & TECHNOLOGY VOLUME 4 ISSUE 1 – APRIL 2015 - ISSN: 2349 - 9303

Multiscale Gradient Based – Directional CFA Interpolation with Refinement Aarthy Poornila.A1

R. Mercy Kingsta2

1

Mepco Schlenk Engineering College, ECE Department aarthypoornila@gmail.com

Assistant Professor Mepco Schlenk Engineering College, ECE Department m.kingsta@gmail.com

3

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.

——————————  ——————————

1.1 Existing Algorithms

1. INTRODUCTION

D

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.

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].

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.

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.Gradientcorrected bilinear interpolation assumes that in a luminance/chrominance decomposition, the chrominance components don`t vary much across pixels. It exploits the interchannel 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.

Figure 1.1: Bayer mosaic of color image

.

90

INTERNATIONAL JOURNAL FOR TRENDS IN ENGINEERING & TECHNOLOGY VOLUME 4 ISSUE 1 – APRIL 2015 - ISSN: 2349 - 9303 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.

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.

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.

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. P ROPOSED SYSTEM DESIGN Fig 2.1 System Framework

2.1. System Description

2.1.1. Initial Directional Color Channel Estimation

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.

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 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 color channel estimates for the missing green pixel values are, đ??ş đ?‘–, đ?‘— − 1 + đ??ş đ?‘–, đ?‘— + 1 2 2. đ?‘… đ?‘–, đ?‘— − đ?‘… đ?‘–, đ?‘— − 2 − đ?‘… đ?‘–, đ?‘— + 2 + 4 đ??ş đ?‘– − 1, đ?‘— + đ??ş(đ?‘– + 1, đ?‘—) đ?‘‰ đ?‘” đ?‘–, đ?‘— = 2 2. đ?‘… đ?‘–, đ?‘— − đ?‘… đ?‘– − 2, đ?‘— − đ?‘…(đ?‘– + 2, đ?‘—) + 4 đ?‘”đ??ť đ?‘–, đ?‘— =

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

91

(1)

(2)

INTERNATIONAL JOURNAL FOR TRENDS IN ENGINEERING & TECHNOLOGY VOLUME 4 ISSUE 1 – APRIL 2015 - ISSN: 2349 - 9303 Here,

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.

đ?‘”đ??ť đ?‘–, đ?‘— - Horizontal green color channel estimation at red pixel đ?‘”đ?‘‰ đ?‘–, đ?‘—

- Vertical green color channel estimation at red

pixel

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.

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. gH i,j -R i,j , if G is interpolated CHg,r i,j = (3) G i,j -rH i,j , if R is interpolated gV i,j -R i,j , if G is interpolated CVg,r i,j = (4) G i,j -rV i,j , if R is interpolated

Fig 2.3: Multiscale Gradient Equation

The Multiscale gradient equations for red and green rows and column values are, G i,j+1 -G i,j-1 R i,j+2 -R i,j-2 G i,j+3 -G i,j-3 + 2 N1 N2 MH i,j = (5) R i,j+4 -R i,j-4 N3

đ??ť đ?‘‰ đ??śđ?‘”,đ?‘&#x; đ?‘–, đ?‘— , đ??śđ?‘”,đ?‘&#x; đ?‘–, đ?‘— are the horizontal and vertical difference estimates between green and red channels.

G i+1,j -G i-1,j R i+2,j -R i-2,j G i+3,j -G i-3,j + 2 N1 N2 MV i,j = (6) R i+4,j -R i-4,j N3

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.

Where đ?‘€đ??ť đ?‘–, đ?‘— , đ?‘€đ?‘‰ đ?‘–, đ?‘— 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

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 fullcolor 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

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

.

Fig 2.2 Bayer pattern

δg,r i,j =

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

wV .f.CVg,r i-1:i+1,j +wH .CHg,r i,j-1:j+1 .f' wC

Here đ?‘¤đ??ś = đ?‘¤đ?‘‰ + đ?‘¤đ??ť

92

(7)

INTERNATIONAL JOURNAL FOR TRENDS IN ENGINEERING & TECHNOLOGY VOLUME 4 ISSUE 1 – APRIL 2015 - ISSN: 2349 - 9303 f = [1/4 2/4 1/4] Where đ?›żđ?‘”,đ?‘&#x; đ?‘–, đ?‘— indicates initial green channel interpolation at red pixel locations.

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.

2.1.5. Green Channel Update Let Q (k, l) be either red or blue sample as shown in Fig 2.4. Let 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.

D (k, l) = G (k, l) – Q (k, l).

đ?›žđ?‘”,đ?‘&#x; đ?‘–, đ?‘— = đ?›żđ?‘”,đ?‘&#x; đ?‘–, đ?‘— . (1 − đ?‘¤ + đ?‘¤đ?‘ . đ?›żđ?‘”,đ?‘&#x; đ?‘– − 2, đ?‘— + đ?‘¤đ?‘† . đ?›żđ?‘”,đ?‘&#x; đ?‘– + 2, đ?‘— +đ?‘¤đ??¸ . đ?›żđ?‘”,đ?‘&#x; đ?‘–, đ?‘— − 2 + đ?‘¤đ?‘ . đ?›żđ?‘”,đ?‘&#x; đ?‘–, đ?‘— + 2 . đ?‘¤ /đ?‘¤đ?‘‡ (8)

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.

Here the four neighbors of the target pixel calculated as north, south, east and west directions. The weights (đ?‘¤đ?‘ , đ?‘¤đ?‘† , đ?‘¤đ??¸ , đ?‘¤đ?‘Š ) 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. đ??ş ′ đ?‘–,đ?‘— = đ?›žđ?‘”,đ?‘&#x; đ?‘–, đ?‘— + đ?‘… đ?‘–, đ?‘— đ??şâ€˛ đ?‘–, đ?‘— = đ?›žđ?‘”,đ?‘&#x; đ?‘–, đ?‘— + đ??ľ(đ?‘–, đ?‘—)

(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.

(11)

B' i,j =G' i,j -Îłg,b i-3:i+3,j-3:j+3 X Prb

(12)

đ?‘„ đ?‘– − 1, đ?‘— = đ??ş đ?‘– − 1, đ?‘— −

đ??ˇ đ?‘– − 1, đ?‘— − 1 + đ??ˇ đ?‘– − 1, đ?‘— + 1 2

đ?‘„ đ?‘–, đ?‘— − 1 = đ??ş đ?‘–, đ?‘— − 1 −

đ??ˇ đ?‘– − 1, đ?‘— − 1 + đ??ˇ đ?‘– + 1, đ?‘— − 1 2

đ?‘„ đ?‘– + 1, đ?‘— = đ??ş đ?‘– + 1, đ?‘— −

đ??ˇ đ?‘– + 1, đ?‘— − 1 + đ??ˇ đ?‘– + 1, đ?‘— + 1 2

đ?‘„ đ?‘–, đ?‘— + 1 = đ??ş đ?‘–, đ?‘— + 1 −

đ??ˇ đ?‘– + 1, đ?‘— − 1 + đ??ˇ đ?‘– + 1, đ?‘— + 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

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 -Îłg,r i-3:i+3,j-3:j+3 X Prb

(13)

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

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

93

INTERNATIONAL JOURNAL FOR TRENDS IN ENGINEERING & TECHNOLOGY VOLUME 4 ISSUE 1 – APRIL 2015 - ISSN: 2349 - 9303 single sensor digital camera is of the pattern GRBG as shown in Fig 2.2.

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: 3.1 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: 3.4 Horizontal color channel estimation Fig: 3.2 Input Kodak Image

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.

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.

94

INTERNATIONAL JOURNAL FOR TRENDS IN ENGINEERING & TECHNOLOGY VOLUME 4 ISSUE 1 – APRIL 2015 - ISSN: 2349 - 9303 Fig: 3.5 Vertical color channel estimation

Fig: 3.8 Initial Green channel Interpolation 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: 3.9 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: 3.7 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: 3.10 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. .

95

INTERNATIONAL JOURNAL FOR TRENDS IN ENGINEERING & TECHNOLOGY VOLUME 4 ISSUE 1 – APRIL 2015 - ISSN: 2349 - 9303 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.

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.

 MAX I2 SNR  10. log 10   MSE

   

SNR  20. log 10 ( MAX I )  10. log 10 ( MSE ) 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.

SSIM x, y  

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.



2 2 x

x

 y  C1 2 xy  C 2 



  y2  C1  x2   y2  C 2



where  x ,  y ,  x ,  y and  xy are the local means, Standard deviation and cross - covariance 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.

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.

96

INTERNATIONAL JOURNAL FOR TRENDS IN ENGINEERING & TECHNOLOGY VOLUME 4 ISSUE 1 – APRIL 2015 - ISSN: 2349 - 9303 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

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 4.1.1: Comparison of CPSNR Error Measure for Different Demosaicing Methods on the BAYER PATTERN

No

MGBD

Proposed

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Avg

0.9186 0.9227 0.9110 0.9135 0.9352 0.8887 0.9204 0.9249 0.9116 0.9169 0.8917 0.8801 0.9167 0.9255 0.9288 0.9142 0.9422 0.9368 0.9182 0.9201 0.9193 0.9250 0.9267 0.9297 0.9183

0.9523 0.9711 0.9595 0.9616 0.9621 0.9586 0.9615 0.9540 0.9488 0.9529 0.9526 0.9600 0.9473 0.9579 0.9668 0.9544 0.9589 0.9638 0.9553 0.9523 0.9561 0.9571 0.9635 0.9550 0.9576

Table 4.2.1: Comparison of SSIM before and after refinement

Performance in terms of SSIM 1

60 50 40 30 20 10 0

0.9

Avg

22

19

Proposed

16

0.8 13

MGBD

MGBD Proposed 7

0.85 1

GBTF

10

Avg

22

19

16

13

10

7

4

LPA

4

SSIM

0.95

1

CPSNR

Performance Measure in terms of CPSNR

Image Number

Image Number

Fig: 4.2.1. Performance comparisons after refinement

Fig: 4.1.1. Performance comparisons after refinement

5. CONCLUSION AND F UTURE WORK

4.2.1. Performance Comparison in terms of SSIM

97

INTERNATIONAL JOURNAL FOR TRENDS IN ENGINEERING & TECHNOLOGY VOLUME 4 ISSUE 1 – APRIL 2015 - ISSN: 2349 - 9303 [17] D. Menon, S. Andriani, and G. Calvagno, ―Demosaicing with directional filtering and a posteriori decision,‖ IEEE Trans. Image Process., vol. 16,no. 1, pp. 132–141, Jan. 2007.

[18] D. Menon and G. Calvagno, ―Regularization approaches to demosaicing,‖IEEE Trans. Image Process., vol. 18, no. 10, pp.

2209–2220, Oct.2009.

[19] C.-Y. Su and W.-C. Kao, ―Effective demosaicing using subband correlation,‖ IEEE Trans. Consumer Electron., vol. 55, no. 1, pp.199-204, Feb. 2009.

[20] Pekkucuksen and Y. Altunbasak, ―Edge oriented directional color filter array interpolation,‖ in Proc. IEEE Int. Conf. Acoust.

Speech Signal Process. May 2011, pp. 993–996.

[21] Wikipedia, the free encyclopedia. Demosaicing, August 2010.

[22] Maschal et al. Review of bayer pattern color fillter array (cfa) demosaicing with new quality assessment algorithms. Technical report, U.S. Army Research Laboratory, 2010 [23] .[3] Henrique S. Malvar, Li wei He, and Ross Cutler. Highquality linear interpolation for demosaicing of bayer-patterned color images. In Proceedings of the IEEE International Conference on Speech, Acoustics, and Signal Processing, 2004.

[24] [4] R Lukac and K N Plataniotis. Normalized color-ratio modeling for CFA interpolation. IEEE Transactions on Consumer Electronics, 2004.

[25] Rami Cohen Demosaicing Algorithms August 30, 2010

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.

6. REFERENCES [1] IbrahimPekkucuksen and Yucelltunbasak, ―Multiscale GradientsBased Color Filter Array Interpolation‖ Fellow, IEEE Trans .Image process , vol. 22, no. 1, January 2013 [2] B. E. Bayer, ―Color imaging array,‖ U.S. Patent 3 971 065, July 1976.

[3] Cok,D. R. ―Signal processing method and apparatus for producing interpolated chrominance values in a sampled color image signal,‖ U.S. Patent 4 642 678, Feb 1987.

[4] K. L. Chung, W. J. Yang, W. M. Yan, and C. C. Wang, ―Demosaicing of color filter array captured images using gradient edge detection masks and adaptive heterogeneity-projection,‖ IEEE Trans. Image Process. , vol. 17, no. 12, pp. 2356-2367, Dec. 2008.

[5] B. Gunturk, Y. Altunbasak, and R. Mersereau, ―Color plane interpolation using alternating projections,‖ IEEE Trans. Image Process., vol. 11, no. 9, pp. 997-1013, Sept. 2002.

[6] J. W. Glotzbach, R. W. Schafer, and K. Illgner, ―A method of color filter array interpolation with alias cancellation properties,‖ in Proc. IEEE Int.Conf. Image Process., vol. 1. 2001, pp. 141– 144.

[7] J. W. Glotzbach, R. W. Schafer, and K. Illgner, ―A method of color filter array interpolation with alias cancellation properties,‖ Proc. IEEE Int.Conf. Image Process. vol. 1, pp. 141-144, Oct. 2001.

[8] K. Hirakawa and T. W. Parks, ―Adaptive homogeneity-directed demosaicing algorithm,‖ IEEE Trans. Image Process., vol. 14, no.

3, pp. 360-369, March 2005.

[9] J. F. Hamilton Jr. and J. E. Adams, ―Adaptive color plane interpolation in single sensor color electronic camera,‖ U.S. Patent 5 629 734, May1997.

[10] Y. Itoh, ―CFA Interpolation using Unified Geometry Map,‖ Proc.

FIT2008, RI-002, Sept. 2008.

[11] T. Kuno and H. Sugiura, ―Practical Color Filter Array Interpolation Part 2 with Non-linear Filter,‖ IEEE Trans.

Consumer Electron. vol. 52, no. 4, pp. 1409-1417, Nov. 2006.

[12] X. Li, ―Demosaicing by successive approximation,‖ IEEE Trans.

Image Process., vol. 14, no. 3, pp. 370-379, March 2005.

[13] R. Lukac and K. N. Plataniotis, ―Data adaptive filters for demosaicing: A framework,‖ IEEE Trans. Consumer Electron., vol. 51, no. 2, pp. 560-570, May. 2005.

[14] W. Lu and Y.-P. Tan, ―Color filter array demosaicing: New method and performance measures,‖ IEEE Trans. Image Process., vol. 12, no. 10, pp. 1194-1210, Oct. 2003.

[15] N.-X. Lian, L. Chang, Y.-P. Tan, and V. Zagorodnov, ―Adaptive filtering for color filter array demosaicing,‖ IEEE Trans. Image Process., vol.16, no. 10, pp. 2515–2525, Oct. 2007.

[16] B. Leung, G. Jeon, and E. Dubois, ―Least-squares luma-chroma demultiplexing algorithm for bayer demosaicing,‖ IEEE Trans.

Image Process., vol. 20, no. 7, pp. 1885–1894, Jul. 2011.

98