 Open Access
 Total Downloads : 294
 Authors : Dr. H. B. Kekre, Dr. Sudeep D. Thepade, Ratnesh N. Chaturvedi
 Paper ID : IJERTV2IS4899
 Volume & Issue : Volume 02, Issue 04 (April 2013)
 Published (First Online): 24042013
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
New Faster ‘Color to Gray and Back’ Using Normalization of Color Components with Orthogonal Transforms
Dr. H. B. Kekre
Sr. Professor Computer Engineering Dept.,
Mukesh Patel School of Technology, Management & Engineering,
NMIMS University, Mumbai, India
Dr. Sudeep D. Thepade Professor & Dean (R&D) Pimpri Chinchwad College of Engineering,
University of Pune, Pune, India
Ratnesh N. Chaturvedi M.Tech (Computer Engg.) Mukesh Patel School of Technology, Management & Engineering,
NMIMS University, Mumbai, India
Abstract
The paper shows performance comparison of two algorithms with Image transforms alias Cosine, Sine, Haar & Walsh and Normalization for Color to Gray and Back. The color information of the image is embedded into its gray scale version/equivalent using transform and normalization method. Instead of using the original color image for storage and transmission, gray image (Gray scale version with embedded color information) can be used, resulting into better bandwidth or storage utilization. Among the two algorithms considered the second algorithm give better performance as compared to the first algorithm as it removes the matted effect from the gray scale version. In second algorithm Discreet Cosine Transform (DCT) using Normalization gives better performance in Color to gray and Back. The intent is to print color images with black and white printers and to be able to recover the color information afterwards.
Key Words:Color Embedding, Transforms, Normalization, Compression, Color to Gray Conversion.

Introduction
Digital images can be classified roughly to 24bit color images and 8bit gray images. We have come to tend to treat colorful images by the development of various kinds of devices. However, there is still much demand to treat color images as gray images from the viewpoint of running cost, data quantity, etc. We can convert a color image into a gray image by linear combination of RGB color elements uniquely. Meanwhile, the inverse problem to find an RGB vector from a luminance value is an illposed problem. Therefore, it is impossible theoretically to completely restore a color image from a gray image.
For this problem, recently, colorization techniques have been proposed [1][4]. Those methods can re store a color image from a gray image by giving color hints. However, the color of the restored image strongly depends on the color hints given by a user as an initial condition subjectively.
In recent years, there is increase in the size of databases because of color images. There is need
to reduce the size of data. To reduce the size of color images, information from all individual color components (color planes) is embedded into a single plane by which gray image is obtained [5][6][7][8]. This also reduces the bandwidth required to transmit the image over the network.
Gray image, which is obtained from color image, can be printed using a blackandwhite printer or transmitted using a conventional fax machine [6]. This gray image then can be used to retrieve its original color image.
In this paper, we have compared the performance of two different methods of colortogray mapping technique one is only using the transforms[8] which is an existing technique and the other using transform with the concept of normalization[9] which is an proposed technique. With method 1 the gray image has the matted effect when the color information is hidden in transform domain [7][8]. And in method 2 the color information is hidden in normalized form which removes the matted effect and the recovered color image is of better quality as compared to method 1. Normalization is the process where each pixel value is divided by 256 to minimize the embedding error [9].
The paper is organized as follows. Section 2 describes various transforms. Section 3 presents the existing and proposed system for Color to Gray and
back. Section 4 describes experimental results and
u(n)
2 v(k) sin (k 1)(n 1) 0 n N 1
N 1
N 1
finally the concluding remarks are given in section 5.

Transforms
N 1 n0 N 1
—–(6)

Discrete Cosine Transform [9][12]
The NxN cosine transform matrix C={c(k,n)},also called the Discrete Cosine Transform(DCT),is defined as

Haar Transfrom [9][10]
The Haar wavelet's mother wavelet function (t) can be described as
1
1
,0 t 1
2
1 k 0,0 n N 1
1
0
0
(t) 1 , t
N
2 1
c(k, n)
2 cos (2n 1)k
1 k N 1,0 n N 1
, Otherwise
N 2N
—–(1)
The onedimensional DCT of a sequence
{u(n),0nN1} is defined as
—–(7)
And its scaling function (t) can be described as,
N 1
N 1
v(k) (k)u(n)cos(2n 1)k
0 k N 1
(t) 1 ,0 t 1
2N
n0
—–(2)
0 , Otherwise
—–(8)
Where (0) 1 , (k)
N
2 for 1 k N 1
N

Walsh Transform [9][11][12]
The inverse transformation is given by
Walsh transform matrix is defined as a set of N rows, denoted Wj, for j = 0, 1, …., N – 1, which have the
N 1
(2n 1)k
following properties[9]
2N
2N
u(n) (k)v(k) cos
k 0
, 0 n N 1

Wj takes on the values +1 and 1.
—–(3)
2.2 Discrete Sine Transform [9]
The NxN sine transform matrix {(k, n)}, also called the Discrete Sine Transform (DST), is defined as
(k, n) 2 sin (k 1)(n 1)
N 1 N 1
—–(4)
0k, nN1
The sine transform pair of onedimensional sequences is defined as

Wj[0] = 1 for all j.

Wj xWkT =0, for j k and WjxWkT, Wj has exactly j zero crossings, for j = 0, 1,
…N1.

Each row Wj is even or odd with respect to its midpoint.

Transform matrix is defined using a Hadamard matrix of order N. The Walsh transform matrix row is the row of the Hadamard matrix specified by the Walsh code index, which must be an integer in the range [0… N1]. For the Walsh code index equal to an integer j, the respective Hadamard output code has exactly j zero crossings, for j = 0, 1… N – 1.
v(k)
2 u(n) sin (k 1)(n 1) 0 k N 1



Existing System& Proposed System
N 1
N 1
N 1 n0 N 1
—–(5)
In this section, we describetwo colortogray
The inverse transformation is given by
mapping algorithm and color recovery method in which method 1 is an existing system and method 2 is an proposed system.

Method 1 : Using Transforms. [6][7][8]
The Color to Gray and Back has two steps as Conversion of Color to Matted Gray Image with color embedding into gray image & Recovery of Color image back. Here the transformbased mapping method is elaborated as per the following steps.
3.1.1 Colortogray Step

First color component (Rplane) of size NxN is kept as it is and second (Gplane) & third (Bplane) color component are resized to N/2 x N/2.

Transform i.e. DCT, DST, Haar or Walsh to be applied to ll the components of image.

First component to be divided into four subbands as shown in figure 1 corresponding to the low pass [LL], vertical [LH], horizontal [HL], and diagonal [HH] subbands, respectively.

LH to be replaced by second color component, HL to replace by third color component and HH by zero..

Inverse Transform to be applied to obtain Matted Gray image of size N x N.
LL
LH
HL
HH
Figure 1: Subband in Transform domain
3.1.2 Recovery Step

Transform to be applied on Matted Gray image of size N x N to obtain four subbands as LL, LH, HL and HH.

Retrieve LL as first color component by replace other three components by zeros of size NxN, LH as second color component and HL as third color component of size N/2 x N/2.

Inverse Transform to be applied on all three color component.

Second and Third color component are resized to N x N.

All three color component are merged to obtain Recovered Color Image.

Method 2 : Using Transforms with the concept of normalization.[6][7][8][9]
3.2.1 Colortogray Step

First color component (Rplane) of size NxN is kept as it is and second (Gplane) & third (Bplane) color component are resized to N/2 x N/2.

Second & Third color component are normalized to minimize the embedding error.

Transform i.e. DCT, DST, Haar or Walsh to be applied to first color components of image.

First component to be divided into four subbands as shown in figure1 corresponding to the low pass [LL], vertical [LH], horizontal [HL], and diagonal [HH] subbands, respectively.

LH to be replaced by normalized second color component, HL to replace by normalized third color component.

Inverse Transform to be applied to obtain Gray image of size N x N.

3.2.2 Recovery Step

Transform to be applied on Gray image of size N x N to obtain four subbands as LL, LH, HL and HH.

Retrieve LH as second color component and HL as third color component of size N/2 x N/2 and the the remaining as first color component of size NxN.

Denormalize Second & Third color component by multiplying it by 256.

Resize Second & Third color component to NxN.

Inverse Transform to be applied on first color component.

All three color component are merged to obtain Recovered Color Image.




Results & Discursion
These are the experimental results of the images shown in figure 2 which were carried out on DELL N5110 with below Hardware and Software configuration.
Hardware Configuration:

Processor: Intel(R) Core(TM) i32310M CPU@
2.10 GHz.

RAM: 4 GB DDR3.

