ppt image analysis(irde, drdo)
TRANSCRIPT
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Image Analysis Using
Wavelet Transformation- From Instrumentation Research & Development Establishment, DRDO,
Dehradun
By : Nidhi GopalB.tech (EC)- M.tech(VLSI)
JV-B/09/1179JVWU, Jaipur
PROJECT ON :-
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Digital image processing : a Brief Overview
Image processing involves a set of computational techniques for analyzing, enhancing, compressing, and reconstructing images. This is a wide field of processing images in a digital form.
Terminologies :•Image segmentation : Extracting information for set of segments/pixels.•Image enhancement and restoration : Reconstruction from degraded image.• Image sharpening and smoothening : Edge and corner detection.• Grey scale Transformation : Deals with contrast transformation, or, setting up the grey level values i.e. RGB values.
Figure : Displaying the word “BASIC” in the form of pixels.
Image : A set of Pixels
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For defense (Army, Navy & Air force) purposes, Image compression is of basic necessity , as-
1.Security : It does not allow the other party, to copy, or to steal information from the opposite one, through secure data transmission.
2.Small target detection.3.Tracking missiles, Vehicle navigation.4.Automatic Target Recognition.. etc
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Objectives of my ProjectWhy wavelet instead of Fourier / STFT?
Algorithms for wavelet transformation
Image Compression& Transmission
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About Fourier Analysis
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An infinite series of sine and cosine functions. It is an explanation for the periodic series. Used in various fields like, optics, electrical engineering, quantum mechanics, image processing etc. Fourier transform, obtained by Fourier series, though, has many disadvantages.. …….
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Fourier Transform
Localized in frequency(gives information according to frequencies
only)
Analysis of periodic signals is possible
Not efficient for Continuous & moving signals
Sinusoids of infinite energy
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Another Approach : STFT (Short Term Fourier Transform) or Windowing
Time/Frequency localization depends on window size.
Once particular window size is chosen, it will be the same for all frequencies.
Many signals require a more flexible approach - vary the window size to determine more accurately either time or frequency.
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Comparison of the three: time-frequency graph
FOURIER TRANSFORM
WAVELET TRANSFORMSTFT
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Overcomes the preset resolution problem of the STFT by using a variable length window:◦ Use narrower windows at high frequencies
for better time resolution.◦ Use wider windows at low frequencies for
better frequency resolution.
Resolution Analysis :
Wide windows do not provide good localization at high frequencies.
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Solution :
Use narrower windows at high frequencies.
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Narrow windows do not provide good localization at low frequencies.
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Use wider windows at low frequencies.
Solution:
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Introduction to wavelet analysis What are Wavelets? Wavelets are functions
that “wave” above and below the x-axis, have
(1) varying frequency, (2) limited duration,
and (3) an average value of
zero.
This is in contrast to sinusoids, used by FT, which have infinite energy.
Sinusoid Wave
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Example - Haar Wavelets (cont’d) Start by averaging the pixels together
(pairwise) to get a new lower resolution image:
To recover the original four pixels from the two averaged pixels, store some detail coefficients.
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Example - Haar Wavelets (cont’d)
Repeating this process on the averages gives the full decomposition:
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Example - Haar Wavelets (cont’d)
The Harr decomposition of the original four-pixel image is:
We can reconstruct the original image to a resolution by adding or subtracting the detail coefficients from the lower-resolution versions.
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Wavelet expansionEfficient wavelet decompositions
involves a pair of waveforms (mother wavelets):
The two shapes are translated and scaled to produce wavelets (wavelet basis) at different locations and on different scales.
φ(t) ψ(t)
φ(t-k) ψ(2jt-k)
encode lowresolution info
encode details orhigh resolution info
Where .. K= scaling/low pass coeff and j= translation coeff/high pass coeff
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Wavelet expansion (cont’d)
f(t) is written as a linear combination of φ(t-k) and ψ(2jt-k) :
Note: in Fourier analysis, there are only two possible values of k ( i.e., 0 and π/2); the values j correspond to different scales (i.e., frequencies).
( ) ( ) (2 )jk jk
k k j
f t c t k d t k
scaling function wavelet function
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Wavelet families
Figure : Wavelet families (a) Haar (b) Daubechies (c) Coiflet1 (d) Symlet2 (e) Meyer (f) Morlet (g) Mexican Hat.
