Compression of MR Images Using DWT by Comparing RGB and YCbCr Color Spaces

doi:10.4236/jsip.2013.44046

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Journal of Signal and Information Processing, 2013, 4, 364-369

Published Online November 2013 (http://www.scirp.org/journal/jsip)

http://dx.doi.org/10.4236/jsip.2013.44046

Open Access JSIP

Compression of MR Images Using DWT by Comparing

RGB and YCbCr Color Spaces

Agrawal Jayprkash1*, Ritu Vijay2

1Department of Electronics and Communication Engineering, Jagnnath Gupta Institute of Engineering and Technology, Jaipur, India;

2AIM & ACT, Banasthali University, Vanasthali, India.

Email: *[email protected]

Received August 6th, 2013; revised September 6th, 2013; accepted September 16th, 2013

License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

ABSTRACT

This paper consists of a lossy image compression algorithm dedicated to the medical images doing comparison of RGB

and YCbCr color space. Several lossy/lossless transform coding techniques are used for medical image compression.

Discrete Wavelet Transform (DWT) is one such widely used technique. After a preprocessing step (remove the mean

and RGB to YCbCr transformation), the DWT is applied and followed by the bisection method including thresholding,

the quantization, dequantization, the Inverse Discrete Wavelet Transform (IDWT), YCbCr to RGB transform of mean

recovering. To obtain the best compression ratio (CR), the next step encoding algorithm is used for compressing the

input medical image into three matrices and forward to DWT block a corresponding containing the maximum possible

of run of zeros at its end. The last step decoding algorithm is used to decompress the image using IDWT that is applied

to get three matrices of medical image.

Keywords: Magnetic Resonance Image (MRI); RGB; YCbCr Transform; Block-Based DWT; Transform Coding

1. Introduction

The basic objective of image compression is to reduce

the size of image data for transmission or store in an effi-

cient manner, while maintaining the suitable quality of

reconstructed images [1-3]. The easy and reliable digital

transmission and storage of biomedical images would be

a tremendous boon to the medical practices. This can

help in instant availability of earlier imaging studies

when patients are re-admitted [4-6]. Both Medical and

surgical teams indulging on patient care could have

simultaneous access to imaging studies on monitors

throughout the hospital. This long-term digital archiving

or rapid transmission is prohibitive without the use of

image compression to reduce the file sizes.

There are two basic types of image compression

schemes:

The first lossless compression scheme encodes and

decodes the data perfectly and the reconstructed image

matches exactly with the original image, which means

there is no loss of data with no degradation. In this

scheme the coding techniques are Huffman encoding,

entropy encoding, and run length ending.

The second lossy compression scheme is used for the

sake of using a minimum storage space. In this scheme

there is a trade-off between compression and image qual-

ity. In lossy compression, the final decompressed image

must be visually lossless and consist of removing the

redundant information in adjacent pixels to minimize the

number of bits [7-9].

In preprocessing step, many decorrelating transforms

like YCbCr, YUV, YIQ [10-12] are used to reduce the

correlation between the R, G and B plane. We can pref-

erably use one of these color space transforms before the

application of wavelet transform. In this paper we are

considering the YCbCr transform to reduce the correla-

tion between the R, G and B space [13].

Block-based DWT [9,14] Shown in Figure 1, decom-

poses a broadband signal into two subbands with smaller

bandwidths and slower sample rates. A series of HP and

LP FIR filters are used to repeatedly divide the input

frequency range. The input signals are in the form of

frames having a frame size as multiple of 2n, where n is

the number of levels. Each unit consists of an LP and HP

FIR filter pair. The halfband filters with a cutoff fre-

*Corresponding author.

Compression of MR Images Using DWT by Comparing RGB and YCbCr Color Spaces 365

quency of Fs/4 are obtained by decimating the output of

each LP and HP filter by a factor of 2.

The aim of this paper is to evaluate the performance of

lossy medical image compression wavelet transforms

followed by wavelet encoders experiments which were

performed by using magnetic resonance images (MRI) as

test images. The performances of the medical images

were evaluated in terms of peak signal-to-noise ratio

(PSNR), bit rate (bpp) and the compression ratio (CR). In

the last step, decoding algorithm is used to decompress

the image using IDWT which is applied to get three ma-

trices of medical image.

