Papoulis
Probability, Random Variables and Stochastic Processes
Athanasios Papoulis
Polytechnic University
S. Unnikrishna Pillai
Thursday, 30 June 2011
Tuesday, 21 June 2011
Probability Random Variables and Stochastic Processes Papoulis
Probability, Random Variables
and
Stochastic Processes
Fourth Edition
Athanasios Papoulis
Polytechnic University
S. Unnikrishna Pillai
McGraw-Hill Education, 2002 - 852 pages
The fourth edition of Probability, Random Variables and Stochastic Processes has been updated significantly from the previous edition, and it now includes co-author S. Unnikrishna Pillai of Polytechnic University. The book is intended for a senior/graduate level course in probability and is aimed at students in electrical engineering, math, and physics departments. The authors' approach is to develop the subject of probability theory and stochastic processes as a deductive discipline and to illustrate the theory with basic applications of engineering interest. Approximately 1/3 of the text is new material--this material maintains the style and spirit of previous editions. In order to bridge the gap between concepts and applications, a number of additional examples have been added for further clarity, as well as several new topics.
Math - McGraw Hil - Probability Random Variables and Stochastic Processes Solutions Manual - A. Papoulis - 2002
Monday, 20 June 2011
Delivering Voice over IP Networks
Delivering Voice over IP Networks
Delivering Voice over IP Networks
Wiley | August 23, 2002 | ISBN-10: 0471386065 | 560 pages | File type: PDF | 4.32 mb
* Includes new coverage on the advances in signaling protocols, second-generation switching and the development of non-switched alternatives, and the implementation lessons learned.
* Contains in-depth coverage of network architectures used to support VoIP, performance and voice quality considerations, compression and integration methods for IP tranmissions.
Download links:http://depositfiles.com/files/h5doyvr8x
http://www.filesonic.com/file/53490797/0471386065.rar
Saturday, 2 April 2011
Information Theory, Inference & Learning Algorithms
Information Theory, Inference & Learning Algorithms
ISBN: 0521642981
Category: Technical
Tag: Programming
Description
David J. C. MacKay “Information Theory, Inference & Learning Algorithms"
Cambridge University Press | 2002-06-15 | ISBN: 0521642981 | 550 pages | PDF | 6,7 MB
Cambridge University Press | 2002-06-15 | ISBN: 0521642981 | 550 pages | PDF | 6,7 MB
Information theory and inference, often taught separately, are here united in one entertaining textbook. These topics lie at the heart of many exciting areas of contemporary science and engineering - communication, signal processing, data mining, machine learning, pattern recognition, computational neuroscience, bioinformatics, and cryptography. This textbook introduces theory in tandem with applications. Information theory is taught alongside practical communication systems, such as arithmetic coding for data compression and sparse-graph codes for error-correction. A toolbox of inference techniques, including message-passing algorithms, Monte Carlo methods, and variational approximations, are developed alongside applications of these tools to clustering, convolutional codes, independent component analysis, and neural networks. The final part of the book describes the state of the art in error-correcting codes, including low-density parity-check codes, turbo codes, and digital fountain codes -- the twenty-first century standards for satellite communications, disk drives, and data broadcast. Richly illustrated, filled with worked examples and over 400 exercises, some with detailed solutions, David MacKay's groundbreaking book is ideal for self-learning and for Undergraduate or graduate courses. Interludes on crosswords, evolution, and sex provide entertainment along the way. In sum, this is a textbook on information, communication, and coding for a new generation of students, and an unparalleled entry point into these subjects for professionals in areas as diverse as computational biology, financial engineering, and machine learning.
Download free
Wednesday, 16 March 2011
Conditionally colored line plot
coloring partialy matlab code
Plots vectors x & y using one color for when y is greater than a given threshold value, and another color when y is less than the threshold.
You can optionally specify any standard formatting string that PLOT accepts (eg 'rx:' for a red dotted line with cross markers).
The plotting follows the standard MATLAB PLOT approach of linearly interpolating between data values. The coloring/linestyle changes at y = threshold, even on the interpolated line.
Plots vectors x & y using one color for when y is greater than a given threshold value, and another color when y is less than the threshold.
You can optionally specify any standard formatting string that PLOT accepts (eg 'rx:' for a red dotted line with cross markers).
The plotting follows the standard MATLAB PLOT approach of linearly interpolating between data values. The coloring/linestyle changes at y = threshold, even on the interpolated line.
Time division multiplexing
Time division multiplexing in matlab
This program perform TDM for as many signals as you want
function [y]=TDM_nik(x)
% x contains all the signals to be multiplexed
% y is multiplexed signal
%----------------------------------------
% Example: if you have to mutiplex two signals e.g. x1 and x2 (of course both of same length)
% if length is not same append zeros in smaller one to make it equal to larger on
% then make x(1,:)=x1, x(2,x2)...x(r, xr) (if you have r signals to be multiplexed)
% then simple run y=TDM_nik(x)
%-Do it x1=1:10, x2=10:-1:1, x3(1:5)=4, x3(6:10)=-4, x(1,:)=x1, x(2,:)=x2,
% x(3,:)=x3 amd y=TDM_nik(x)
%If you have any problem or feedback please contact me @
%%===============================================
% NIKESH BAJAJ
% Asst. Prof., Lovely Professional University, India
% Almameter: Aligarh Muslim University, India
% +919915522564, bajaj.nikkey@gmail.com
%%===============================================
[r c]=size(x);
k=0;
% Multiplexing
for i=1:c
for j=1:r
k=k+1;
y(k)=x(j,i);
end
end
% Ploting
color='ybrgmkc';
figure(1)
sig='x1';
for i=1:r
sig(2)=i+48;
j=mod(i,7)+1;
subplot(r,1,i)
stem(x(i,:),color(j),'linewidth',2)
title(sig)
ylabel('Amplitude')
grid
end
xlabel('Time')
t=1/r:1/r:c;
figure(2)
for i=1:r
j=mod(i,7)+1;
stem(t(i:r:r*c),y(i:r:r*c),color(j),'linewidth',2)
hold on
grid
end
hold off
title('Time Division Multiplexed Sequence')
xlabel('Time')
ylabel('Amplitude')
Amplitude Modulation_matlab
% MATLAB Script for Amplitude Modulation
% Although it is possible to modulate any signal over a sinusoid, however I
% will use a low frequency sinusoid to modulate a high frequency sinusoid
% without the loss of generality.
format long;
% Clear all previuosly used variables and close all figures
clear all;
close all;
% Amplitude, Frequency and Phase Shift for Modulating Signal
A1 = 2; f1 = 5; p1 = 0;
% Amplitude, Frequency and Phase Shift for Carrier Signal
A2 = 4; f2 = 20; p2 = 0;
% Sample Rate - This will define the resolution
fs = 1000;
% Time Line. Longer the signal, better will be the fft
t = 0: 1/fs : 1;
% Generate the message signal
s1 = A1*sin(2*pi*f1*t + p1);
% Plot the message signal
figure(1);
plot(t,s1);
xlabel('Time (sec)');
ylabel('Amplitude');
title(['Message Signal with frequency = ',num2str(f1),' Hz']);
grid on;
% Generate the Carrier wave
s2 = A2*sin(2*pi*f2*t + p2);
% Plot the carrier wave
figure(2);
plot(t,s2);
xlabel('Time (sec)');
ylabel('Amplitude');
title(['Carrier Signal with frequency = ',num2str(f2),' Hz']);
grid on;
% Finally the Modulation
% Ref. Modern Analogue and Digital Communication Systems - B. P. Lathi
% Amplitude Modulation with Suppressed Carrier
% Double Sideband with Suppressed Carrier (DSB-SC)
s3 = s1.*s2;
% Generate the Envelope
s3_01 = A1*A2*(sin(2*pi*f1*t));
s3_02 = -A1*A2*(sin(2*pi*f1*t));
% Amplitude Modulation with Large Carrier
% Double Sideband with Large Carrier (DSB - LC)
s4 = (A2 + s1).*sin(2*pi*f2*t);
% Generate the Envelope
s4_01 = A2 + s1;
s4_02 = -A2 - s1;
% ----------------------------------------------------------
% Let's Check out the frequency content of the two Modulations
% Number of FFT points. N should be greater than Carrier Frequency
% Larger the better
N = 2^nextpow2(length(t));
f = fs * (0 : N/2) / N;
% Find FFT
s3_f = (2/N)*abs(fft(s3,N));
s4_f = (2/N)*abs(fft(s4,N));
%-------------------------------------------------------------
% Plot the two Modulations
% Plot the DSB-SC Signal
figure(3);
subplot(2,1,1);
plot(t,s3);
hold on;
plot(t,s3_01,'r');
hold on;
plot(t,s3_02,'g');
xlabel('Time (sec)');
ylabel('Amplitude');
title('Double Sideband with Suppressed Carrier');
grid on;
subplot(2,1,2);
plot(f(1:100),s3_f(1:100));
xlabel('Frequency (Hz)');
ylabel('| Amplitude |');
title('Spectral Anaalysis (Single Sided PSD)');
grid on;
% Plot the DSB-LC Signal
figure(4);
subplot(2,1,1);
plot(t,s4);
hold on;
plot(t,s4_01,'r');
hold on;
plot(t,s4_02,'g');
xlabel('Time (sec)');
ylabel('Amplitude');
title('Double Sideband with Large Carrier');
grid on;
subplot(2,1,2);
plot(f(1:100),s4_f(1:100));
xlabel('Frequency (Hz)');
ylabel('| Amplitude |');
title('Spectral Anaalysis (Single Sided PSD)');
grid on;
Edge detection
Feature detection is an importatnt aspect of any image or video processing application. The given code can be used for detecting cornera and edges in a RGB or grayscale image.It is based upon the famous paper on the topic titled
"A Combined Corner and Edge Detector" by Harris and stephens.
%%%% This function can be used for corner and edge detection
%%%% for any RGB or grayscale image. It is based upon the famous
%%%% paper on the topic titled "A Combined Corner and Edge Detector"
%%%% by Harris and stephens.
