IMAGE COMPRESSION USING SOFM AND SPIHT WITH

WAVELET

PROJECT GUIDE:

Mr.Sivaprakash M.E.,

Assistant professor.

Submitted by

M.Aarathy

Presentation Details Abstract Image Compression Project Description Wavelet Transform Sub band Decomposition Vector Quantization Self Organizing Feature Map of Kohonen Image Reconstruction Bibliography

i) Abstract The main objective of this project is to implement

the concept of wavelet based compression to gray scale images using two different techniques namely SOFM and SPIHT

Wavelet Transform is a superior approach to other time frequency analysis tools because its time scale width of the window can be stretched to match the original signal especially in image analysis.

It is more advantageous than the Fourier transform

By using SOFM technique,we have made an attempt in employing lossy technique i.e., Vector Quantisation to encode the sub bands formed by the application of wavelet Transform.

ii

In the second Technique,ROI coding functionality is incorporated with the set partitioning in hierarchical trees algorithm for wavelet based image coding.

Both the Compression Techniques use wavelet transform output as the input for SOFM and SPIHT encoding.

Image Compression Image compression operation reduce the data

content of a digital image and represent the image in more compact form,usually before storage or transmission.

Compression Techniques are classified as • Loss less• Lossy

Lossy Compression results in the decompressed image being similar but not the same as the original image.

Much higher compression is achievable,and under normal viewing conditions,no visible loss is perceived

Project Description The Main Objective of this project is to implement

the concept of wavelet based compression to gray scale images.Vector quantisation is used to encode the sub bands formed by the application of wavelet Transform

We have also used a clustering property of self organizing Feature Map of Kohonen,an unsupervised training algorithm formulated by Kohonen.

Sofm serves as a tool for selecting the best vectors as they are being trained and the codebooks are formed using the trained vectors.Instead of storing the grayscale image,we store only the codebook and their corresponding index values.This reduces the space required to store the image,hence the compression of the image is achieved

Block Diagram representation of the compression algorithm

Input Image

Sub band Decomposition using wavelet

Vector Quantisation of the Sub bands

Code book formation using SOFM

a

Storage of the codebook and their indices

a

Mapping of index values with the code vectors

Application of IDWT on the index mapped code vectors

Arranging the sub bands in proper order

Reconstructed image

Wavelet Transform A wavelet is a waveform of effectively limited

duration. Wavelet is a small wave,which has its energy

concentrated in time to give a tool for the analysis of time varying phenomena.wavelets are suited to modeling phenomena whose signals are not continuous.

wavelets are well suited for approximating data with sharp discontinuities.

Wavelets not only have an oscillating characteristic but also have the ability to allow simultaneous time and frequency analysis with a flexible mathematical foundation.

According to wavelet transformation,a function,which can represent an image,a curve,signal etc.,can be described in terms of a coarse level description in addition to others with details

Wavelets are constructed by considering a complex valued window function (t) called the Mother Wavelet or a Basic Wavelet.

The compressed version packs all its oscillation in a small interval while the stretched version spreads them.

Discrete Wavelet Transform: The Discrete wavelet Transform of a finite

length signal x(n) having N components.Each wavelet coefficient represents information in a certain frequency range at a certain spatial location.

Its basis function is a scale varying function,which can be used to extract information from a given function at different scales.

The important application of wavelets is separating the smooth variations and details of the image,which is done by wavelet decomposition of the image using DWT.

Advantages of DWT: It is fast,linear in its operation. Invertible and orthogonal,hence

reconstruction is easier Window size is variable They are capable of providing the time and

frequency information simultaneously.

Wavelet Filter Coefficients: A Particular set of wavelets is specified by the

particular set of numbers called wavelet filter coefficients.

Any input signal f(t) can be expressed in the notation for wavelet transform as:

f(t)= cj(k) (2j t-k) + dj (2j t-k)

where,

cj(k) are the approximation coefficients

dj(k) are the detail coefficients

(t) is the scaling function

(t) is the wavelet function

Haar Scaling Function:

The Haar scaling function is the simple unit-width,unit-length,pulse-function can be used to construct (t) by

(t)= (2t)+ (2t-1) with the scaling coefficient h(n)

1 0 t

Sub band Decomposition Images being a two dimensional matrix,filtering

is applied to both horizontal and vertical elements of the image matrix.

To begin the decomposition, the input image is divided into sub bands and sub sampled.Each coefficient represents a spatial area corresponding to approximately a 2X2 area of the original image.

The total number of components we have after vertical and horizontal decompositions is four.These components are referred as sub bands.

Sub bands arranged after two level

decomposition

LL LH

HL HH

LL LH

HL HH

Parent

Children

Schematic of a vector quantisation block

Group into Vectorblocks

Input image Sub band

Find ClosestCode-Vector

--- Look up Table

--

Reconstruction

Unblock

Decoder

Encodercodebook

Index

codebook Index

Advantage and Disadvantage of VQ

Advantages: For a given rate,use of Vector Quantisation

results in a lower distortion Higher compression is achieved

Disadvantage: Changing either the block size or the codebook

size will allow the compression ratio to vary,but involves the training and storage of many code books.

Large memory is required

Self Organizing Feature Map Of Kohonen Self Organizing Feature Map (SOFM) developed

by Kohonen is an unsupervised training algorithm.

In unsupervised learning,the NET seeks to find patterns of regularity of the input data without the aid of the tutor.

We have used to train the vectors formed from each sub band and to select the best vector to form the code book.

The new weight vectors can be found by

Wj(new)=Wj (old)+ [x-wj(old)] X----input vector

wj----weight vector for unit j ---Learning rate coefficient

Image ReconstructionCodebook Remapping: In the reconstruction segment i.e., at the

decoder or decompressor,the code vectors are arranged according to the indices.

The resulting output will be an approximation of the input image.In this approximate image,the sub bands are only obtained.To get the reconstructed image,the approximate image should be subjected to IDWT

Reconstruction using IDWT: Reconstruction of the original image

coefficients can be obtained from a combination of the scaling function and wavelet coefficient.

The filter pair used here is called as synthesis filter.

Bibliography Books: 1.A primer on wavelets by James.s.Walker. 2. Digital Image Processing by Gonzalez. 3. Neural Networks and Application by Lauren Facet.

Website: www.wavelet.org www.sanbi.ac.za/tdrcourse/materials.html

IEEE Reference:• “ Initialization and Training Methods for Kohonen

Self Organizing Feature Map in Image Quantization” by Xiao Rei, chip-Hong Chang.

• “Image Compression by Vector Quantisation”by Robert.S.H

Wavelet Transform Output

Input image Single Decomposition output

Compression Output

Literature SurveyTill Date: