Design and Implementation of EZW & SPIHT Image Coder for Virtual Images

Priyanka Singh & Priti Singh
International Journal of Computer Science and Security (IJCSS), Volume (5) : Issue (5) : 2011 433
Design and Implementation of EZW & SPIHT Image Coder for
Virtual Images
Priyanka Singh priyanka10ec@gmail.com
Research Scholar, ECE Department
Amity University
Gurgaon (Haryana, India)
Priti Singh pritip@rediffmail.com
Professor, ECE Department
Amity University
Gurgaon (Haryana, India)
Abstract
The main objective of this paper is to designed and implemented a EZW & SPIHT Encoding
Coder for Lossy virtual Images. Embedded Zero Tree Wavelet algorithm (EZW) used here is
simple, specially designed for wavelet transform and effective image compression algorithm. This
algorithm is devised by Shapiro and it has property that the bits in the bit stream are generated in
order of importance, yielding a fully embedded code. SPIHT stands for Set Partitioning in
Hierarchical Trees. The SPIHT coder is a highly refined version of the EZW algorithm and is a
powerful image compression algorithm that produces an embedded bit stream from which the
best reconstructed images. The SPIHT algorithm was powerful, efficient and simple image
compression algorithm. By using these algorithms, the highest PSNR values for given
compression ratios for a variety of images can be obtained. SPIHT was designed for optimal
progressive transmission, as well as for compression. The important SPIHT feature is its use of
embedded coding. The pixels of the original image can be transformed to wavelet coefficients by
using wavelet filters. We have anaysized our results using MATLAB software and wavelet toolbox
and calculated various parameters such as CR (Compression Ratio), PSNR (Peak Signal to
Noise Ratio), MSE (Mean Square Error), and BPP (Bits per Pixel). We have used here different
Wavelet Filters such as Biorthogonal, Coiflets, Daubechies, Symlets and Reverse Biorthogonal
Filters .In this paper we have used one virtual Human Spine image (256X256).
Keywords: Image Compression, Embedded Zerotree Wavelet, Set Partitioning in Hierarchical
Trees, CR, PSNR, MSE, BPP.
1. INTRODUCTION
With the growth of technology and the entrance into the Digital Age, the world has found itself a
vast amount of information. Dealing with such enormous amount of information can often present
difficulties. Digital information must be stored, retrieved, analyzed and processed in an efficient
manner, in order for it to be put to practical use. Image compression is technique under image
processing having wide variety of applications. Image data is perhaps the greatest single threat to
the capacity of data networks [1,2].As image analysis systems become available on lower and
lower cost machines, the capability to produce volume of data becomes available to more and
more users. New data storage technologies have been developed to try to keep pace with the
potential for data creation.
1.1 Image Compression
The fundamental components of compression are redundancy and irrelevancy reduction.
Redundancy means duplication and Irrelevancy means the parts of signal that will not be noticed
by the signal receiver, which is the Human Visual System (HVS).
There are three types of redundancy can be identified:

• Spatial Redundancy i.e. correlation between neighboring pixel values.
• Spectral Redundancy i.e. correlation between different color planes or spectral bands.
• Temporal Redundancy i.e. correlation between adjacent frames in a sequence of images.
Image compression focuses on reducing the number of bits needed to represent an image by
removing the spatial and spectral redundancies. The removal of spatial and spectral redundancy
is often accomplished by the predictive coding or transforms coding. Quantization is the most
important means of irrelevancy reduction [2].
1.2 Basic Types of Image Compression
Basic types of image compression are lossless and lossy. Both compression types remove data
from an image that isn't obvious to the viewer, but they remove that data in different ways.
Lossless compression works by compressing the overall image without removing any of the
image's detail. As a result the overall file size will be compressed. Lossy compression works by
removing image detail, but not in such a way that it is apparent to the viewer. In fact, lossy
compression can reduce an image to one tenth of its original size with no visible changes to
image quality [2, 3].
One of the most successful applications of wavelet methods is transform-based image
compression (also called coding). The overlapping nature of the wavelet transform alleviates
blocking artifacts, while the multiresolution character of the wavelet decomposition leads to
superior energy compaction and perceptual quality of the decompressed image. Furthermore, the
multiresolution transform domain means that wavelet compression methods degrade much more
gracefully than block-DCT methods as the compression ratio increases. Since a wavelet basis
consists of functions with both short support (for high frequencies) and long support (for low
frequencies), large smooth areas of an image may be represented with very few bits, and detail
added where it is needed. Wavelet-based coding provides substantial improvements in picture
quality at higher compression ratios. Over the past few years, a variety of powerful and
sophisticated wavelet-based schemes for image compression, as discussed later, have been
developed and implemented. Because of the many advantages, wavelet based compression
algorithms are the suitable candidates for the new JPEG-2000 standard. Such a coder operates
by transforming the data to remove redundancy, then quantizing the transform coefficients (a
lossy step), and finally entropy coding the quantizer output. The loss of information is introduced
by the quantization stage which intentionally rejects less relevant parts of the image information.
Because of their superior energy compaction properties and correspondence with the human
visual system, wavelet compression methods have produced superior objective and subjective
results [4]. With wavelets, a compression rate of up to 1:300 is achievable [5]. Wavelet
compression allows the integration of various compression techniques into one algorithm. With
lossless compression, the original image is recovered exactly after decompression. Unfortunately,
with images of natural scenes, it is rarely possible to obtain error-free compression at a rate
beyond 2:1 [5-6]. Much higher compression ratios can be obtained if some error, which is usually
difficult to perceive, is allowed between the decompressed image and the original image.
2. EMBEDDED ZERO TREE WAVELET (EZW)
The EZW algorithm was introduced in the paper of Shapiro [2]. The core of the EZW compression
is the exploitation of self-similarity across different scales of an image wavelet transform. The
Embedded Zero-tree Wavelet (EZW) algorithm is considered the first really efficient wavelet
coder. Its performance is based on the similarity between sub-bands and a successive-
approximations scheme. Coefficients in different sub-bands of the same type represent the same
spatial location, in the sense that one coefficient in a scale corresponds with four in the prior level.
This connection can be settled recursively with these four coefficients and its corresponding ones
from the lower levels, so coefficient trees can be defined. In natural images most energy tends to
concentrate at coarser scales (higher levels of decomposition), then it can be expected that the

nearer to the root node a coefficient is, the larger magnitudes it has. So if a node of a coefficient
tree is lower than a threshold, it is likely that its descendent coefficients will be lower too.
We can take profit from this fact, coding the sub-band coefficients by means of trees and
successive-approximation, so that when a node and all its descendent coefficients are lower than
a threshold, just a symbol is used to code that branch The successive-approximation can be
implemented as a bit-plane encoder. The EZW algorithm is performed in several steps, with two
fixed stages per step: the dominant pass and the subordinate pass. In Shapiro's paper the
description of the original EZW algorithm can be found. However, the algorithm specification is
given with a mathematical outlook. We present how to implement it, showing some
implementation details and their impact on the overall codec performance. Consider we need n
bits to code the highest coefficient of the image (in absolute value). The first step will be focused
on all the coefficients that need exactly n bits to be coded. In the dominant pass, the coefficients
which falls (in absolute value) in this range are labeled as a significant positive/negative (sp/sn),
according to its sign. These coefficients will no longer be processed in further dominant passes,
but in subordinate passes. On the other hand, the rest of coefficients are labeled as zero-tree root
(zr), if all its descendants also belong to this range, or as isolated zero (iz), if any descendant can
be labeled as sp/sn. Notice that none descendant of a zero-tree root need to be labeled in this
step, so we can code entire zero-trees with just one symbol. In the subordinate pass, the bit n of
those coefficients labeled as sp/sn in any prior step is coded. In the next step, the n value is
decreased in one so we focus now on the following least significant bit [7]. Compression process
finishes when a desired bit rate is reached. That is why this coder is so called embedded. In the
dominant pass four types of symbols need to be code (sp, sn, zr, iz), whereas in the subordinate
pass only two are needed (bit zero and bit one). Finally, an adaptive arithmetic encoder is used to
get higher entropy compression. EZW approximates higher frequency coefficients of a wavelet
transformed image. Because the wavelet transform coefficients contain information about both
spatial and frequency content of an image, discarding a high-frequency coefficient leads to some
image degradation in a particular location of the restored image rather than across the whole
image. Here, the threshold is used to calculate a significance map of significant and insignificant
wavelet coefficients. Zerotrees are used to represent the significance map in an efficient way.
Figure 1 shows the Embedded Zerotree Scanning process.
FIGURE 1 Scanning of a Zerotree
3. EZW ENCODING ALGORITHM
1. Initialization: Set the threshold T to the smallest power of that is greater than max (i,j) |c i,j|/2,
where Ci,j are the wavelet coefficients.
2. Significance map coding: Scan all the coefficients in a predefined way and output a symbol
when |Ci,j | > T. When the decoder inputs this symbol, it sets ci,j = ±1.5T.

