A Comparative Study: Block Truncating Coding, Wavelet and ... · [email protected] ... Fractal Image Compression . Fractal is one effective method to describe natural modality

A Comparative Study: Block Truncating Coding, Wavelet and Fractal Image

Compression

Dinesh Gupta, Pardeep Singh, Nivedita, Sugandha Sharma

Assistant Professor PG Student PG Student Assistant Professor

DAVIET College Indo Global College SBS College (SBSCET) Indo Global College

Jallandhar Mohali Ferozepur Mohali

[email protected] [email protected] [email protected] [email protected]

Abstract

We undertake a study of the performance difference of

different transform coding techniques i.e. Block truncating

coding, wavelet and fractal image compression. This paper

focuses important features of transform coding in

compression of still images, including the extent to which the

quality of image is degraded by the process of compression

and decompression. The above techniques have been

successfully used in many applications. The techniques are

compared by using the performance parameters PSNR, CR

and reduced size. Images obtained with those techniques yield

very good results.

Keywords-Block Truncating Coding (BTC), Compression

ratio(CR) , Image Compression, Fractal Image Compression,

Wavelet.

I. Introduction

Multimedia data requires considerable storage capacity and

transmission bandwidth. The data are in the form of graphics,

audio, video and image. These types of data have to be

compressed during the transmission process. The compression

offers a means to reduce the cost of storage and increase the

speed of transmission. Image compression is used to minimize

the size in bytes of a graphics file without degrading the

quality of the image. There are two types of image

compression is present. They are lossy and lossless. In

lossless compression, the reconstructed image after

compression is numerically matching to the original image. In

lossy compression scheme, the reconstructed image contains

degradation relative to the original I. lossy techniques provide

for greater compression ratios than lossless techniques i.e.

Lossless compression gives good quality of compressed

images, but yields only less compression whereas the lossy

compression techniques lead to loss of data with higher

compression ratio. The approaches for lossless image

compression include variable-length encoding, Adaptive

dictionary algorithms such as LZW, bit-plane coding, lossless

predictive coding, etc. The approaches for lossy compression

include lossy predictive coding and transform coding.

Transform coding, which applies a Fourier-related transform

such as DCT and Wavelet Transform such as DWT are the

most commonly used approach.

In this paper, we will do comparison with Block

truncation coding (BTC), wavelet compression and widely

used fractal image compression algorithm different

performance measure such as Peak to Noise Ratio (PSNR),

Mean Square Error (MSE) and CR.

The paper is organized as follows: Section II

explains BTC image compression; Section III explains

Wavelet Image Compression; Section IV fractal Image

Compression; Section V include Experiment Results and

Discussion and Section VI gives the conclusion.

II. BLOCK TRUNCATING CODING (BTC)

A simple effective lossy image compression method is block

truncation coding (BTC) [1]. The BTC is an efficient image

coding method that has been adopted to obtain the statistical

properties of a block in image compression. Low

computational complexity and superior channel error resisting

ability make it attractive in real-time image compression. The

BTC output data set includes a binary bit plane, which defines

the quantization level of each pixel, and two reconstruction

level values (a and b), determined by the mean and standard

deviation of the block.

Pardeep Singh et al ,Int.J.Computer Technology & Applications,Vol 3 (2), 566-571

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In BTC, an input nxn pixel image, A4, is segmented into kxk

non-overlapping blocks of pixels, and a two-level (one-bit)

quantizer is independently designed for each block. Both the

quantizer threshold and the two reconstruction levels are

varied in response to the local statistics of a block. Thus,

encoding is essentially a local binarisation process, and the

representation of a block consists of an nxn bit map indicating

the reconstruction level associated with each pixel and the

overhead information specifying the two reconstruction levels.

Decoding is the simple process of placing the appropriate

reconstruction value at each pixel location as per the bit

map[2].

