Major Final Ppt

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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.pdf


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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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