3. Refinement: Refine each significant coefficient by sending one more bit of its binary
representation. When the decoder receives this, it increments the current coefficient value by
±0.25T.
4. Set Tk = Tk-1/2, and go to step 2 if more iterations are needed [7-8].
The next scheme, called SPIHT, is an improved form of EZW which achieves better compression
and performance than EZW.
4. SET PARTITIONING IN HIERARICHAL TREES (SPIHT)
SPIHT sorts the coefficients and transmits their most significant bits first. A wavelet transform has
already been applied to the image and that the transformed coefficients are sorted.The next step
of the encoder is the refinement pass. The encoder performs a sorting step and a refinement step
in each iteration. SPIHT uses the fact that sorting is done by comparing two elements at a time,
and each comparison results in a simple yes/no result. The encoder and decoder use the same
sorting algorithm, the encoder can simply send the decoder the sequence of yes/no results, and
the decoder can use those to duplicate the operations of the encoder. The main task of the
sorting pass in each iteration is to select those coefficients that satisfy 2n<=|ci,j |<2n+1. This task
is divided into two parts. For a given value of n, if a coefficient ci,j satisfies |ci,j|>=2n, then that it is
said as significant; otherwise, it is called insignificant. The encoder partitions all the coefficients
into a number of sets Tk and performs the significance test.
………………………….eq. (1)
On each set Tk. The result may be either “no” This result is transmitted to the decoder. If the
result is “yes,” then Tk is partitioned by both encoder and decoder, using the same rule, into
subsets and the same significance test is performed on all the subsets. This partitioning is
repeated until all the significant sets are reduced to size 1. The result, Sn(T), is a single bit that is
transmitted to the decoder.
The sets Tk are created and partitioned using a spatial orientation tree. This set partitioning
sorting algorithm uses the following four sets of coordinates:
1. The set contain the coordinates of the four offspring of node is Off [i,j]. If node is a leaf of a
spatial orientation tree, then Off [i, j] is empty.
2. The set contain the set of coordinates of the descendants of node is called Des[i,j].
3. The set contain the set of coordinates of the roots of all the spatial orientation trees called R.
4. Next the set is a difference set Des[i,j]- Off[i,j]. This set contains all the descendants of tree
node except its four offspring as Diff [i,j].
The spatial orientation trees are used to create and partition the sets Tk. The partitioning rules
are given below:
1. Each spatial orientation tree need initial set.
2. If set Des[i, j] is significant, then it is partitioned into Diff[i, j] plus the four single element sets
with the four offspring of the node.
3. If Diff[i, j] is significant, then it is partitioned into the four sets Des[k, l], where k=1..4 of node .

FIGURE 2 Shows the Spatial Orientation Trees in SPIHT.
5. SPIHT Algorithm
It is important to have the encoder and decoder test sets for significance .So the coding algorithm
uses three lists called SP for list of significant pixels, initialized as empty, IP is list of insignificant
pixels for the coordinates of all the root node belongs to root set R, and IS is list of insignificant
sets to the coordinates of all the root node in R that have descendants and treated as special
type entries [5].
Procedure:
Step 1: Initialization: Set n to target bit rate.
for each node in IP do:
if Sn [ i, j] = 1,(according to eq 4.1)
move pixel coordinates to the SP and
keep the sign of ci,j ;
Step 2: for each entry in the IS do the following steps:
if the entry is root node with descendants
if Sn(Des[i, j]) = 1, then
for each offspring (k, i ) in Off[i, j] do:
if ( Sn(k, i) = 1) then
{ add to the SP,
output the sign of ck,l;}
else
attach (k, l) to the IP;
if (Diff[i, j] <> 0)
{move (i, j) to the end of the IS,
go to X;}
else
remove entry from the IS;
If the entry is root node without descendants then
output Sn(Diff[i, j]);
if Sn(Diff[i, j]) = 1, then
append each (k, l) in Off(i, j) to the IS as a special
entry and remove node from the IS:
Step 3: Refinement pass: for each entry in the SP, except those included in the last process for
sorting, output the nth most significant bit of |i,j|;
Step 4: Loop: reduced n by 1 and go to X if needed.

