ENHANCED PERFORMANCE OF COLOR TO GRAY AND BACK BY USING HYBRID WAVELET TRANSFORMS

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International Journal of Emerging Technology and Advanced Engineering

Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 4, April 2013)

455

ENHANCED PERFORMANCE OF COLOR TO GRAY AND

BACK BY USING HYBRID WAVELET TRANSFORMS

Ms.Atkar Geeta B.

1

_{, Gore Sonal}

2

_,

1_{Computer Engineering Department, PCCOE, Pune} 2_{Computer Engineering Department, PCCOE, Pune}

1

[email protected] 2_{[email protected]}

Abstract— Image color conversion from color to gray and back by using single orthogonal wavelet transform has been previously proposed.Hybrid wavelet transform is nothing but combination of two orthogonal transforms such as haar-kekre hybrid wavelet transform is combination of haar wavelet transform and kekre’s wavelet transform. Papers discuss about six different combinations of Haar, Kekre and Walsh transforms. Combinations are HK (Haar-Kekre), HW (Haar-Walsh), WH (Walsh-Haar), KH (Kekre-Haar), KW (Kekre-Walsh) and WK (Walsh-Kekre). Atlast paper closes with discussion of comparison between original image and recovered image after applying hybrid wavelet transforms.

Keywords - Hybrid Wavelet transforms, HK, matted grey scale image, HW and WK.

I. INTRODUCTION

One of the advantages of image color convesrion from color to gray and back is minimization of storage space. Whenever color image is transformed into gray image by color hiding technique, colors get stored in the hidden form in this gray image.Storage space required for this gray image is less than that of color image.Therefore, it is very easy to transfer this gray image through fax than transferring color image.After transferring through fax, color can be extracted by color extraction technique [2]. In this way, compression and steganography get achived.

Another advantage of technique is it overcomes the drawback of unavailability of color printer.Suppose color printer is unavailable but only black and white printer is available and color print out is required.At that time color

hiding techniues are applied on color image, which will gives gray image.This gray image is pass throgh black and white printer.After getting print out, color extraction technique is applied on this print out to get color image [3].

Paper describes three different combinations of haar, Walsh and kekre’s wavelet transform and their results are compared by using MSE (Mean Squared Error) [3], [5].

M S E

=

1

Where I (i, j) is pixel value of image I and Q (i, j) is pixel value of image Q.

II. ALGORITHM

Basic algorithm for color conversion technique is shown in figure 1.RGB image is converted into gray image by color spaces.Supppose gray image is YCbCr.Wavelet transform is applied on Y component of YCbCr.Image is divided into LL, LH, HL and HH parts.LH and HL are replaced with scale down versions of Cb and Cr.Then apply inverse transform to get matted gray image, in which colors are in hidden form [2], [3], [4].

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International Journal of Emerging Technology and Advanced Engineering

[image:2.612.67.285.160.680.2]

456

Figure 1-Algorithm for color to gray and back

III. GENERATION OF HYBRID WAVELET

TRANSFORMS

To generate 8*8 hybrid wavelet transform, two orthogonal transform matrices A of size 2*2 and B of size 4*4 are required. That is p=2, q=4 therefore N=p*q =8.

Here first q number of rows of hybrid wavelet transform matrix is calculated as product of each element of first row of orthogonal matrix A with each column of orthogonal matrix B.

For next q number of rows of hybrid wavelet transform matrix, the second row of orthogonal transform matrix A is shift rotated after being appended with zeros. In similar way, other rows of hybrid wavelet transform matrix are generated [2].

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RGB->ABC by using color spaces

Component “A” is transformed into T1

Divide T1 into four regions-LL, LH, HL,

and HH

Replace” LH” and “HL” by scale down versions of “B” and

”C

Apply inverse transform to get “matted grey scale”

image

Matted grey image is first read and scanned

Image is transformed into the transformed

domain

Extract regions “B” and “C” and scale up them to approximations of

original color image Retrieve approximation

for “A”, replacing “B” and”C” regions by

zeroes These approximations are used toconvert the

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International Journal of Emerging Technology and Advanced Engineering

457 a11

a12

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a1p

a21

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International Journal of Emerging Technology and Advanced Engineering

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Figure 2 represents general matrix of hybrid wavelet transform which is generated from any two single orthogonal transforms.In this paper three different Combinations of haar, Walsh and kekre’s transforms are taken.These combinations are HK (Haar-Kekre), HW (Haar-Walsh), WH (Walsh-Haar), KH (Kekre-Haar), KW (Kekre-Walsh) and WK (Walsh-Kekre).Figure 3 shows combination of 2*2 haar matrix and 4*4 Kekre’s matrix.Therefore,p=2 ,q=4 and N=2*4=8 that is 8*8 matrix is generated. Equation 4 represents haar matrix, Equation 5 represents kekre’s matrix and equation 6 represents Haar-Kekre hybrid wavelet transform matrix.

4

5

[image:4.612.306.564.178.487.2]

6

Figure 3-Haar Kekre’s Hybrid Wavelet Transform

IV RESULTS AND DISCUSSION

Here, performance of image color conversion from color to gray and back is measured by using Mean Squared Error(MSE).MSE between Original color image and reconstructed color image is calculated. Table1 shows MSE values of all six hybrid wavelet transforms with first three texture images from USC SIPI database. Figure 4 shows graphical representations of MSE for all six combinations with three texture images from USC SIPI database.MSE values of Haar-Walsh hybrid wavelet transform is less than remaining five transforms.

Table 1 –MSE values of original and reconstructed images

MSE

 HK HW KH WH KW WK

Image 1

666.8 222.2 791.8 322.2 74.09 222.2

Image 2

1456.3 1011.8 1581.3 1111. 8

863.7 1011.8

Image

3 1121.7 677.2 1246.7 777.2 529.0 677.2

0 200 400 600 800 1000 1200 1400 1600

IMAGE1 IMAGE2 IMAGE3

HK HW KH WH KW WK

Figure 4 -MSE values of original and reconstructed images

V CONCLUSION

As MSE values for Kekre -Walsh Hybrid Wavelet Transform is less, it gives best reconstructed image than remaining transforms. In future, it can be possible to generate hybrid transforms of DCT (Discrete Cosine Transform) and DST (Discrete Sine Transform).

REFERENCES

[1] H.B. Kekre, Sudeep D. Thepade ,”Improving Color to Gray and Back using Kekre’s LUV Color Space”, IEEE International Advanced Computing Conference 2009(IACC09),Thapar University ,Patiala,India, 6-7 March-2009.

[image:4.612.58.283.324.551.2]

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[3] H.B. Kekre, Sudeep D. Thepade, Adib Parkar ,”An Extended

Performance Comparison of Color to Grey and Back using the Haar, Walsh, and Kekre ,Wavelet Transforms”, (IJACSA) International Journal of Advanced Computer Science and Applications, Special Issue on Artificial Intelligence,2011

[4] H.B. Kekre, Sudeep D. Thepade, Adib Parkar, “A Comparison of Haar Wavelets and Kekre's Wavelets for Storing Color Information in a Gray scale Image”, International journal of computer applications (0975 – 8887), Volume 11– No.11, December 2010

[5] H. B. Kekre, Sudeep D. Thepade, Adib Parkar, “Storage of Color Information in a Gray scale Image using Haar Wavelets and Various Color Spaces”, International Journal of Computer Applications (IJCA) (0975-8887), Vol-6, No.7, September-10 Applications (IJCA)(0975-8887),Vol. 6,No.7,September-2010.

[6] R. V. L. Hartley, "A more symmetrical Fourier analysis applied to transmission problems," Proceedings of IRE 30, pp.144–150, 1942.

[7] R. N. Bracewell, "Discrete Hartley transform," Journal of Opt. Soc. America, Volume 73, Number 12, pp. 1832–183 ,1983.

[8] Dr.H.B.Kekre, Dr.Tanuja K.Sarode, Dr.Sudeep D. Thepade, ”Inception of Hybrid Wavelet Transform using Two Orhogonal Transforms and It’s use for image compression,”IJSIS,Vol.9,Number 6,2011.

[9] Charles K.Chui, “An introduction to Wavelets”, Academic Press, 1922, San Diego, ISBN 0585470901.

[10] Ricardo L. de Queiroz, Senior Member, IEEE, and Karen M. Braun, “Color to Gray and Back: Color Embedding into Textured Gray Images”, IEEE transactions on image processing, Volume.15, No. 6, June 2006.