IMAGE COMPRESSION USING SOFM AND SPIHT WITH WAVELET

1. IMAGE COMPRESSION USING SOFM AND SPIHT WITH WAVELET PROJECT GUIDE: Mr.Sivaprakash M.E., Assistant professor. Submitted by M.Aarathy

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

3. 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.

4. 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.

5. 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

6. 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

7. 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

8. a Storage of the codebook and their indices 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

9. 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.

10. 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.

11. 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.

12. 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

13. 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) t 0 1

14. 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.

15. Sub bands arranged after two level decomposition LH Parent LL LH LL HL HH Children HL HH

16. Schematic of a vector quantisation block Find Closest Code-Vector Group into Vector blocks Index Decoder Reconstruction Unblock --- Look up Table Input image Sub band Encoder codebook -- codebook Index

17. 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

18. 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

19. Image Reconstruction Codebook 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.

20. 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

21. Wavelet Transform Output Input image Single Decomposition output

22. Compression Output

23. Literature Survey Till Date: