Block Truncation Coding using Enhanced Interpolations and Lookup Procedures for Image Compression. S.Vimala. Dept. of Comp. Sci. Mother Teresa Women's.
International Journal of Computer Applications (0975 – 8887) Volume 29– No.1, September 2011
Block Truncation Coding using Enhanced Interpolations and Lookup Procedures for Image Compression S.Vimala
P.Uma Edwin
Dept. of Comp. Sci. Mother Teresa Women’s University Kodaikanal – 624 102
Dept. of Comp. Sci. J.A.Arts and Sci. College University of Madras
P.Anne Raja Reega Ruth Dept. Comp. Applications RVS College of Engineering and Technology Dindigul – 624 005
Chennai, Tamilnadu, India
Tamil Nadu, India
Tamilnadu, India
ABSTRACT Block Truncation Coding is one of the easy and efficient techniques for lossy image compression. In this paper, we have proposed few methods to enhance the existing Interpolative and Lookup procedures to reduce the bitrate and to improve the PSNR obtained with the Block Truncation Coding (BTC) based image compression methods. Of the existing BTC based methods, we have implemented the Minimum Mean Square Error (MMSE) method which gives better PSNR (quality of the reconstructed images) value to generate the bitplane and statistical moments. The size of the bitplane is reduced using Interpolation and Lookup procedures with noticeable degradation in PSNR value. This degradation is minimized using the proposed methods. Hence the proposed methods give less bitrate and better PSNR, when compared to the existing methods.
General Terms Image Compression, Block Truncation Coding, Interpolative Techniques and Lookup Procedure.
Keywords Image compression, bit-rate, bit-plane, BTC, PSNR, MMSE, Interpolation.
1. INTRODUCTION Generally image files occupy much storage and take more time for transmission. Images are being used in many areas like medical imaging, web applications, digital photos, satellite imaging, multimedia messaging in cellular phones etc. As the demand for images has become more now-a-days, an efficient image coding technique is essential. Image compression techniques [1] play a vital role in reducing the cost of storage and transmission. Compression techniques deal with reducing the storage required to save the image and ultimately increase the transmission speed [2]. All types of images like binary, gray scale, color images, video frames can be compressed efficiently using various image compression techniques.
Image compression is of two types, lossy and lossless [3], [4]. For most applications, where little loss of data is not vital, lossy compression is used. Lossless techniques are suitable for medical imaging where a small loss in data may even lead to loss of human lives. Block Truncation Coding (BTC) [5], Vector quantization (VQ) [6], Discrete Cosine Transform (DCT) [7] and Discrete Wavelet Transformation (DWT) [8] are some of the lossy image compression methods. Of these techniques, BTC is a simple and fast image compression technique, introduced by Delp and Mitchell [5]. BTC is based on the conservation of statistical properties. Although it is a simple technique, BTC has plays an important role in the history of image compression. Many image compression techniques have been developed based on BTC [9]. It achieves 2 bits per pixel (bpp) with low computational complexity. It is easy to implement when compared to vector quantization [10] and transform coding [11], [12]. Some irrelevant data is removed when an image is compressed and hence the reconstructed image will not be exactly equal to the original image. The difference between the original image and the compressed image is called Mean Square Error (MSE) and is calculated using the equation (1).The quality of the reconstructed image called the Peak Signal to Noise Ratio (PSNR) is calculated using the equation (2) and is the inverse of MSE.
MSE =
1 N
N
∑(y
i
− xi ) 2
)
(1)
i =1
255 2 PSNR = 10 log10 MSE
(2)
where yi is the reconstructed pixel value, xi is the original pixel value and N is the number of pixels in an image. The performance of any image compression technique is measured in terms of the PSNR and bpp.
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International Journal of Computer Applications (0975 – 8887) Volume 29– No.1, September 2011 In this paper, we have incorporated our novel ideas in enhancing the existing Interpolation and Lookup procedures in MMSE (a BTC based method for image compression) to improve the performance in terms of bits per pixel (bpp) and PSNR. In Section 2, we briefly outline the existing BTC, AMBTC, MMSE, New lookup and Interpolative methods. The proposed methods are explained in Section 3. The experimental results are discussed in Section 4 and the conclusion is given in Section 5.
2. EXISTING BTC BASED COMPRESSION TECHNIQUES 2.1 Standard Block Truncation Coding In BTC method, the given image is divided into N number of non-overlapping blocks , each of size 4 x 4 pixels. For each block, the statistical moments, the mean x and standard deviation σ are preserved and are calculated using the equations (3) and (4).
(3)
∑ (x − x ) i
m
x
x
the higher mean h and lower mean l are preserved instead of the mean and standard deviation values. Pixels in an image block are then classified into two groups of values. One group (higher range) comprising of gray levels which are greater than or equal to the mean ( x ) and the remaining gray levels are brought into another group (lower range). The mean
xh
of
higher range and l of the lower range are calculated using the equations (7) and (8).
1 Xi (m − q ) ∑ xi < x
(7)
(4)
where xi represents the i th pixel value of the image block and m is the total number of pixels in that block. Taking x as the threshold value, a two-level bit plane is obtained by comparing each pixel value xi with the threshold value. If xi < x then the pixel is replaced with ‘0’, otherwise with ‘1’. By this process, each block is reduced to a bit plane of size 16 bits. The bit plane along with x and σ form the compressed data. Hence a block of 4 x 4 pixels will give a 32 bit compressed data, amounting to 2 bpp [13]. To reconstruct the image at the receiving end, two quantizers a and b are computed using the equations (5) and (6). In the decoder, an image block is reconstructed by replacing 1’s in the bit plane with ‘b’ and the 0’s with ‘a’.
a = X −σ
Lema and Mitchell presented a simple and fast variant of BTC [14], named Absolute Moment BTC (AMBTC). In this method,
xl =
2
=
2.2 Absolute Moment Block Truncation Coding
x
1 m ∑ xi X = m i =1
σ
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q m−q
(5)
m−q q
b = X +σ (6) where m-q and q are the number of 0’s and 1’s in the compressed bit plane respectively.
x
h
=
1 q
∑
x
i
xi ≥ x
(8) where q is the number of pixels whose gray levels are greater than or equal to x . Then a two level quantization is performed for all the pixels in that block to form a bit plane of 1’s and 0’s.
x
x
For each block, the encoder generates l , h and bitplane to a file thus leading to 2 bpp like BTC. But AMBTC involves less number of computations when compared to BTC as standard deviation involves more multiplications.
2.3. Minimum Mean Square Error (MMSE) MMSE is the iterative process of AMBTC [15]. This technique is used to reduce the error (MSE value) between the original and the compressed images. In this method, the threshold value t is initialized by taking the average of minimum and maximum values of each block. The two statistical moments a and b are calculated using the equations (9) and (10) and are optimized as shown Fig. 1. a = Xmin
(9)
b = Xmax
(10)
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International Journal of Computer Applications (0975 – 8887) Volume 29– No.1, September 2011 a = xmin b = xmax
t = (a+b)/2
a'=
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(m − q ) ∑ x