The basic algorithm computes two quantized values, and

YIb,y preserving the first moment and the second moment in

each block. The quantized values of Yn and YI can be defined

as

(1)

(2)

where mean (X) is the mean of pixel values in a block; σ is

the standard deviation of the pixel values in a block; a is the

number of X, which is greater than Xth; ,B is the number of

X; which is less than or equal to Xth. A bitmap records each

pixel which belongs to an alternative quantized values. The

bitmap, the mean, and the standard deviation need to be

transmitted. The bitrate of basic BTC is 2 bits/pixel. When a

two-dimension coding scheme is used [l], the bitrate can be

reduced to 1.625 bits/pixel. The coding process of basic BTC

takes only a few computation steps. Since basic BTC

algorithm bases on preserving statistical moments, the quality

of reconstructed image is commendable. Although holding

manifold advantages,the main problem of BTC is its low

compression ratio. As a result, there is interest in finding a fast

algorithm of high compression ratio.[3]

III. Wavelet

Wavelet is the common methods used in signal and image

compression. Wavelet transform (WT) are very powerful

because its ability to describe any type of signals both in time

and frequency domain simultaneously[4].

Wavelets are having an average value of zero and it

can be defined over a finite interval. The process behind the

wavelet transform is any arbitrary function (t) can be defined

in the form of a superposition of a set of such wavelets or

basis functions. These basis functions are simply called as the

baby wavelets. These baby wavelets are obtained from the

mother wavelets by scaling (contractions) and shifts

(translations). The Discrete Wavelet Transform of a finite

length signal is represented as x(n). It is having N components

and it can be represented by an N x N matrix. The Wavelet

based transform can also be called as Sub band coding.

Because there is no need to block the input image and its basis

functions, have variable length. The blocking artifacts can be

avoided if the wavelet based schemes performed in a higher

compression ratio[5].

Wavelet is compactly supported orthonomal where

the function is

(3)

Wavelet series can be defined as below

(4)

The components of ak and bk, are the coefficients

defined by

(5)

(6)

By looking at Haar scaling and wavelet function[7],[8], we

already can guess what type of signal that Haar is the best to

do the compression process. Because of a step or block

function, Haar is only powerful for block or step type of

signal. I f we have sine or cosine type of signal, Haar

obviously be the worst and we can see clearly that FFT

outperformed the Haar method [9] . . For wavelets, it

decomposes a signal into high frequency (details) and low

frequency (approximation) of coefficients. That could be

possible because of high pass and low pass filter in wavelets

function. Then, the signal can be compressed and

reconstructed to recover the original signal where we will get

almost the same type, shape, characteristics of the original

signal[6].

IV. Fractal Image Compression

Fractal is one effective method to describe natural modality in

the process of transformation and iteration. In 1973, Benoit


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Mandelbrot firstly brought forward the idea of fractal

geometry, Infinity self-similarity is the soul of fractal. It was

Michael Barnsley and his research group who first give out

the method of fractal-based image compression, via IFS

(Iterated Function Systems), according to the local and global

self-similar principle. In 1989, Amaud Jacquin and Michal

Barnsley realized a first automatic fractal encoding system.

[10]

Fractal image compression is also called as fractal image

programming because compressed images are represented by

contractive transforms. These transforms are composed of

group of a number of affine mappings on the whole image,

known as Iterated Function System (IFS). Contractive

transformation is applied to the IFS’s called Collage theorem.

This theorem is the technique core of the fractal coding [11].

Fractal image compression is a modern image compression

technique based on self similarity.

In FIC the image is decomposed two times, into overlapping

domain blocks with size D*D to make a domain pool. Then

we decompose the image again into non-overlapping range

blocks with size R*R, and usually D=2*R. This type of

decomposition is closely related to quad –tree (parent child

relationship) where domain block forms parent and small four

range block forms children. The whole process of fractal

image encoding is shown in Fig. 1. [12]

After decomposition, for each range block we search for best

matched domain block in the domain pool with a contractive

affine transformation Wi, which can be defined by the

following function

Where x and y are the spatial coordinates of the image block

and pxy is the pixel value at the position (x,y); ai, bi, ci and di

denote the combinations of some of the eight symmetrical

transformations; ui, vi are the location luminance values; si is

the scaling coefficient; oi is the luminance offset[13]. Finally

the best matched domain block can be found for each range

block in the original image.

V. EXPERIMENTAL RESULTS In this paper we selects grey scale image of Barbra.gif image

to stimulate for decomposition and reconstruction, and

compare BTC, wavelet and Fractal algorithm result. The

simulation result showed in TABLE 1, TABLE 2, TABLE 3,

Figure 2, Figure 3 and Figure 4. TABLE I performance

evaluation of BTC algorithm, Table II show compressed size,

Compression Ratio, Peak to Noise Ratio (PSNR), Mean

Square Error (MSE) for different level of decomposition of

wavelet . TABLE III show compressed size, Compression

Ratio, Peak to Noise Ratio (PSNR), Mean Square Error

(MSE) for different coefficients represents the Fractal image

compression. Figure 2 shows images of Barbara.gif at

different block size for BTC.