2. Methodology

The block diagram of DWT based medical image com-

pression/decompression model shown in Figure 2. In

this paper, the method is dedicated to lossy medical im-

age compression DWT based and two phases of com-

pression/decompression. The input to the system is a

medical image and the output is the compressed one. The

compression technique is built with several steps and

each will be explained in details.

2.1. RGB to YCbCr Transformation

RGB is not very efficient when dealing with real-word

images. All three RGB components need to be of equal

bandwidth to generate any color within the RGB color

cube. The result of this is a frame buffer that has the

same pixel depth and display resolution for each RGB

component. The processing an image with the RGB color

space is usually not the most efficient method. To modify

the intensity or color of a given pixel, the three RGB

values must be read from the frame buffer, with the steps

of intensity or color calculation, performing desired

modifications, calculating new RGB values and at last

returning back to the frame buffer. If the system had ac-

Figure 1. Block-based DWT.

Figure 2. Compression algorithm scheme. (a) Compression

phase; (b) Decompression phase.

cess to an image stored directly in the intensity and color

format, some processing steps would be faster. For these

and other reasons, many video standard uses luma and

two color difference signals. The most common are the

YUV, YIQ and YCbCr color spaces [10-12].

In this paper the RGB to YCbCr transformation, the

mean value of three plane images R, G and B are re-

moved and the almost signal energy of the new trans-

formed YCbCr image is contained in the Y plane. Con-

sequently, we can achieve high compression ratio in the

Cb and Cr without losses in quality of compressed image

when returned to the original RGB space.

The transformation from RGB to YCbCr performed

respecting to

Y1665.738 129.05725.064R

Cb12837.94574.494 112.439G

256

Cr128112.43994.15418.285 B



 



 

 



 



 





 

(1)

where R, G and B take the typical values from 0 to 255

(8-bit precision), Y is the same range (0 - 255), and Cb,

Cr components are into the range (16 - 240).

The inverse transformation is expressed by

R1.0 0.0001.371Y

G1.00.3360.698 Cb

B1.0 1.7320.000Cr



 



 

 



 



 



 

(2)

A original MRI image shown in Figure 3(a) and we

define the RGB to YCbCr transformation for removing

the mean values of R, G, and B plane. Figures 3(b)-(d)

are the block displays which show an M-by-N matrix

element values to specified range of RGB colors. Fig-

ures 3(e)-(g) are the block displays which specified

range of YCbCr colors. It confirms that RGB to YCbCr

transformation approach is necessary to get superier per-

formance.

2.2. Block Based DWT Transform

For any color image, after the RGB to YCbCr transfor-

mation, each one of the new three planes YCbCr are par-

titioned to blocks and each block is transformed by DWT.

The DWT blocks perform a single-level one-dimen-

sional wavelet decomposition with respect to either a

particular wavelet (Daubechies, Coiflets, Symlets, Dis-

crete Meyer, Biorthogonal, Reverse Biorthogonal) [9,

14] or particular wavelet LP and HP decomposition fil-

ters.

As shown in Figure 4 the original signals are firstly

decomposed into two subspaces, low-frequency subband

and high frequency subband. It first scanned in a hori-

zontal direction and passed through LP and HP decom-

position filters producing low frequency as well as

high-frequency data in the horizontal direction. Filtered

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Compression of MR Images Using DWT by Comparing RGB and YCbCr Color Spaces

Open Access JSIP

366

Figure 3. (a) Original test MRI image; (b)-(d) are the block displays an M × N matrix element values to specified range of

RGB colors; (e)-(g) are the block displays specified range of YCbCr colors.

Figure 4. Pyramidal algorithm of one-level forward DWT

decomposition.

output data are then scanned in a vertical direction and

again these filters are applied separately to generate dif-

ferent frequency subbands. The transform generates sub-

bands LL, LH, HL and HH each with one-fourth the size

of the original image. Most of the energy is concentrated

in low-frequency subband LL, whereas higher-frequency

subbands LH, HL and HH contain detailed information

of the image in vertical, horizontal and diagonal direc-

tions, respectively. For higher level decomposition, DWT

can be applied again to the LL subband recursively in a

similar way to further compact energy into fewer low-

frequency coefficients. The appropriate choice of filters

for the transform is very important to achieve high cod-

ing efficiency.

2.3. Quantization and Transform Coding

A transform coder decomposes a signal in an orthogonal

basis and quantizes the decomposition coefficients [15].

The distortion of the restored signal is minimized by op-

timizing the quantization, the basis, and the bit allocation.

It is desirable to perform quantization by dividing the

transformed coefficients by quantization value. For low

frequency, coefficients are divided by smaller values

while the high frequency coefficients are divided by lar-

ger values

In this paper, we code the data using transform coding

scheme of following steps:

Source coding is to represent information in bits, with

the natural aim of using a small number of bits. The “in-

formation” is denoted by a real column vector

or a sequence of such vectors. A vector might be formed

from pixel values in an image; K. N pixels can be ar-

ranged as a sequence of K vectors of length N. The vec-

tor length N is defined such that each vector in a se-

quence is encoded independently.

x

Transform codes are the most used source codes be-

cause they are easy to apply at any rate and even with

very large values of N. The essence of transform coding

is the modularization shown in the Figure 5 first, an in-

vertible linear transform of the source vector x is com-

puted, producing y = Tx. Each component of y is called a

transform coefficient. The N transform coefficients are

then quantized independently of each other by N scalar

quantizers.

A quantizer q is a mapping from a source alphabet

to a reproduction code. It can be decomposed into

two operations









. The lossy encoder

is specified by a partition of into partition cells













2,xii



  and the reproduction de-

coder is . If N = 1, the quantizer is called a

scalar quantizer and if N ˃ 1, it is vector quantizer.





Several quality measures can be found in open litera-

ture of the field. The mean square error (MSE) and the

Peak signal to noise ratio (PSNR) are the most used

Compression of MR Images Using DWT by Comparing RGB and YCbCr Color Spaces 367

Figure 5. Transform coding scheme: A source code can be

decomposed so that the encoder is a linear transform T and

a set of N scalar quantizer encoders. In decoder are N sca-

lar quantizer decoders and another linear transform U.

Usually U = T−1.

measures.

Mean square error (MSE) is the some sort of average

or sum of the squares of the error between two images.

For M × N images u(m, n) and û(m, n), the least square

error (LSE) is,



1ˆ

LSE, ,

umn umn

MN 



 (3)

and average LSE is called the Mean square error (MSE),



1ˆ

MSE, ,

Eumn umn

MN 















 (4)

where u(m, n) and û(m, n) are the original and recon-

structed intensities belonging to R, G and B plane. The

PSNR is defined in decibels (dB) as,

PSNR10log MSE



 (5)

where 2



is the variance of the original image. For

medical image we used the relation given as

  

PSNR 10logMSE RMSE GMSE B















(6)

The size of the compressed image is evaluated with the

CR or Bit-rate per pixel (BPP), defined by

Original image size in bits

CR compressed image in bits

 (7)

The various steps during compression and decompres-

sion algorithms are summarized as follows:

Compression algorithm:

1) Input: Medical image I(RGB);

2) Break the input image into three matrices I(R), I(G)

and I(B);

3) Transformation of the I(R), I(G) and I(B) matrices

into I(Y), I(Cb) and I(Cr);

4) Perform DWT transform of sub-band I(Y), I(Cb)

and I(Cr) separately;

5) Transform coder decomposes and quantizes the de-

composition coefficients;

6) Output: Compressed medical image I(YCbCr).

Decompression algorithm:

1) Input: Compressed medical image I(YCbCr);

2) Inverse sub-band transform and dequantization of

reproduction code;

3) IDWT is applied and get Î(Y), Î(Cb) and Î(Cr);

4) Transformation of the Î(Y), Î(Cb) and Î(Cr) into

Î(R), Î (G) and Î (B);

5) Convert Î(R), Î(G) and Î(B) to Î(RGB);

6) Output: Decompressed medical image Î(RGB).

3. Results

Various results got hold of and summarized after per-

forming different experiment with YCbCr color space on

standard medical MR images (Figure 6). The YCbCr

transform applied in RGB color space and the respective

reconstructed images are shown in Figure 7. Different

size images were tested on the different color images

both in the RGB space and in the YCbCr color space.

Table 1 shows the results demonstrating, the superior-

ity of performance of the proposed technique when

working in the YCbCr domain. From the Table, it ob-

serve that PSNR in YCbCr color space increased and the

percentage of increased PSNR in Cb and Cr color space

is high. Similarly it is observed that, bpp is high in

YCbCr color space as compare to RGB color space.

4. Discussion

The major objective of image compression is to reduce

the size of the image data for transmission or to obtain

the best visual quality with minimum bit utilization. The

(a) (b) (c) (d) (e)

(f) (i) (j)

(h)

(g)

Figure 6. Original test medical MR images. (a) MR1; (b)

MR2; (c) MR3; (d) MR4; (e) MR5; (f) MR6; (g) MR7; (h)

MR8; (i) MR9 and (j) MR10.

(a) (b) (c) (d) (e)

(f) (g) (h) (i) (j)

Figure 7. Reconstructed medical MR images. (a) MR1; (b)

MR2; (c) MR3; (d) MR4; (e) MR5; (f) MR6; (g) MR7; (h)

MR8; (i) MR9 and (j) MR10.

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Compression of MR Images Using DWT by Comparing RGB and YCbCr Color Spaces

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368

Table 1. PSNR, and bpp for different test medical images of RGB and YCbCr color space.

PSNR bpp

Medical

Images R G B Y Cb Cr R G B Y Cb Cr

MR1 11.83 11. 83 11. 84 12.91 57.93 58.63 0.279 0.279 0.278 0.301 0.502 0.502

MR2 13.28 13.28 13.25 14.26 50.52 47.54 0.225 0.226 0.205 0.253 0.491 0.503

MR3 14.66 14.61 14.76 15.85 36.02 34.1 0.293 0.289 0.287 0.310 0.500 0.504

MR4 11.66 11. 54 11. 57 12.49 43.85 41.85 0.226 0.223 0.226 0.255 0.503 0.503

MR5 16.84 16.84 16.84 18.08 42.94 60.78 0.226 0.223 0.226 0.255 0.503 0.503

MR6 17.4 17.29 17.24 18.47 52.93 51.08 0.075 0.082 0.088 0.131 0.505 0.498

MR7 18.37 18.37 18.37 19.61 147 147 0.118 0.118 0.118 0.163 0.502 0.502

MR8 18.38 18.38 18.38 19.61 147 147 0.141 0.141 0.141 0.183 0.502 0.502

MR9 18.62 18.62 18.62 19.85 147 147 0.140 0.140 0.140 0.182 0.502 0.502

MR10 16.57 16.57 16.57 17.81 147 147 0.268 0.268 0.268 0.292 0.502 0.502

15.761 15.733 15.744 16.894 87.21988.1980.188 0.190 0.189 0.223 0.502 0.502

parameters PSNR and bpp are generally used for assess-

ing the quality of the reconstructed image. Earlier studies

[1-8,13,14] discussed the image compression and [4-6]

addressed the compression of images. The results were

obtained in the present study, using the preprocessing

step followed by the bisection method including thresh-

olding, the quantization, dequantization and the IDWT

were compared with the 3-D transforms, such as discrete

Hartley transform (DHT), discrete cosine transform

(DCT) and discrete Fourier transform (DFT) [6]. From

Table 1 high bit rate result improved the quality of the

reconstructed image. The performance of the MRI com-

pression using algorithm yielded better results than other

transforms. It can be concluded that YCbCr color space

was found to be better PSNR than the RGB color space.

The user can improve the bit rate and CR depending on

his reconstructed image quality requirements.

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