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IMAGE COMPRESSION BY EZW COMBINING HUFFMAN AND ARITHMETIC ENCODER

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IMAGE COMPRESSION BY EZW COMBINING HUFFMAN AND ARITHMETIC ENCODER Powered By Docstoc
					  International Journal of JOURNAL OF COMPUTER (IJCET), ISSN 0976-
 INTERNATIONALComputer Engineering and Technology ENGINEERING
  6367(Print), ISSN 0976 – 6375(Online) Volume 4, Issue 3, May – June (2013), © IAEME
                          & TECHNOLOGY (IJCET)

ISSN 0976 – 6367(Print)
ISSN 0976 – 6375(Online)                                                  IJCET
Volume 4, Issue 3, May-June (2013), pp. 297-307
© IAEME: www.iaeme.com/ijcet.asp
Journal Impact Factor (2013): 6.1302 (Calculated by GISI)
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      IMAGE COMPRESSION BY EZW COMBINING HUFFMAN AND
                   ARITHMETIC ENCODER

                                      K.P.Paradeshi
              Associate Professor, Department of Electronics Engineering, PVPIT,
                                 Budhgaon,State-Maharashtra


  ABSTRACT

          The objective of an image compression algorithm is to exploit the redundancy in an
  image such that a smaller number of bits can be used to represent the image while
  maintaining an “acceptable” visual quality for the decompressed image. The embedded zero
  tree wavelet algorithms (EZW) is a simple, yet remarkably effective, image compression
  algorithm, having the property that the bits in the bit stream are generated in order of
  importance, yielding a fully embedded code. EZW is computationally very fast and among
  the best image compression algorithm known today. This paper proposes a technique for
  image compression which uses the Wavelet-based Image Coding in combination with
  Huffman and Arithmetic encoder for further compression. Implementation of Huffman
  coding followed by arithmetic compression gives another 15% extra compression ratio.

  Key Words: Image Compression, DWT, Embedded Zero tree Wavelet (EZW), Huffman
  Encoder, Arithmetic Encoder.

  I. INTRODUCTION

  A. Introduction
          Image compression can improve the performance of the digital systems by reducing
  time and cost in image storage and transmission without significant reduction of the image
  quality. Image compression is very important in many applications, especially for progressive
  transmission, image browsing and multimedia applications. The whole aim is to obtain the
  best image quality and yet occupy less space. Embedded zero tree wavelet compression
  (EZW) is a kind of image compression that can realize this goal. EZW algorithm is fairly
  general and performs remarkably well with most types of images. Also, it is applicable to

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transmission over a noisy channel. Discrete wavelet transform (DWT) become a cutting edge
technology in image data compression. Image compression is typically comprised of three
basic steps. Firstly, the image is transformed into wavelet coefficients which are then
quantized in a quantizer and finally threshold which makes the coefficient smaller than a
chosen threshold value (zero) obtained from the quantizer. As a result, some bits are reduced
producing an output bit stream [2].
         The main contribution of EZW encoding with Huffman and Arithmetic Encoder is
that it visually improves the compression of an image by increasing the decomposition level 8
as compared to the paper Shapiro, J. M. R. B., 1993, “Embedded Image Coding Using
Zerotrees of Wavelet Coefficients”[1]. decoder “where” the few non-zeros are!!! Significance
map (SM): binary array indicating location of Zero/non zero Coefficients. Typically requires
a large fraction of bit budget to specify the SM.Wavelets provide a structure (zerotrees) to the
SM that yields efficient coding

B. WAVELET TRANSFORMATION OF IMAGES
        Wavelets [7] are mathematical functions that decompose data into different frequency
components, and then study each component with a resolution matched to its scale. They
have advantages over traditional Fourier methods [4] in analyzing physical situations where
the signal contains discontinuities and sharp spikes. Wavelets were developed independently
in the fields of mathematics, quantum physics, electrical engineering, and seismic geology.
Interchanges between these fields during the last ten years have led to many new wavelet
applications such as image compression, turbulence, human vision, radar, and earthquake
prediction.
        The wavelet transformation [7] is a mathematical tool for decomposition. The wavelet
transform is identical to a hierarchical sub band filtering system [3], where the sub bands are
logarithmically spaced in frequency. The basic idea of the DWT for a two-dimensional image
is described as follows. An image is first decomposed into four parts based on frequency sub
bands, by critically sub sampling horizontal and vertical channels using sub band filters and
named as Low-Low (LL), Low-High (LH), High- Low (HL), and High- High (HH) sub bands
as shown in figure 1.




                                Figure 1: Wavelet Transform

        Each level has various bands information such as low–low, low–high, high–low, and
high–high frequency bands. Furthermore, from these DWT coefficients, the original image
can be reconstructed. This reconstruction process is called the inverse DWT (IDWT). If C
[m, n] represents an image, the DWT and IDWT on each dimension and separately

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C. Why Wavelets?
        Traditional DCT & sub band coding: trends “obscure” anomalies that carry
information. E.g., edges get spread, yielding many non-zero coefficients to be coded.
Wavelets are better at localizing edges and other anomalies Yields a few non-zero
coefficients & many zero coefficients Difficulty: telling the decoder “where” the few non-
zeros are!!! Significance map (SM): binary array indicating location of Zero/non zero
Coefficients. Typically requires a large fraction of bit budget to specify the SM.Wavelets
provide a structure (zero trees) to the SM that yields efficient coding

D. EZW ENCODING
        EZW encoder was originally designed to operate on images (2D-signals) but it can
also be used on other dimensional signals. It is based on progressive encoding to compress an
image into a bit stream with increasing accuracy. This means that when more bits are added
to the stream, the decoded image will contain more detail, a property similar to JPEG
encoded images. Using an embedded coding algorithm, an encoder can terminate the
encoding at any point thereby allowing a target rate or target accuracy to be met exactly [5,
6]. The EZW algorithm is based on four key concepts: 1) a discrete wavelet transform or
hierarchical sub band decomposition, 2) prediction of the absence of significant formation
across scales by exploiting the self-similarity inherent in images, 3) entropy-coded successive
approximation quantization, and 4) universal lossless data compression which is achieved via
adaptive Huffman encoding [8].

The EZW encoder is based on two important observations

      1. Natural images in general have a low pass spectrum. When an image is wavelet
transformed the energy in the sub bands decreases as the scale decreases (low scale means
high resolution), so the wavelet coefficients will, on average, be smaller in the higher sub
bands than in the lower sub bands. This shows that progressive encoding is a very natural
choice for compressing wavelet transformed images, since the higher sub bands only add
detail [8].
    2. Large wavelet coefficients are more important than small wavelet coefficients.

       These two observations are exploited by encoding the wavelet coefficients in
decreasing order, in several passes. For every pass a threshold is chosen against which all the
wavelet coefficients are measured. If a wavelet coefficient is larger than the threshold it is
encoded and removed from the image, if it is smaller it is left for the next pass. When all the
wavelet coefficients have been visited the threshold is lowered and the image is scanned
again to add more detail to the already encoded image. This process is repeated until all the
wavelet coefficients have been encoded [7].

E. Concept of Zerotree
        A wavelet transform transforms a signal from the time domain to the joint time-scale
domain. i.e. the wavelet coefficients are two-dimensional. To compress the transformed
signal not only the coefficient values, but also their position in time has to be coded. When
the signal is an image then the position in time is better expressed as the position in space.
After wavelet transforming an image it can be represented using trees because of the sub
sampling that is performed in the transform. A coefficient in a lower sub band can be thought

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of as having four descendants in the next higher sub band as shown in Figure 2 the four
descendants each also have four descendants in the next higher sub band, which gives a quad
tree, with every root having four leafs [9].
        A zero tree is defined as a quad-tree of which all nodes are equal to or smaller than
the root and the root is smaller than the threshold against which the wavelet coefficients are
currently being measured. The tree is coded with a single symbol and reconstructed by the
decoder as a quad-tree filled with zeroes [10]. The EZW encoder codes the zero tree based on
the observation that wavelet coefficients decrease with scale. In a zero tree all the coefficients
in a quad tree are smaller than the threshold if the root is smaller than this threshold. Under
this case the whole tree can be coded with a single zero tree (T) symbol [11].




      Figure 2: The relation between wavelet coefficients in sub bands as quad tree


                              Raster Scan               Morton Scan




          Figure 3: Different scanning patterns for scanning wavelet coefficients

        A scanning of the coefficient is performed in such a way that no child node is scanned
before its parent. For an N scale transform, the scan begins at the lowest frequency sub band,
denoted as LLN, and scans sub bands HLN, LHN, and HHN, at which point it moves on to
scale N-1 etc.[12] The two such scanning patterns for a three-scale pyramid can be seen in
Figure 2. Note that each coefficient within a given sub band is scanned before any coefficient
in the next sub band Given a threshold level T to determine whether a coefficient is
significant, a coefficient x is said to be an element of a zero tree for threshold T if itself and
all of its descendents are insignificant with respect to T. An element of a zero tree for
threshold T is a zero tree root if it is not the descendents of a previously found zero tree root
for threshold T, i.e., it is not predictably insignificant from the discovery of a zero tree root at

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a coarser scale at the same threshold[13]. A zero tree root is encoded with a special symbol
indicating that the insignificance of the coefficient at finer scales is completely predictable.
The significance map can be efficiently represented as a string of symbols from a 3-symbol
alphabet which is then entropy encoded [14].

F. HUFFMAN CODING
         Huffman coding is an entropy encoding algorithm used for lossless data compression.
The term refers to the use of a variable-length code table for encoding a source symbol (such
as a character in a file) where the variable length code table has been derived in a particular
way based on the estimated probability of occurrence for each possible value of the source
symbol. It uses a specific method for choosing the representation for each symbol, resulting
in a prefix code that expresses the most common source symbols using shorter strings of bits
than are used for less common source symbols.
         The Huffman algorithm is based on statistical coding, which means that the
probability of a symbol has a direct bearing on the length of its representation. The more
probable the occurrence of a symbol is, the shorter will be its bit-size representation. In any
file, certain characters are used more than others. Using binary representation, the number of
bits required to represent each character depends upon the number of characters that have to
be represented. Using one bit we can represent two characters, i.e., 0 represents the first
character and 1 represents the second character. Using two bits we can represent four
characters, and so on[10].
         Unlike ASCII code, which is a fixed-length code using seven bits per character,
Huffman compression is a variable-length coding system that assigns smaller codes for more
frequently used characters and larger codes for less frequently used characters in order to
reduce the size of files being compressed and transferred[15].

G. ARITHMATIC CODING
        Arithmetic coding bypasses the idea of replacing an input symbol with a specific
code. It replaces a stream of input symbols with a single floating-point output number. More
bits are needed in the output number for longer, complex messages. This concept has been
known for some time, but only recently were practical methods found to implement
arithmetic coding on computers with fixed-sized registers.
        The output from an arithmetic coding process is a single number less than 1 and
greater than or equal to 0. This single number can be uniquely decoded to create the exact
stream of symbols that went into its construction [16].

I.IMPLEMENTATION

A. wavelet basis choosing

        Many issues relating to the choice of filter bank for image compression remain
unresolved. Constraints on filter bank include perfect reconstruction, finite-length, and the
regularity requirement that the iterated low pass filters involved converge to continuous
functions. According to [17], it shows that the bi orthogonal wavelet filter banks have a very
good performance for wavelet image compression. They have good localization properties as
well as their symmetry allows for simple edge treatments. They also produce good results
empirically since the original paper on EZW is using this wavelet basis. Moreover, using

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properly scaled coefficients, the transformation matrix for a discrete wavelet transforms
obtained using these filters is so close to unitary that it can be treated as unitary for the
purpose of lossy compression.

B. EZW coding algorithm
Coding the wavelet coefficients is performed by determining two lists of coefficients:

1. The dominant list D contains information concerning significance of coefficients, which
will be coded using Huffman encoding followed by arithmetic coding for further compression
2. The significant list S contains the amplitude values of the significant coefficients, which
will undergo uniform scalar quantization followed by Huffman arithmetic coding.




           Figure 4: Example of decomposition to three resolutions for an 8*8 matrix


Significance test

        The wavelet transform coefficients are scanned for the path as shown in the fig below.
In our implemented method, we used Mortan scan as show in Figure 5, which is more
accurate and produces standard results




                    Figure 5: Mortan scanning scheme in EZW algorithm

Each coefficient is assigned a significance symbols (P, N, Z, T), by comparing with the actual
threshold.


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     1. P (significance and positive): if the absolute value of the coefficient is higher than
         the threshold T and is positive.
     2. N (significance and positive): if the absolute value of the coefficient is higher than
         the threshold T and is negative.
     3. T (zerotree): if the value of the coefficient is lower than the threshold T and has only
         insignificant descendants4. Z (isolated zero): if the absolute value of the coefficient
         is lower than the threshold T and has one or more significant descendents.
        The insignificant coefficients of the last sub bands, which do not accept descendents
and are not themselves descendents of a zerotree, are also considered to be zero tree.The
significance symbols are then placed in a list D which is subjected to Huffman encoding
followed by Arithmetic encoding.The dominant list and the significance list are shown
below: The dominant list and the significance list are shown below:

   D1: P N Z T P T T T T Z T T T T T T T P T T
   S1: 1 0 1 0
   D2: Z T N P T T T T T
   S2: 1 0 0 1 1 0

C. Huffman coding algorithm

The steps involved in encoding dominant list D is as follows:

5. In the dominant list since the probability of occurrence of the symbol T is more when
compared to others, this symbol should be coded with the less number of bits.

6. The other symbols probability of occurrence are less when compared to the symbol T, they
should be coded with more number of bits.

7. After encoding all the symbols with binary digits, a separator is appended to the end of the
encoded bit stream to indicate the end of the stream.

