M.Tech(DE)Project-B.B.S.Kumar

Image Analysis Using WaveletsImage Analysis Using WaveletsBy By

BeeraBeera BabuBabu SrinivasSrinivas KumarKumar

USN: USN: 2BV04LDE052BV04LDE05

M.TechM.Tech(DE)(DE)

Under the Under the GuidancesGuidances ofof

Mr.R.B.SHETTARMr.R.B.SHETTAR Mrs.SILVIMrs.SILVI JAGANATHJAGANATH

Asst. Professor, Manager, IT Group,Asst. Professor, Manager, IT Group,BVBCET, HubliBVBCET, Hubli--31 ITI Ltd., Bangalore31 ITI Ltd., Bangalore--1616

PROJECTPROJECT OVERVIEWOVERVIEW

� Introduction

� Image Decomposition, Reconstruction & Compression

� Image Denoising� Image Denoising

� Algorithms

� Experimental Results

� Conclusion

INTRODUCTIONINTRODUCTION

� Objective

� To investigate the still image compression and denoising of a gray scale image using different wavelets families.

� The “Image Analysis Using Wavelets” is implemented in software � The “Image Analysis Using Wavelets” is implemented in software using MATLAB7 version Wavelet Toolbox and 2-D DWT technique.

� The main framework of this project-comparing the results of wavelet families & knowing the best wavelet.

� Wavelet

� The Wavelets are functions that satisfy certain mathematical requirements and are used in representing data.

� The wavelet provides powerful insight into spatial and frequency characteristics of an image.

� The Fourier transform, on the other hand, reveals only frequency attributes of an image.

� The advantages over Fourier methods in analyzing physical situations where the signal contains discontinuities and sharp spikes.

� The DWT

� Separability, Scalability and Translatability� Multiresolution Compatibility� Orthogonality

IMAGE DECOMPOSITION, IMAGE DECOMPOSITION,

RECONSTRUCTION & COMPRESSIONRECONSTRUCTION & COMPRESSION

�� DecompositionDecomposition

Figure: 2D Decomposition Wavelet Analysis

Figure: Decomposition levels of Subsignal

Figure: 2-D DWT

�� ReconstructionReconstruction

Figure: 2-D IDWT

Figure: 2-D DWT Decomposition: a) Original image, b) One level decomposition, c) Two levels decomposition, d) Three levels

decomposition

�� CompressionCompression

� Reducing the amount of data required to represent a digital image. Compression is achieved by the removal of one or more of three basic data redundancies.

� Coding Redundancy -which is present when less than optimal (i.e., the smallest length) code words are used.

� Interpixel Redundancy -which results from correlation between the pixels of an image.pixels of an image.

� Psychovisual Redundancies -which is due to data that is ignored by the human visual system(i.e., visually nonessential information).

� Image compression algorithms aim to remove redundancy in data in a way which makes image reconstruction possible.

Lossy image compression system

� Image Compression techniques classified into two categories:� Lossy Compression � Lossless Compression

Figure: Compression Technique

IMAGE DENOISINGIMAGE DENOISING

Figure: Denoising Technique

ALGORITHMSALGORITHMS

� Decomposition

Step 1: Start-Load the source image data from a file into an array.Step 2: Choose a WaveletStep 3: Decompose-choose a level N, compute the wavelet

decomposition of the signals at level NStep 4: Compute the DWT of the dataStep 4: Compute the DWT of the dataStep 5: Read the 2-D decomposed image to a matrixStep 6: Retrieve the low pass filter from the list based on the wavelet

typeStep 7: Compute the high pass filter i=1Step 8: i >= 1decomposed level, then if Yes goto step 10, otherwise if

No goto step 9Step 9: Perform 2-D decomposition on the image i++ and goto to step 8Step 10: Decomposed image

� Reconstruction

Step 1: Start-Load the source image data from a file into an array.Step 2: Choose a WaveletStep 3: Decompose-choose a level N, compute the wavelet

decomposition of the signals at level NStep 4: Compute the DWT of the dataStep 5: Read the 2-D decomposed image to a matrixStep 6: Retrieve the low pass filter from the list based on the wavelet Step 6: Retrieve the low pass filter from the list based on the wavelet

typeStep 7: Compute the high pass filter i=decomp levelStep 8: i <= 1, then if Yes goto step 10, otherwise if No goto step 9Step 9: Perform 2-D reconstruction on the image and goto to step 8Step 10: Reconstruction image

� Compression

Step 1: Start-Load the source image data from a file into an arrayStep 2: Choose a WaveletStep 3: Decompose-choose a level N, compute the wavelet

decomposition of signals at level NStep 4: Threshold detail coefficients, for each level from 1 to N, Step 5: Remove(set to zero) all coefficients whose value is below a

threshold(this is the compression step)threshold(this is the compression step)Step 6: Reconstruct, Compute wavelet reconstruction using the

original approximation coefficients of level N and the modified detail coefficients of levels from 1 to N

Step 7: Compare the resulting reconstruction of the compressed image to the original image.

� Denoising

Step 1: Start-Load the source image data from a file into an arrayStep 2: Choose a WaveletStep 3: Decompose-choose a level N, compute the wavelet

decomposition of the signals at level NStep 4: Add a random noise to the source image data Step 5: Threshold detail coefficients, for each level from 1 to N, Step 6: Reconstruct, Compute wavelet reconstruction using the Step 6: Reconstruct, Compute wavelet reconstruction using the

original approximation coefficients of level N and the modified detail coefficients of levels from 1 to N

Step 7: Compare the resulting reconstruction of the denoised image to the original image.

EXPERIMENTAL RESULTSEXPERIMENTAL RESULTS

Image Used (grayscale)=kumar.jpg, Image size=147 X 81

� Decomposition & Reconstruction

Figure: Original Image

Figure: 1st level Decomposition Figure: 2nd level Decomposition

Figure: Decomposition approximations

� Compression - At different Decomposition levels:

Threshold (thr) = 20, Image Used (grayscale)=kumar.jpg,

Image size=147 X 81

Graph: Compression Comparison at Decomposition

Graph: Nul Coeffs Comparison(Compression) at Decomposition

Graph: Nul Coeffs Comparison(Denoised Compression) at Decomposition

� Compression - At different Thresholds levels:

Level (n)= 5, Image Used (grayscale)=kumar1.jpg,

Image size=109 X 87

Graph: Nul Coeffs Comparison(Compression) at Threshold

Graph: Compression Comparison at Threshold

Graph: Nul Coeffs Comparison(Denoised Compression) at Threshold

Graph: Denoised Compression Comparison at Threshold

� De-noising Image Used (grayscale)=kumar.jpg, Image size=147 X 81

CONCLUSIONCONCLUSION� All the wavelets having good denoised compression image with

clarity, but differ in energy retaining & percentage of zeros.

� The denoising at lower level of decomposition having reasonable clarity but at the higher levels the image is not clear.

� It is found the best wavelet for compression & denoising at decomposition & thresholding is Biorthogonal wavelet.

� The Discrete Meyer wavelet is having very poor compression and Haar wavelet is having very poor denoising then the other wavelet Haar wavelet is having very poor denoising then the other wavelet families.

� Future Work

� To find the best thresholding strategy, wavelet for a given image, to investigating other complex wavelet families.

� Analyzing different image formats and experimenting such as TIFF, GIF, BMP, PNG, and XWD.

Thank youThank youThank youThank you