System Type: 64 bit Operating System.
Software Configuration:
1. Operating System: Windows 7 Ultimate [64 bit]. 2. Software: Matlab 7.0.0.783 (R2012b) [64 bit].
The quality of Color to Gray and Back' is measured using Mean Squared Error (MSE) of original color image with that of recovered color image, also the difference between original gray image and reconstructed gray image (where color information is embedded) gives an important insight through user acceptance of the methodology. This is the experimental result taken on 10 different images of different category as shown in Figure 2. Figure 3 shows the sample original color image, its gray equivalent and reconstructed gray image and recovered color image using DCT, DST, Haar and Walsh transform using method 1 and method 2. As it can be observed that the gray image obtained from method 1 has matted effect which can give a clue that something is hidden in gray image is removed using method 2 as the gray image obtained from method 2 does not gives any clue about the color information hidden into it as the normalization process reduces the embedding error.
Figure 2:Test bed of Image used for experimentation.
Original Color Original Gray
DCT DST Haar Walsh
Reconstructed Gray (Method 1) Reconstructed Gray (Method 1) Reconstructed Gray (Method 1) Reconstructed Gray (Method 1)
Recovered Color (Method 1) Recovered Color (Method 1) Recovered Color (Method 1) Recovered Color (Method 1)
Reconstructed Gray (Method 2) Reconstructed Gray (Method 2) Reconstructed Gray (Method 2) Reconstructed Gray (Method 2)
Recovered Color (Method 2) Recovered Color (Method 2) Recovered Color (Method 2) Recovered Color (Method 2)
Figure 3: Color to gray and Back of sample image using Method 1 and Method 2
Table 1:MSE between Original Gray &Reconstructed Gray Image
DCT 
DST 
Haar 
Walsh 

Method 1 
Method 2 
Method 1 
Method 2 
Method 1 
Method 2 
Method 1 
Method 2 

Img 1 
10456 
8087.7 
17091 
8083.2 
16851 
7949.7 
13989 
7949.7 
Img 2 
22150 
16082 
35222 
16076 
35136 
16039 
28508 
16039 
Img 3 
7829.1 
4974.3 
17784 
4970.9 
17640 
4892.9 
12790 
4892.9 
Img 4 
21591 
15351 
29234 
15334 
29185 
15319 
22857 
15319 
Img 5 
5456.1 
5173.4 
15408 
5173.7 
15357 
5150.5 
14706 
5150.5 
Img 6 
3971.1 
2266.8 
7089.1 
2265.9 
7050.3 
2246.6 
4756 
2246.6 
Img 7 
30403 
21684 
49176 
21659 
49195 
21681 
39901 
21681 
Img 8 
33285 
26777 
39693 
26748 
39706 
26772 
33725 
26772 
Img 9 
7887.2 
4732.9 
16227 
4729.9 
16193 
4722 
11705 
4722.1 
Img 10 
5051.6 
3556 
9915.8 
3556.3 
9864.7 
3529.7 
7691.1 
3529.7 
Average 
14808.01 
10868.51 
23683.99 
10859.69 
23617.8 
10830.24 
19062.81 
10830.25 
25000
20000
15000
10000
5000
0
19062.81 

14808.01 10868.51 
10859.69 
10830.24 
10830.25 

Method 1 
Method 2 
Method 1 
Method 2 
Method 1 
Method 2 
Method 1 
Method 2 

DCT 
DST 
Haar 
Walsh 
19062.81 

14808.01 10868.51 
10859.69 
10830.24 
10830.25 

Method 1 
Method 2 
Method 1 
Method 2 
Method 1 
Method 2 
Method 1 
Method 2 

DCT 
DST 
Haar 
Walsh 
23683.99
Avg. MSE
23617.8
Figure 4: Average MSE of Original Gray w.r.t Reconstructed Gray for Method 1 & Method 2
Table 2:MSE between Original ColorRecovered Color Images
DCT 
DST 
Haar 
Walsh 

Method 1 
Method 2 
Method 1 
Method 2 
Method 1 
Method 2 
Method 1 
Method 2 

Img 1 
400.983 
400.5921 
402.1958 
402.1958 
493.5136 
493.5136 
493.5136 
493.5136 
Img 2 
86.7375 
86.6151 
89.6663 
89.6663 
121.3339 
121.3339 
121.3339 
121.3339 
Img 3 
224.7077 
224.5669 
226.7168 
226.7168 
280.6049 
280.6049 
280.6049 
280.6049 
Img 4 
91.3811 
90.792 
95.5502 
95.5502 
116.5854 
116.5854 
116.5854 
116.5854 
Img 5 
24.4245 
24.3226 
24.1318 
24.1318 
41.9297 
41.9297 
41.9297 
41.9297 
Img 6 
62.5822 
62.4987 
63.0204 
63.0204 
77.6847 
77.6847 
77.6847 
77.6847 
Img 7 
93.5613 
93.5108 
106.7863 
106.7863 
103.2414 
103.2414 
103.2414 
103.2414 
Img 8 
48.7362 
48.6133 
56.4814 
56.4814 
57.3388 
57.3388 
57.3388 
57.3388 
Img 9 
45.2142 
45.1501 
48.2119 
48.2119 
60.9927 
60.9927 
60.9927 
60.9927 
Img 10 
168.6834 
168.5498 
168.3113 
168.3113 
188.7353 
188.7353 
188.7353 
188.7353 
Average 
124.7011 
124.5211 
128.1072 
128.1072 
154.196 
154.196 
154.196 
154.196 
Avg. MSE
200
150
100
50
0
124.7011 124.5211 128.1072 128.1072
154.196 154.196 154.196 154.196 