6. Experimental Results & Analysis
In this paper we have implemented our result on a grayscale virtual image named Humane Spine
having size (256X256) using various Wavelet filter families. Here we used MATLAB 2011(a)
software and wavelet toolbox for analysing our results. The results of experiments are used to
find the CR (Compression Ratio), BPP (Bits per Pixel), PSNR (Peak Signal to Noise Ratio) values
and MSE (Mean Square Error) values for the reconstructed images. Fig 3(a) shows the Original
Image and fig 3(b) shows the compressed image by EZW. Similarly fig 4(a) shows original image
and fig 4(b) shows the compressed image by SPIHT image compression algorithms. The result
got by EZW & SPIHT is shown in the Following Tables 1-2.Table 1 shows the results of CR, BPP,
MSE & PSNR by using EZW algorithm. Table 2 shows the values for SPIHT Algorithms.
FIGURE 3(a) Original Image 3(b) Compressed Image by EZW
FIGURE 4(a) Original Image 4(b) Compressed Image by SPIHT

Image ---Spine, Size---2.37 KB, Entropy--4.102
Wavelet CR BPP mse psnr
db
% Db
bior3.1 13.98 1.12 0.57 50.55
dmey 19.06 1.52 0.26 54.04
db8 19.13 1.53 0.26 53.98
sym5 17.91 1.43 0.27 53.89
coif2 17.91 1.43 0.47 51.46
rbio4.4 20.29 1.62 0.25 54.09
TABLE 1: Various Parameters Values of Different Wavelet for EZW Algorithm
Image ---Spine , Size---2.37 KB, Entropy--4.102
Wavelet CR BPP mse psnr
db% Db
bior3.1 8.73 0.7 0.61 50.29
dmey 7.85 0.63 0.42 51.94
db8 8.23 0.66 0.41 51.99
sym5 7.63 0.61 0.4 52.1
coif2 7.7 0.62 0.6 50.35
rbio4.4 8.77 0.7 0.38 52.32
TABLE 2: Various Parameters Values of Different Wavelet for SPIHT Algorithm
The graphical representation of CR, BPP, PSNR and MSE values are expressed as a bar graph
are shown in Fig. 5, 6, 7 and Fig. 8. The main features of EZW include compact multiresolution
representation of images by discrete wavelet transformation, zerotree coding of the significant
wavelet coefficients providing compact binary maps, successive approximation quantization of
the wavelet coefficients, adaptive multilevel arithmetic coding, and capability of meeting an exact
target bit rate with corresponding rate distortion function (RDF) [7]. The SPIHT method provides
highest image quality, progressive image transmission, fully embedded coded file, Simple
quantization algorithm, fast coding/decoding, completely adaptive, lossless compression.

FIGURE 5 Comparison Chart of CR using EZW & SPIHT Algorithms.
FIGURE 6 Comparison Chart of BPP using EZW & SPIHT Algorithms.

FIGURE 7 Comparison Chart of MSE using EZW & SPIHT Algorithms.
FIGURE 8 Comparison Chart of PSNR using EZW & SPIHT Algorithms.
7. CONCLUSION & FUTURE WORK
In this paper, the results of two different wavelet-based image compression techniques are
compared. The effects of different wavelet functions filter orders, number of decompositions,
image contents and compression ratios are examined. The results of the above techniques EZW
and SPIHT are compared by using four parameters such as CR, BPP, PSNR and MSE values
from the reconstructed image. These compression algorithms provide a better performance in
picture quality at low bit rates. We found from our experimental results that SPIHT is better
algorithm than EZW. Its results are 60-70% better than EZW as we can see from Table 1-2.We
have analyzed that CR is reduced. BPP is also low comparative to EZW.MSE is low and PSNR is
increased by a factor of 13-15%.as we can verify from our experiments. The above algorithms
can be used to compress the image that is used in the web applications. Furthermore in future we
can analyze different Image coding algorithms for improvement of different parameters.

8. REFERENCES
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Trans. Signal Processing, vol. 41, pp. 3445- 3462, 1993.
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[4] Bopardikar, Rao “Wavelet Transforms: Introduction to Theory and Applications.”
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2010
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[8] Loujian yong, Linjiang, Du xuewen “Application of Multilevel 2- D wavelet Transform in Image
Compression”. IEEE Trans on 978-1-4244-3291-2, 2008.
[9] Javed Akhtar, Dr Muhammad Younus Javed “Image Compression With Different Types of
Wavelets” IEEE Trans on Emerging Technologies, Pakistan, Nov 2006.
[10] Rafael C. Gonzalez and Richard E. Woods, “Digital Image Processing”, 2nd Edition,
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[11] Khalid Sayood, “Introduction to Data Compression”, 3rd Edition 2009
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