%%%%%%%%%%%%% input arguments
%%%%% input = The input image whose corners and edges are to be detected.
%%%%% sigma(optional) = Standard deviation of gaussian filter . Default is
%%%%% 1.
%%%%% kernelsize(optional) = The size of gaussian kernel. Default is 8.
%%%%% thresh(optional) = threshhlod value to be used as described in the
%%%%% algorithm. Default is 0.002.
%%%%% ratio(optional) = The algorithm requires that gradients be convolved
%%%%% with a larger gaussian the second time around. This is the ratio of the
%%%%% of sigma to be used second time to that used first time. Default is
%%%%% 1.5.
%%%%%%%%%%%% output arguments
%%%%%% O= output binary image containing detected corners and regions.
%%%%%%% Example:-
%%%%%%%%%%%% O = feature_detection('bus10.jpg',1(sigma),8 (kernelsize),
%%%%%%%%%%%% 0.002 (thresh),1.5(ratio));
function O=feature_detection(input,varargin)
%%%% validate the arguments
error(nargchk(1,5,nargin));
%%% assign values to the input paraameters as per number of arguments
%%% specified by the user.
sigma=1;
kernelsize=8;
thresh=0.002;
ratio=1.5;
if(nargin>1)
sigma=varargin{1}(:);
end
if(nargin>2)
kernelsize=varargin{2}(:);
end
if(nargin>3)
thresh=varargin{3}(:);
end
if(nargin>4)
ratio=varargin{4}(:);
end
%%%% Read the image.
I=imread(input);
%%% if the image is RGB, convert it into grayscale.
if(size(I,3)==3)
I=rgb2gray(I);
end
%%% convert the image to double and display it.
I=im2double(I);
imtool(I);
%%% smoothen the image using gaussian filter.
h=fspecial('gaussian',kernelsize,sigma);
I=imfilter(I,h,'conv');
O=zeros(size(I,1),size(I,2));
% Calculate the gradient using the 7-tap Coefficients given by Farid and
% Simoncelli given in their paper "Differentiation of Discrete
% Multi-Dimensional Signals".
p = [ 0.004711 0.069321 0.245410 0.361117 0.245410 0.069321 0.004711];
d1 = [ 0.018708 0.125376 0.193091 0.000000 -0.193091 -0.125376 -0.018708];
FX=conv2(p,d1,I,'same');
FY=conv2(d1,p,I,'same');
FX=FX.^2;
FY=FY.^2;
FXY=conv2(d1,p,I,'same');
%%%% convolve the gradients with a larger gaussian.
gauss=fspecial('gaussian',ceil(ratio*kernelsize),sigma);
FX=imfilter(FX,gauss,'conv');
FY=imfilter(FY,gauss,'conv');
FXY=imfilter(FXY,gauss,'conv');
%%% each point in the image compute the scalar interest measure and
%%% compare it with specified thresh. If greater then set the
%%% corresponding pixel in output to be 1.
for y=1:1:size(I,1)
for x=1:1:size(I,2)
mat=[FX(y,x),FXY(y,x);FXY(y,x),FY(y,x)];
V=eigs(mat);
lambda1=abs(V(1));
lambda2=abs(V(2));
calc=(lambda1*lambda2)-0.06*(lambda1+lambda2).^2;
if(calc>abs(thresh))
O(y,x)=1;
end
end
end
imshow(O);
Tuesday, 15 March 2011
TRAFFIC SIMULATION
TRAFFIC_SIMULATION
Simulate Traffic at a Light
function traffic ( cycle_num )
%*****************************************************************************80
%
%% TRAFFIC simulates the cars waiting at one traffic light.
%
%
%
% Parameters:
%
% Input, integer CYCLE_NUM, the number of 10-second time cycles to model.
%
% Local Parameters:
%
% Local, integer CARS, the number of cars waiting at the light.
%
% Local, integer CARS_IN, the total number of cars that have come.
%
% Local, integer CARS_OUT, the total number of cars that have left.
%
% Local, integer CYCLE, the number of time cycles that have elapsed.
%
% Local, integer CYCLE_LENGTH, the number of seconds in one time cycle.
%
% Local, integer GREEN_CYCLES, the number of 10-second time cycles that
% a green light lasts.
%
% Local, integer GREEN_TIMER, keeps track of the number of time cycles the
% green light has been on.
%
% Local, integer LIGHT, the state of the light.
% 'r', the light is now red.
% 'g', the light is now green.
%
% Local, real P, the probability that a new car will come to the light
% in the next second.
%
% Local, integer RED_CYCLES, the number of 10-second time cycles that
% a red light lasts.
%
% Local, integer RED_TIMER, keeps track of the number of time cycles the
% red light has been on.
%
%
% Initialize.
%
cars = 0;
cars_in = 0;
cars_out = 0;
car_wait_cycles = 0;
cycle = 0;
cycle_length = 10;
green_cycles = 2;
green_timer = 0;
light = 'r';
p = 0.3;
red_cycles = 4;
red_timer = 0;
%
% Set up the plot data.
