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SIDDAGANGA INSTITUTE OF TECHNOLOGYDEPARTMENT OF ELECTRONICS AND COMMUNICATION
ENGINEERING
PRESENTATION
ON
SPIHT ALGORITHM
BY
NEERAJ KUMAR (1SI09EC061)
UNDER THE GUIDANCE OF
SWETHA N. , M.Tech.,
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CONTENTS
INTRODUCTION
OBJECTIVE
IMAGE COMPRESSION
WAVELET TRANSFROM WAVELET DECOMPOSITION
SPIHT CODEC
FLOW CHART
NUMERICAL RESULTS
APPLICATIONS
CONCLUSION
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INTRODUCTION
It is a fast and efficient method with good image quality,
high PSNR, especially for color images.
Produces a fully embedded coded file.
Simple quantization algorithm.
Fast coding/decoding algorithm.
It can be used for lossless compression.
It can code to exact bit rate or distortion.
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OBJECTIVE
Digital information must be stored, retrieved, analyzed
and processed in an efficient manner, in order for it to be
put to practical use.
The bandwidth required to transmit the image of size
720*1280 pixels is very large so we need to compress
these images in order to transmit them without wasting
the bandwidth.
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IMAGE COMPRESSION
Image compression is technique under image processing
having wide variety of applications.
The fundamental components of compression are
redundancy and irrelevancy reduction.
Redundancy means duplication.
Irrelevancy means the parts of signal that will not be
noticed by the Human Visual System. Image compression focuses on reducing the number of
bits needed to represent an image.
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WAVELET TRANSFORM
It is used to provide multiresolution analysis.
The DWT analyzes the signal at different frequency
bands with different resolutions by decomposing the
signal into a coarse approximation and detail
information.
It employs two sets of functions, called scaling functions
and wavelet functions, which are associated with low
pass and high pass filters.
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Fig 3:-DWT coefficients at different levels
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WAVELET DECOMPOSITION
The level of decomposition is given by: - level=log2n,
n is the number of pixels in a given row or column.
It produce a pyramid structure where an image isdecomposed sequentially by applying low pass and high
pass filters and then decimating the resulting images.
These are one-dimensional filters that are applied incascade (row then column) to an image.
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Fig 4:- Image decomposition using wavelets
It creates a four-way decomposition: LL, LH, HL and
finally HH The resulting LL version is again four-way
decomposed. This process is repeated until the top of the
pyramid is reached.
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SPIHT CODEC
There exists a spatial relationship among thecoefficients
at different levels in the pyramid structure.
A wavelet coefficient at location (i,j) in the pyramid
representation has four direct descendants (off-springs)
at locations:
O(i,j)={(2i,2j),(2i,2j+1),(2i+1,2j),(2i+1,2j+1)} This pyramid structure is commonly known as spatial
orientation tree.
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Fig 5:-: Off-spring dependencies in the pyramid structure
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ENCODING/DECODING ALGORTIHM
O(i,j): set of coordinates of all offspring of node (i,j);
children only
D (i,j): set of coordinates of all descendants of node (i,j);
children, grandchildren, great-grand, etc.
H (i,j): set of all tree roots (nodes in the highest pyramid
level);parents L (i,j): D (i,j) O(i,j) (all descendents except the
offspring);grandchildren, great-grand, etc.
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Initialization:-
n = log2 (max |coeff|)
LIP = All elements in H
LSP = Empty
LIS = Ds of Roots
Step 1: Initialization: Set n to target bit rate.