In case of BTC when size of block increases quality

of image degrade subjectively as well as objectively , means

visual quality degrade. Blurriness increases in image and peak

signal to noise ratio also decreases. So with increase of block

size loss of data increases.

In case of wavelet when we increases value of

decomposition level compression ratio increases but quality of

image degrades. We get better quality image at decomposition

level one and also better psnr value at one .when there is

increase in decomposition level image visual quality decreases

.as shown in figure 3 we can note that at decomposition level

5 image cannot visually displayed because blurriness

increases too much.

In fractal image compression we use criteria to

increase size of search block. In fractal image compression we

get highest psnr value at a negligible loss of quality of image.

So this technique provides better quality result because psnr

value is very high. As shown in figure 4 we can see that there

are negligible changes with increase in search block size

which are mentioned in table III.

VI. Conclusion: In this paper, the results of different compression techniques

are compared i.e. Block truncation coding(BTC), Wavelet

compression algorithm and fractal image compression on a

typical image having original size 291688 bytes. The effects

of different number of decompositions, image contents and

compression ratios are examined and noted down in table I, II,

III. The results of the above techniques are compared by using

two parameters such as Compressed Size, Compression Ratio,

PSNR and MSE values from the reconstructed image. These

compression algorithms provide a better performance in

picture quality at higher compression ratio. These techniques

are successfully tested on Barbara.gif. It is observed that

fractal image compression provides a better result when

compare to BTC and wavelet. The fractal algorithm is coupled

with the power of iteration function system, creating fractals

and providing mapping in these fractal, yields significant

compression, psnr with little quality loss. The above

algorithms can be used to compress the image that is used in

the web applications. So we can conclude that fractal image

compression is better techniques from these three techniques

because of achieving higher psnr value.


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VII. Result on Images: TABLE I Performance Evaluation of BTC Algorithm

TABLE II PERFORMANCE EVALUATION OF WAVELET ALGORITHM

TABLE III PERFORMANCE EVALUATION OF FRACTAL ALGORITHM

Block Compressed Size MSE PSNR CR

2*2 196435 20.431 35.0279 1.320

4*4 141312 67.0447 29.8672 1.9054

8*8 90179 106.856 27.8428 2.98579

16*16 53152 165.973 25.9304 5.06577

32* 32 32553 248.393 24.1794 8.27131

Level Size compressed MSE PSNR CR

1 251559 4.9741

41.16dB 1.1595

2 125576 78.5204 29.18dB 2.3228

3 57376 215.4544 24.80dB 5.0838

4 28681 373.9971 22.40dB 10.1701

5 20963 628.8154 20.15dB 13.9144

Increases of

value of

search block

Compressed Size MSE PSNR Encode time Decode time CR

1 257767 277.1334 71.9026 193.0770 21.7030 1.1568

2 216455 350.7918 70.8790 186.2100 19.2530 1.3776

3 219141 348.0821 70.9126 209.5020 19.0180 1.3607

4 218122 369.8990 70.6486 243.5580 18.7450 1.3671

5 213371 365.1981 70.7042 191.5610 19.7450 1.3975


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Experimental Results:

Block Truncation result Wavelet Image Compression Fractal Image Compression

Figures sequence (a) original image (b) at level 1 (c) at level 2(d) at level 3 (e) at level 4 (f) at level 5


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VIII. Refrences:

1. M. Rabbani, p.w. jones, digital image compression techniques, pie optical engineering press, 1991, pp.421-427.

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3. Liang-gee chen and yuan-chen liu an efficient visual pattern block truncation coding,2000,pp.312-318

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8. s. A. A. Karim, b. A. Ismail, m. T. Hasan, and j.

Sulaiman,"applications of wavelet method in stock exchange problem,"proceedings of international conference on

fundamental and applied sciences (icfas 2010), 15-17 june 2010,

kualalumpur convention center, 2010. In cd, 201oa.

9. c. K. Chui, an introduction to wavelets, academic press, new york,1992 pp.334-340.

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A Comparative Study: Block Truncating Coding, Wavelet and ... · [email protected] ... Fractal Image Compression . Fractal is one effective method to describe natural modality