Method 1 
Method 2 
Method 1 
Method 2 
Method 1 
Method 2 
Method 1 
Method 2 

DCT 
DST 
Haar 
Walsh 
154.196 154.196 154.196 154.196 

Method 1 
Method 2 
Method 1 
Method 2 
Method 1 
Method 2 
Method 1 
Method 2 

DCT 
DST 
Haar 
Walsh 
Figure 5: Average MSE of Original Color w.r.t Recovered Color for Method 1 & Method 2
It is observed in Table 2and Figure 5 that DCT using method 2 gives least MSE between Original Color Image and the Recovered Color Image. Among all considered image transforms, DCT using method 2 gives best results. And in Table 1 and Figure 4 it is observed that Haar using method 2 gives least MSE between Original Gray Image and the Reconstructed Gray Image. Among all considered image transforms, less distortion in Gray Scale image after information embedding is observed for Haar Transform using method 2. The quality of the matted gray is not an issue, just the quality of the recovered color image matters. This can be observed that when DCT using method 2 is applied the recovered color image is of best quality as compared to other image transforms used in method 1 and method 2.
5. Conclusion
This paper have presentedtwo method to convert color image to gray image with color informationembedding into it andmethod of retrieving color information from gray image. These methods allows one to send color imagesthrough regular black and white fax systems, by embedding thecolor information in a gray image. These methods are based on transforms i.e DCT, DST, Haar, Walshand Normalization technique. DCT using method 2 is proved to be the best approach with respect to other transforms using method 1 and method 2 for ColortoGray and Back Our next research step couldbe to test wavelet transforms and hybrid wavelets for ColortoGray and Back.
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BIOGRAPHICAL NOTES
Dr. H. B. Kekre has received B.E. (Hons.) in Telecomm. Engineering. From Jabalpur Uiversity in 1958, M.Tech (Industrial Electronics) from IIT Bombay in 1960, M.S.Engg. (Electrical Engg.) from University of Ottawa in 1965 and Ph.D. (System Identification) from IIT Bombay in 1970 He has worked as Faculty of Electrical Engg. and then HOD Computer Science and Engg. at IIT Bombay. For 13 years he was working as a professor and head in the Department of Computer Engg. at Thadomal Shahani Engineering. College, Mumbai. Now he is Senior Professor at MPSTME, SVKMs NMIMS University. He has guided 17 Ph.Ds, more than 100 M.E./M.Tech and several B.E./B.Tech projects. His areas of interest are Digital Signal processing, Image Processing and
Computer Networking. He has more than 450 papers in National / International Conferences and Journals to his credit. He was Senior Member of IEEE. Presently He is Fellow of IETE and Life Member of ISTE. Recently fifteen students working under his guidance have received best paper awards. Eight students under his guidance received Ph. D. From NMIMS University. Currently five students are working for Ph. D. Under his guidance
Sudeep D. Thepade has Received Ph.D. Computer Engineering from SVKMs NMIMS in 2011, M.E. in
Computer Engineering from University of Mumbai in 2008 with Distinction, B.E.(Computer) degree from North Maharashtra University with Distinction in 2003. He has about 10 years of experience in teaching and industry. He was Lecturer in Dept. of Information Technology at Thadomal Shahani Engineering College, Bandra(w), Mumbai for nearly 04 years, then worked as Associate Professor and HoD Computer Engineering at Mukesh Patel School of Technology Management and Engineering, SVKMs NMIMS, Vile Parle(w), Mumbai. Currently he is Professor and Dean (R&D), at Pimpri Chinchwad College of Engineering, Pune. He is member of International Advisory Committee for many International Conferences, acting as reviewer for many referred international journals/transactions including IEEE and IET. His areas of interest are Image Processing and Biometric Identification. He has guided five M.Tech. Projects and several B.Tech projects. He more than 185 papers inInternational Conferences/Journals to his credit with a Best Paper Award at International Conference SSPCCIN2008, Second Best Paper Award at ThinkQuest2009, Second Best Research Project Award at Manshodhan 2010, Best Paper Award for paper published in June 2011 issue of International Journal IJCSIS (USA), Editors Choice Awards for papers published in International Journal IJCA
(USA) in 2010 and 2011.
Ratnesh N. Chaturvedi is currently pursuing M.Tech. (Computer Engg.) from MPSTME, SVKMs NMIMS
University, Mumbai. B.E.(Computer) degree from Mumbai University in 2009. Currently working as T.A in Computer Engineering at Mukesh Patel School of Technology Management and Engineering, SVKMs NMIMS University, VileParle(w), Mumbai, INDIA. He has about 04 years of experience in teaching. He has published papers in several international journals like IJIP, IJCA, IJAET, IJACR etc. His area of interest
is Image Colorization & Information Security.