for each node in LIP do:
if Sn [ i, j] = 1,move pixel coordinates to the LSP and
keep the sign of c(i,j) ;
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Significance Map Encoding (Sorting Pass)
Process LIP
for each coeff (i,j) in LIPOutput Sn(i,j)
If Sn(i,j)=1, Output sign of coeff(i,j): 0/1 = -/+
Move (i,j) to the LSPEnd if
End loop over LIP
Process LIS
for each set (i,j) in LIS
if type D
Send Sn(D(i,j))
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If Sn(D(i,j))=1
for each (k,l) O(i,j), output Sn(k,l)
if Sn(k,l)=1,
then add (k,l) to the LSP and output sign of coeff: 0/1 = -/+
if Sn(k,l)=0, then add (k,l) to the end of the LIP
end for
End if
else (type L )
Send Sn(L(i,j))
If Sn(L(i,j))=1
add each (k,l) O(i,j) to the end of the LIS as an entry of type D
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remove (i,j) from the LIS
end if on type
End loop over LIS
Refinement Pass
Process LSP
for each element (i,j) in LSPexcept those just added above
Output the nth most significant bit of coeff
End loop over LSP
Update
Decrement n by 1
Go to Significance Map Encoding Step
..\kedia\SPIHT_Charts.pdf
http://localhost/var/www/apps/conversion/tmp/kedia/SPIHT_Charts.pdfhttp://localhost/var/www/apps/conversion/tmp/kedia/SPIHT_Charts.pdfhttp://localhost/var/www/apps/conversion/tmp/kedia/SPIHT_Charts.pdfhttp://localhost/var/www/apps/conversion/tmp/kedia/SPIHT_Charts.pdfhttp://localhost/var/www/apps/conversion/tmp/kedia/SPIHT_Charts.pdfhttp://localhost/var/www/apps/conversion/tmp/kedia/SPIHT_Charts.pdf7/30/2019 Major Final Ppt
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FLOW CHART
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NUMERICAL RESULTS
Fig 6: Compression of Lena color image with rate=1
PSNR:
P1=34.7835
P2=35.2734
P3=34.5560
TOTAL=34.8710
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Fig 7: Compression of cameraman image with rate=1
PSNR:
db1-35.05
db4-35.04
bior4.4-35.56sym2-34.93
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Comparison of different images
RATE/
IMAGES
1.0 bpp 0.75bpp 0.5bpp 0.25bpp
Lena.jpeg 34.8710 32.9807 30.3955 27.2055
Sunset.jpeg 39.1100 37.7216 35.7141 32.8820
Fruits.jpeg 34.2636 32.5162 30.1835 27.0384
Tulips.jpeg 33.4383 31.1407 28.7387 25.3465
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Results on Lena image
COMPONENT
/
RATE
Y Cb Cr
1 1 1 34.8735 35.2734 34.5560
0.5 0.5 0.5 30.3266 30.4771 30.3827
1 0.5 0.5 34.6729 35.1478 34.4722
1 0.2 0.2 34.2094 34.9236 33.5824
0.5 1 1 30.3674 30.5519 30.2674
0.2 1 1 26.5395 26.5875 26.4919
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Results on grayscale image
RATE/FILTERS
1.0 bpp 0.75bpp 0.5 bpp 0.25bpp
db1 35.05 32.26 29.68 26.46
coif1 35.07 32.44 29.94 26.50
sym2 34.93 32.28 29.69 26.39
bior4.4 35.56 33.01 30.50 27.13
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COMPARISON OF EZW & SPIHT
RATE COMPRESSION EZW SPIHT
1.0 8:1 39.55 39.92
0.5 16:1 36.28 36.68
0.25 32:1 33.17 33.38
0.125 64:1 30.23 30.40
0.0625 128:1 27.54 27.69
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APPLICATIONS
SPIHT has been successfully tested in natural (portraits,
landscape, weddings, etc.) and medical (X-ray, CT, etc)
images.
It is effective in a broad range of reconstruction qualities. It
can code fair-quality portraits and high-quality medical
images equally well.
It is used in compression of elevation maps, scientific data.
It is also being used in case of ECG signals.
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CONCLUSION
SPHIT algorithm uses the principle of partial ordering by
magnitude, set partitioning by significance of magnitudes
with respect to a sequence of octavely decreasing threshold,
ordered bit-plane transmission, and self-similarity acrossscale in an image wavelet transform.
The realization of these principles in matched encoding and
decoding algorithms is a new one and is shown to be effectivethan in previous implementations of EZW algorithm.
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REFERENCE
AMIR SAID AND WILLIAM A. PEARLMAN, ANew, Fast, and
Efficient Image Codec Based on Set Partitioning in Hierarchical
Trees. IEEE Transaction on circuits & systems for video
technology Vol. 6 No. 3, 1996.
J. M. Shapiro, Embedded image coding using zerotrees of wavelet
coefficients. IEEE Trans. Signal Processing vol.41 pp 3445-3462,
Dec 1993.
ALDO MORALES AND SEDIG AGILI, Implementingthe SPIHT
Algorithm in MATLAB.Proceedings of the 2003 ASEE/WFEO
International Colloquium
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J. MAL, P. RAJMIC,DWT-SPIHT image codec
implementation.
JAMES S. WALKER, Wavelet-based Image
Compression.
KAHLID SAYOOD, SPIHT_CHARTS.
ROBI POLIKAR,Wavelettutorial.
WAVELETTRANSFORMS by Raghuveer M Rao. FUNDEMENTALS OF MULTIMEDIA by Ze-Nian
Li and Mark S Drew.
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THANK YOU
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ANY QUERRIES???