%
plot_data = zeros(2,cycle_num+1);
%
% Handle the "0"-th cycle.
%
plot_data(1,cycle+1) = cycle;
plot_data(2,cycle+1) = cars;
prq ( cars, light, cycle );
%
% Handle cycles 1 through CYCLE_NUM.
%
for cycle = 1 : cycle_num
%
% Each second of the cycle, choose a random number.
% If it is less than P, then a new car appeared at the light at that second.
%
r = rand ( cycle_length, 1 );
cars_new = sum ( r < p );
cars = cars + cars_new;
cars_in = cars_in + cars_new;
%
% Handle this time cycle depending on whether the light is green or red.
%
if ( light == 'g' )
[ cars, cars_out, light, green_timer ] = go ( green_cycles, cars, ...
cars_out, light, green_timer );
else
[ cars, light, red_timer ] = stop ( red_cycles, cars, light, red_timer );
end
%
% At the end of this cycle, how many cars are waiting?
%
car_wait_cycles = car_wait_cycles + cars;
%
% Print the current status.
%
prq ( cars, light, cycle );
plot_data(1,cycle+1) = cycle;
plot_data(2,cycle+1) = cars;
end
plot ( plot_data(1,1:cycle_num+1), plot_data(2,1:cycle_num+1) )
xlabel ( 'Time Cycles' )
ylabel ( 'Cars Waiting' )
title ( 'Traffic waiting at a Light' )
fprintf ( 1, '\n' );
fprintf ( 1, ' Number of cycles = %d\n', cycle_num );
fprintf ( 1, ' Simulated time = %d seconds\n', cycle_num * cycle_length );
fprintf ( 1, ' Number of cars in = %d\n', cars_in );
fprintf ( 1, ' Number of cars waiting = %d\n', cars );
fprintf ( 1, ' Number of cars out = %d\n', cars_out );
fprintf ( 1, ' Percentage Out/In = %7.1f%%\n', 100 * cars_out / cars_in );
wait_average_seconds = car_wait_cycles * cycle_length / cars_in;
fprintf ( 1, ' Average wait = %7.2f seconds\n', wait_average_seconds );
wait_average_lights = car_wait_cycles / cars_in / ( red_cycles + green_cycles );
fprintf ( 1, ' Average wait = %7.2f light cycles\n', wait_average_lights );
return
end
function [ cars, cars_out, light, green_timer ] = go ( green_cycles, cars, ...
cars_out, light, green_timer )
%*****************************************************************************80
%
%% GO simulates traffic when the light is green.
%
%
%
% Parameters:
%
% Input, integer GREEN_CYCLES, the number of 10-second time cycles that
% a green light lasts.
%
% Input, integer CARS, the number of cars stopped at the light.
%
% Input, integer CARS_OUT, the total number of cars that have gone
% through the light.
%
% Input, integer LIGHT, the state of the light.
% 'r', the light is now red.
% 'g', the light is now green.
%
% Input, integer GREEN_TIMER, keeps track of the number of time cycles the
% green light has been on.
%
% Output, integer CARS, the number of cars stopped at the light.
%
% Output, integer CARS_OUT, the total number of cars that have gone
% through the light.
%
% Output, integer LIGHT, the state of the light.
% 'r', the light is now red.
% 'g', the light is now green.
%
% Output, integer GREEN_TIMER, keeps track of the number of time cycles the
% green light has been on.
%
%
% In one 10-second time cycle, we estimate 8 cars can move out.
%
cars_through = min ( 8, cars );
cars = cars - cars_through;
cars_out = cars_out + cars_through;
%
% Advance the timer. If the green light has timed out, reset the timer
% and switch to red.
%
green_timer = green_timer + 1;
if ( green_cycles <= green_timer )
light = 'r';
green_timer = 0;
end
return
end
function [ cars, light, red_timer ] = stop ( red_cycles, cars, light, ...
red_timer )
%*****************************************************************************80
%
%% STOP simulates the traffic when the light is red.
%
% Parameters:
%
% Input, integer RED_CYCLES, the number of 10-second time cycles that
% a red light lasts.
%
% Input, integer CARS, the number of cars stopped at the light.
%
% Input, integer LIGHT, the state of the light.
% 'r', the light is now red.
% 'g', the light is now green.
%
% Input, integer RED_TIMER, keeps track of the number of time cycles the
% red light has been on.
%
% Output, integer CARS, the number of cars stopped at the light.
%
% Output, integer LIGHT, the state of the light.
% 'r', the light is now red.
% 'g', the light is now green.
%
% Output, integer RED_TIMER, keeps track of the number of time cycles the
% red light has been on.
%
%
% Advance the timer.
% If the red light has timed out, reset the timer and switch to green.
%
red_timer = red_timer + 1;
if ( red_cycles <= red_timer )
light = 'g';
red_timer = 0;
end
return
end
function prq ( cars, light, cycle )
%*****************************************************************************80
%
%% PRQ prints the current traffic waiting at the light.
%
% Parameters:
%
% Input, integer CARS, the number of cars stopped at the light.
%
% Input, integer LIGHT, the state of the light.
% 'r', the light is now red.
% 'g', the light is now green.
%
% Input, integer CYCLE, the current 10-second time cycle.
%
fprintf ( 1, '%4d ', cycle );
if ( light == 'r' )
fprintf ( 'R ' );
else
fprintf ( 'G ' );
end
i = cars;
c = floor ( i / 100 );
i = i - 100 * c;
for j = 1 : c
fprintf ( 'C' );
end
x = floor ( i / 10 );
i = i - 10 * x;
for j = 1 : x
fprintf ( 'X' );
end
for j = 1 : i
fprintf ( 'I' );
end
fprintf ( 1, '\n' );
return
end
Eye detection using wavelets and ANN
EYE DETECTION USING WAVELETS AND ANN
Project with matlab code
ABSTRACT
A Biometric system provides perfect identification of individual based on a unique biological feature or characteristic possessed by a person such as finger print, hand
writing, heart beat, face recognition and eye detection. Among them eye detection is a better approach since Human Eye does not chan ge throu ghout the life of an individual. It is regarded as the most reliable and accurate biometric identification system available.
In our project we are going to develop a system for ‘eye detection using wavelets and ANN’ with software simulation package such as matlab 7.0 tool box in order to verify the uniqueness of the human eyes and its performance as a biometric. Eye
detection involves first extracting the eye from a digital face image, and then encoding the unique patterns of the eye in such a way that they can be compared with pre-
registered eye patterns. The eye detection system consists of an automatic segmentation system that is based on the wavelet transform, and then the Wavelet analysis is used as a pre-processor for a back propagation neural network with conjugate gradient learning.
The inputs to the neural network are the wavelet maxima neighborhood coefficients of face images at a particular scale. The output of the neural network is the classification of the input into an eye or non-eye region. An accuracy of 81% is observed f or test images under different environment conditions not included during training.
Eye detection system is being extensively used in biometrics security solutions by U.S. Department of Defense (DOD), which includes access control to ph ysical facilities,
security systems or information databases. Suspect tracking, surveillance and intrusion detection and by various Intelligen ce agencies through out the world, also in the
corrections/laws enforcement marketplaces.
1.1. Biometric Technology:
A biometric system provides automatic recognition of an individual based on some sort of unique feature or characteristic possessed by the individual. Biometric systems have been developed based on fingerprints, facial features, voice, hand geometry, handwriting,
the retina, and the one presented in this project, the eye.
Biometric systems work by first capturing a sample of the feature, such as recording a digital sound sign al for voice recognition, or taking a digital color image for eye
detection. The sample is then transformed using some sort of mathematical function into a biometric template. The biometric template will provide a normalized, efficient and highly discriminating representation of the feature, which can then be objectively
compared with other templates in order to determine identity. Most biometric systems allow two modes of operation. A training mode or enrolment mode for adding templates
to a database, and an identification mode, where a template is created for an individual and then a match is searched for in the database of pre-en rolled templates.
A good biometric is characterized by use of a feature that is; highly unique so that the chance of any two p eople having the same characteristic will be minimal, stable so that the feature does not change over time, and be easily captured in order to provide
convenience to the user, and prevent misrepresentation of the feature.
1.2. EYE: The Perfect ID
The randomness and uniqueness of human eye p atterns is a major breakthrough in the search for quicker, easier and highly reliable forms of automatic human identification, where the human eye serves as a type of 'biological passport, PIN or password’.
Results of a study by John Daugman and Cathryn, of over two million different pairs of human eyes in images taken from volunteers in Britain, USA and Japan show that no two
eye patterns were the same in ev en as much as one-third of their form. Even genetically
identical faces - for example from twins or in the probable future, from human clones - have different eye patterns.
The implications of eye detection are highly signif icant at a time when organizations such as banks and airlines are looking for more effective security measures. The possible
applications of eye detection span all aspects of daily life, from computer login, national border controls and secur e access to bank cash machine accounts, to ticket-less air travel,
access to premises su ch as the home and office, benefits entitlement and credit card authentication.
Compared with other biometric technologies, such as face, speech and finger recognition, eye recognition can easily be considered as the most reliable form of biometric. However,
there have been no independent trials of the technology, and source cod e for systems is not available in working condition.
1.3. Objective:
The objective will be to implement an open-source eye detection system in order to verify the claimed performance of the technolog y. This project is
based on a novel method, which is robust and efficient in extracting eye windows using Wavelets and Neur al Networks. Wavelet analysis is used as a pre processor for a back propagation neur al network with conjugate gradient learning. The inputs to the neural
network are the wavelet maxima neighborhood coefficients of face images at a particular scale. The output of the neural network is the classification of th e input into an eye or non-eye region. The updated weight and bias values for a particular person is stored in a
database. The image to be verified is wavelet transformed before being applied to the neural network with those updated weight and bias values. The person is identified when
the neural network output of one of the test images matches with that of the verified image. . An accuracy of 90% is observed for test images under different environment conditions not included during training.
2.1. INTRODUCTION
The transform of a signal is just another form of representing the signal. It does not change the information content present in the signal. The Wavelet
transform provides a time-frequency rep resentation of the signal. It was developed to overcome the shortcoming of the Short Time Fourier Transform (STFT), which can also be used to analyze non-stationary signals. While STFT gives a constant resolution at all frequencies,
the Wavelet Transform uses multi-resolution technique by which different frequenciesare analyzed with different resolutions.
A wave is an oscillating function of time or space and is periodic. In contrast, wavelets are localized waves. They have their ener gy concentrated in time or space and are suited to analysis of transient signals. While Fourier Transform and STFT use waves to analyze signals, the Wavelet Transform uses wavelets of finite energy.
The wavelet analysis is done similar to the STFT an alysis. The signal
to be analyzed is multiplied with a wavelet function just as it is multiplied with a window function in STFT, and then the transform is computed for each segment generated.
However, unlike STFT, in Wavelet Transform, the width of the wavelet function changes with each spectral component. The Wavelet Transform, at high frequencies, gives good
time resolution and poor frequency resolution, while at low frequencies; the Wavelet Transform gives good frequency resolution and poor time resolution.
2.2 The Continuous Wavelet Transform and the Wavelet Series
The Continuous Wavelet Transform (CWT) is provided by equation 2.1, where
x(t) is the signal to be analyzed. (t) is the mother wavelet or the basis function. All the wavelet functions used in the transformation are derived from the mother wavelet through translation (shifting) and scaling (dilation or compression).
The mother wavelet used to generate all the basis functions is designed based on some desired characteristics associated with that functio n. The translation par ameter relates to
the location of the wavelet function as it is shifted through the signal. Thus, it corresponds to the time information in the Wavelet Transform. The scale parameter s is
defined as |1/frequency| and corresponds to frequency information. Scaling either dilates (expands) or compresses a signal. Large scales (low frequencies) dilate the signal and
provide detailed information hidden in the signal, while small scales (high frequencies) compress the signal and provide global information about the signal. Notice that the Wavelet Transform merely performs the convolution operation of the signal and the basis
function.
The above an alysis becomes ver y useful as in most practical applications; high
frequen cies (low scales) do not last fo r a long duration, but instead, appear as short bursts, while low frequencies (high scales) usually last for entire duration of the signal.
The Wavelet Series is obtained by discretizing CWT. This aids in computation of CWT using computers and is obtained by sampling the time-scale plane. The sampling rate can
be changed accordingly with scale change without violating the Nyquist criterion. Nyquist criterion states that, the minimum sampling rate that allows reconstruction of the original signal is 2 radians, where is the highest frequency in the signal. Therefor e, as the scale goes higher (lower frequen cies), the sampling rate can be decreased thus
reducing the number of computations.
The Wavelet Series is obtained b y discretizing CWT. This aids in computation of CWT using computers and is obtained by sampling the time-scale plane. The sampling rate can be changed accordingly with scale change without violating the Nyquist criterion. Nyquist criterion states that, the minimum sampling rate that allows
reconstruction of the o riginal signal is 2 radians, where is the highest frequency in the signal. Therefore, as the scale goes higher (lower frequencies), the sampling rate can be decreased thus reducing the number of computations.
DISCRETE WAVELET TRANSFORM
3.1. INTRODUCTION
The Wavelet Series is just a sampled version of CWT and its computation may consume significant amount of time and resources, depending on the resolution required. The Discrete Wavelet Transform (DWT), which is based on sub-b and coding, is found to yield a fast computation of Wavelet Transform. It is easy to implement and reduces the computation time and resources required.
The foundations of DWT go back to 1976 when techniques to decompose discrete time signals were devised. Similar work was done in speech sign al coding which was named as sub-band coding. In 1983, a technique similar to sub-band coding was developed which was named pyramidal coding. Later man y improvements were made to these coding schemes, which resulted in efficient multi-resolution analysis schemes.
In CWT, the signals are analyzed using a set of basis functions, which relate to each other b y simple scaling and translation. In the case of DWT, a time-scale representation of the digital signal is obtained using digital filtering techniques. The
signal to be analyzed is passed through filters with different cutoff frequencies at different scales.
3.2. DWT and Filter Banks
3.2.1 Multi-Resolution Analysis using Filter Banks
Filters are one of the most widely used signal processing functions. Wavelets can be realized by iteration of filters with rescaling. The resolution of the signal, which is a measure of the amount of detail information in the signal, is determined by the filtering operations, and the scale is determined by upsampling and downsampling (subsampling) operations.
The DWT is computed by successive lowpass and highpass filtering of the discrete time-domain signal as shown in figure 3.1. This is called the Mallat algorithm or
Mallat-tree decomposition. Its significance is in the manner it connects the continuous- time multiresolution to discrete-time filters. In the figure, the sign al is denoted by the sequence x [n], where n is an integer. The low pass filter is denoted by G0 while the high pass filter is denoted by H0. At each level, the high pass filter produces detail information; d[n], while the low pass filter associated with scaling function produces coarse approximations, a[n].