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1D Haar Wavelets Haar scaling and wavelet
functions:
computes average computes details
φ(t) ψ(t)
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Haar wavelet transform & its functions
Mother scaling function:
• Father Scaling Function :
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Example - Haar basis (revisited)
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[9 7 3 5]
low-pass,down-sampling
high-pass, down-sampling
(9+7)/2 (3+5)/2 (9-7)/2 (3-5)/2
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[9 7 3 5]
high-pass, down-sampling
low-pass,down-sampling
(8+4)/2 (8-4)/2
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Convention for illustrating 1D Haar wavelet decomposition
x x x x x x … x x
detailaverage
…
re-arrange:
re-arrange:
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Standard Haar wavelet decomposition (cont’d)
x x x … xx x x … x
… … .x x x ... x
(1) row-wise Haar decomposition:
…
detailaverage
…
… … .
…
…
… … .
re-arrange terms
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Standard Haar wavelet decomposition (cont’d)
(1) row-wise Haar decomposition:
…
detailaverage
…
…… … .
…
… … . …
row-transformed resultfrom previous slide:
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Standard Haar wavelet decomposition (cont’d)
(2) column-wise Haar decomposition:
…
detailaverage
…
…… … .
……
…… … .
…
row-transformed result column-transformed result
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Example
……
…… … .
row-transformed result
…
… … .
re-arrange terms
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Example (cont’d)
……
…… … .
column-transformed result
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Applications of Wavelet Transformation
Wavelet Analysis
Speech Compressio
n
De-Noising
Edge Detection
Feature Extraction
Speech RecognitionEcho
cancellation Audio &
Video compressio
nFrequency Division
MultiplexingBiomedical Imaging
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Programs for wavelet analysis clear all; %close all; clc; x=imread('test.jpg'); imshow(x) [xar,xhr,xvr,xdr] = dwt2(x(:,:,1),'haar'); [xag,xhg,xvg,xdg] = dwt2(x(:,:,2),'haar'); [xab,xhb,xvb,xdb] = dwt2(x(:,:,3),'haar'); xa(:,:,1)=xar; xa(:,:,2)= xag; xa(:,:,3)=xab ; xh(:,:,1)=xhr; xh(:,:,2)= xhg; xh(:,:,3)=xhb ; xv(:,:,1)=xvr; xv(:,:,2)= xvg; xv(:,:,3)=xvb ; xd(:,:,1)=xdr; xd(:,:,2)= xdg; xd(:,:,3)=xdb ; x1 = [xa*0.003 log10(xv)*0.3 ;log10(xh)*0.3 log10(xd)*0.3]; figure(); imshow(x1)
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[xaar,xhhr,xvvr,xddr] = dwt2(xa(:,:,1),'haar'); [xaag,xhhg,xvvg,xddg] = dwt2(xa(:,:,2),'haar'); [xaab,xhhb,xvvb,xddb] = dwt2(xa(:,:,3),'haar'); xaa(:,:,1)=xaar; xaa(:,:,2)= xaag; xaa(:,:,3)=xaab ; xhh(:,:,1)=xhhr; xhh(:,:,2)= xhhg; xhh(:,:,3)=xhhb ; xvv(:,:,1)=xvvr; xvv(:,:,2)= xvvg; xvv(:,:,3)=xvvb ; xdd(:,:,1)=xddr; xdd(:,:,2)= xddg; xdd(:,:,3)=xddb ; x11 = [xaa*0.001 log10(xvv)*0.3 ;log10(xhh)*0.3
log10(xdd)*0.3]; figure(); imshow(x11) [r,c,s] =size(xv); figure(); imshow( [x11(1:r,1:c,:) xv*0.05 ; xh*0.05 xd*0.05])
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Output :
ORIGINAL IMAGE IN .JPG
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LEVEL ONE DECOMPOSITION
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LEVEL TWO DECOMPOSITION
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The algorithm used in programming was transferred into an FPGA chip, and then to the computers. Further, the scaling and translating coefficients (instead of whole image) were sent to the receiving end, then, by inverse wavelet transformation, the original image was reconstructed.
Consequently, this helped in feature extraction and de-noising of image.
CONCLUSION
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Any Queries ??