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.
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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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ISSN:2229-6093
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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