For e.g.:

In the said algorithm to encode the symbols P, N, Z and T we used the binary bits as follows:

P is encoded as 1110

N is encoded as 110

Z is encoded as 10

Since the probability of occurrence is less when compared to T.

T is encoded as 0 (since the probability of occurrence is more when compared to other bits)

Then we insert a separator bits i.e. a stream of 1 s .Here
We used 11111 to indicate the end of the bit stream

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8. After getting bit stream, it converts into decimal number and then converts decimal number
into character to get resultant byte stream

For e.g. 65 coded as A

D. Arithmetic coding algorithm
9. The system model, T, keeps record of the symbols that have been encoded. Based on this
table the probability of each symbol is estimated. Probability for symbol m is: (T (m+1)-T
(m+2))/T 10. Once character probabilities are known, individual symbols need to be assigned
a range along a “probability line,” nominally 0 to 1. It doesn’t matter which characters are
assigned which segment of the range, as long as it is done in the same manner by both the
encoder and the decoder. Each character is assigned the portion of the 0 to 1 range that
corresponds to its probability of appearance.

For e.g. Character Probability     Range
            A         1/10          0.10


II. EXPERIMENTS AND RESULTS

A. performance of EZW algorithm
        Firstly, original image is applied to the compression program, EZW encoded image is
obtain, which is further compressed by combining Huffman and Arithmetic. To reconstruct
compressed image, compressed image is applied to decompression program, by which EZW
decoded image is obtained. Compression Ratio (CR) and Peak-Signal-to-Noise Ratio (PSNR)
are obtained for the original and reconstructed images. In the experiment the original image
“Lena.bmp” having size 256 x 256 (65,536) Bytes). The different statistical values of the
image Lena.jpg for Various Thresholds are summarized in the table.

                    Image: Lena.bmp               Image Size: 256x256
            Parameter              TH=5       TH=10       TH=20      TH=30       TH=60
   Original File Size(byte)        66614      66614       66614      66614       66614
   Compressed File Size(byte)      17852       10075       5181         5181      2328
   Compression Ratio(CR)             3.4          5.9      11.5         11.5      25.9
   Compression Ratio                 3.7          6.6      12.9         12.9      28.6
   Bits Per Pixel(Bpp)              2.40        1.37       0.71         0.71      0.31
   Peak-Signal-to–noise Ratio      27.79       27.85       27.65        26.61     26.21
   (PSNR)(db)
   Encoding Time (sec)             127.8       87.82       60.19        52.91     27.72
   Decoding Time (sec)             334.1       293.5      152.15        140.7     90.63
   Total Time(sec)                 462.3       353.6      212.34        193.6     118.3



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Discussion: As mentioned previously, one of the advantages of EZW is that it encodes the
image from lossy to lossless in one algorithm. People at the receiver can choose the quality of
the image by control the bit budget. As the bit rate increases, you will get more detailed
information and of course the image quality becomes better and better. Figure 6 shows this
procedure. You can clearly observe some block effect at the lower bit budget; this is due to
our implementation in MATLAB which is very slow doing large number of for loop. Figure 7
shows the threshold vs. CR (compression ratio) curve.




                      Figure.6 Decoded image given different bit budget.
                Left top: highest bit rate (bpp), Right bottom: lowest bit rate (bpp)


                                     Threshold Vs CR
           35
           30
           25
                                                                        Huffman encoder
       C   20
       R   15
           10                                                           Combine Huffman and
            5                                                           Arithmatic encoder
            0
                     5        10         20       30        60
                                        Threshold


                                   Figure 7 Thresholds vs. CR



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       The curves of Threshold Verses CR have been calculated and depicted in the figure.7.
In which Image encoded using EZW algorithm for 8 level decomposition and compressed
using combining Huffman and Arithmetic gives better BPP and PSNR values than Image
Compressed directly using Huffman Encoder.

III. CONCLUSION

        A technique for image compression which uses the Wavelet based Image Coding in
combining Huffman and Arithmetic encoding is proposed here. This approach utilizes zero
tree structure of wavelet coefficients at decomposition level 8 with combining Huffman and
Arithmetic encoder is very effectively, which results in higher compression ratio . The
algorithm is tested on different images , and it is seen that the results obtained by Image
encoded using EZW algorithm and compressed using combining Huffman and Arithmetic
are consistently better than these obtained by Image Compressed directly using Huffman
Encoder. It is also observed that the results are better than these reported Earlier.
Furthermore, since no training of any kind is required, the algorithm is fairly general and
performs remarkably well with most types of images.

REFERENCES

[1] Still Image Compression by Combining EZW Encoding with Huffman Encoder ,Janaki. R
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[12] Uytterhoeven G., “Wavelets: Software and Applications”, U. Leuven Celestijnenlaan,
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