At each decomposition level, the half band filters produce signals spanning only half the frequency band. This doubles the frequency resolution as the uncertainty in
frequen cy is reduced by half. In accord ance with Nyquist’s rule if the original signal has a highest frequency of , which requires a sampling frequency of 2 radians, then it now
has a highest frequency of /2 radians. It can now be sampled at a frequency of radians thus discarding half the samples with no loss of information. This decimation by 2 halves
the time resolution as the entire signal is now represented by only half the number of samples. Thus, while the half band low pass filtering removes half of the frequencies and
thus halves the resolution, the decimation by 2 doubles the scale.
With this approach, th e time resolution becomes arbitrarily good at high frequencies, while the frequency resolution becomes arbitrarily good at low frequencies.The filtering and decimation process is continued until the desired level is reached. The maximum number of levels depends on the length of the signal. The DWT of the original signal is then obtained by concatenating all the coefficients, a[n] and d[n], starting from the last level of decomposition.
Figure 3.2 shows the reconstruction of the original signal from the wavelet
coefficients. Basically, the reconstruction is the reverse process of decomposition. The approximation and detail coefficients at every level are upsampled by two, passed through the low pass and high pass synthesis filters and then added. This process is
continued through the same number of levels as in the decomposition pr ocess to obtain the original signal. The Mallat algorithm works equally well if the analysis filters, G0 and H0, are exchanged with the synthesis filters, G1 & H1.
3.2.2 Conditions for Perfect Reconst ruction
In most Wavelet Transform applications, it is required that the origin al signal b e synthesized from the wavelet coefficients. To achieve perfect reconstruction the analysis and synthesis filters have to satisfy certain conditions. Let G0(z) and G1(z) be the low pass analysis and synthesis filters, respectively and H0(z) and H1(z) the high pass analysis and synthesis filters respectively. Then the filters have to satisfy the following two
conditions:
The first condition implies that the reconstruction is aliasin g-free and th e second
condition implies that the amplitude distortion has amplitude of one. It can be observed that the perfect reconstruction condition does not change if we switch the analysis and synthesis filters.
There are a number of filters, which satisfy these conditions. But not all of them
give accurate Wavelet Transforms, especially when the filter coefficients are quantized.The accuracy of the Wavelet Transform can be determined after reconstruction by
calculating the Signal to Noise Ratio (SNR) of the signal. Some applications like pattern recognition do not need reconstruction, and in such applications, the above conditions
need not apply.
3.2.3 Classification of wavelets
We can classify wavelets into two classes:
(a) orthogonal and (b) biorthogonal.
Based on the application, either of them can be used.
(a) Features of orthogonal wavelet filter banks
The coefficients of orthogonal filters are r eal numbers. The filters are of the same length and are not symmetric. The low pass filter, G0 and the high pass filter, H0 are related to each other b y
H0 (z) = z -N G0 (-z-1)…………………………………...(3.3 )
The two filters are alternated flip of each other. The alternating flip automatically gives double-shift orthogonality between the lowpass and highpass filters, i.e., the scalar product of the filters, for a shift by two is zero. i.e., G[k] H[k-2l] = 0, where k,l Z. Filters that satisf y equation 3.3 are known as Conjugate Mirror Filters (CMF). Perfect reconstruction is possible with alternating flip.
Also, for perfect r econstruction, the synthesis filters are identical to the analysis filters except for a time reversal. Orthogonal filters offer a high number of vanishing moments. This property is useful in many signal and image processing applications. They have regular structure, which leads to easy implementation and scalable architecture.
(b)Features of biorthogonal wavelet filter banks
In the case of the biorthogonal wavelet filters, the low pass and the high pass filters do not have the same length. The low pass filter is always symmetric, while the high pass filter could be either symmetric or anti-symmetric. The coefficients of the filters are either real numbers or integers.
For perfect r econstruction, biorthogonal filter bank has all odd length or all even length filters. The two analysis filters can be symmetric with odd length or one symmetric and the other antisymmetric with even length. Also, the two sets of analysis and synthesis filters mu st be dual. The linear phase biorthogonal filters are the most popular filters for d ata compression applications.
3.3 Wavelet Families
There are a number of basis functions that can be used as the mother wavelet for Wavelet Transformation. Since the mother wavelet produces all wavelet functions used in the transformation through translation and scaling, it determines the characteristics of the resulting Wavelet Transform. Therefore, the details of the particular
application should be taken into account and the appropriate mother wavelet should be chosen in order to use the Wavelet Transform effectively.
Figure 3.3 illustrates some of the commonly used wavelet functions. Haar wavelet is one of the oldest and simplest wavelet. Therefore, any discussion of wavelets starts with the Haar wavelet. Daubechies wavelets are the most popular wavelets. They represent the foundations of wavelet signal processin g and ar e used in numerous applications. These are also called Maxflat wavelets as their fr equency responses have maximum flatness at frequencies 0 and . This is a very desirable property in some applications. The Haar, Daubechies, Symlets and Coiflets are compactly supported orthogonal wavelets. These wavelets along with Meyer wavelets are capable of perfect reconstruction. The Meyer, Morlet and Mexican Hat wavelets are symmetric in shape. The wavelets ar e chosen based on their shape and their ability to analyze the signal in a particular application.
METHODS OF EYE DETECTION
4.1 INTRODUCTION:
A lot of research work has been published in the field of eye detection in the last decade. Variou s techniques have been proposed using texture, depth, shape and
color information or combinations of these for eye detection. Vezhnevets focus on several landmark points (eye corners, iris border points), from which the approximate
eyelid contours are estimated. The upper eyelid points are found using on the observation that eye border pixels are significantly darker than surrounding skin and sclera. The
detected eye bound ary points are filter ed to remove outliers and a polynomial curve is fitted to the remaining boundary points. The lower lid is estimated from the known iris and eye. Some of the famous eye detection techniques are discussed below.
4.2 TEMPLATE MATCHING METHOD:
Reinders present a method where based on the techniq ue of template matching the positions of the eyes on the face image can be followed throughout a sequence of video images. Template matching is one of the most typical techniques for
feature extraction. C orrelation is commonly exploited to measure the similarity between a stored template and the window image under consideration. Templates should be
deliberately designed to cover variety of possible image variations. During the search in the whole image, scale and rotation should also be considered carefully to speed up the process. To increase the robustness of the tracking scheme the method automatically
generates a codebook of images representing the encountered different appearances of the eyes. Yuille first proposed using deformable templates in locating human eye. Th e
weaknesses of the deformable templates are that the processing time is lengthy and success relies on the initial position of the template. Lam introduced the concept of eye
corners to improve the deformable template appro ach.
4.3 USING PROJECTION FUNCTION:
Saber and Jeng proposed to use facial features geometrical
structure to estimate the location of eyes. Takacs developed iconic filter banks for detecting facial landmarks. projection functions have also been employed to locate eye
windows. Feng and Yeun developed a variance projection function for locating the corner points of the eye. Zhou and Geng propose a h ybrid projection function to locate the eyes.
By combining an integral projection fun ction, which considers mean of intensity, and a variance projection function, which considers the variance of intensity, the hybrid function better captures the vertical variation in intensity of the eyes. Kumar suggest a
technique in which possible eye areas are localized using a simple thresholding in color space followed b y a connected component analysis to quantif y spatially connected
regions and further reduce the search space to determine the contending eye pair windows. Finally the mean and variance projection functions are utilized in each eye pair
window to validate the presence of the eye. Feng and Yeun emplo y multi cues for eye detection on gray images using variance projection function.
4.4 IR METHOD:
The most common approach employed to achieve eye detection in real-time is by using infrared lighting to capture the physiological properties of eyes and an
appearance-based model to represent the eye patterns. The appearance-based approach detects eyes based on the intensity distribution of the eyes by exploiting the differences in
appearance of eyes from the rest of the face. This method requires a significant number of training data to enumerate all possible appearances of eyes i.e. representing the eyes of different subjects, under different face orientations, and diff erent illumination conditions.
The collected data is used to train a classifier such as a neural net or support vector machine to achieve detection.
4.5 SUPPORT VECTOR MACHINES (SVMs).
Support Vector Machines (SVMs) have been recently proposed
by Vapnik and his co-workers as a very effective method for general-purpose pattern recognition. Intuitively, given a set of points belonging to two classes, a SVM finds the hyper-plane that separates the largest possible fraction of points of the same class to the same side while maximizing the distances from either class to the hyper-plane. This hyper-plane is called Optimal
Separating Hyper-plane (OSH). It minimizes the risk of misclassifying not only the samples in the training set but also the unseen samples in the test set. The application of SVMs to computer vision area has emerged recently. Osuna train a SVM for face detection, where the discrimination is between two classes: face and non-face, each with thousands of samples. Guo and Stan show that the SVMs can be effectively trained for face recognition and is a better learning algorithm than the nearest center approach.
Graph Matching. After all images, including the gallery images and the probe images, are
extracted using EBGM procedure, the faces are represented as labelled face graphs. The matching procedure then involves the distance computation of the jets between different graphs, which is
4.6 Hidden Markov Models (HMMs):
HMMs are generally used for the statistical modelling of non-
stationary vector time series. By considering the facial configurable information as a time varying sequence, HMMs can be applied to face recognition. The most significant facial features of a frontal face image, including the hair, forehead, eyes, nose and mouth, occur in a natural order from top to bottom, even if the image has small rotations in the image plane, and/or rotations in the plane perpendicular to the image plane. Based on this observation, the image of a face may be modeled using a one-dimensional HMM by assigning each of these regions a state as
Given a face image for one subject in the trainin g set, the goal of the training stage is to
optimize the parameters to best describe the observation. Recognition is carried out by matching the test image against each of the trained models. To complete this procedure,
the image is converted to an observation sequence and the likelihood is computed for each stored model. The model with the highest likelihood reveals the identity of the unknown face. The HMM approach has shown the ability to yield satisfactory
recognition rates. However, HMMs are processor intensive models, which implies that the algorithm may run slowly. The HMM lead to the efficient detection of eye strips.
4.7 WAVELET BASED METHOD:
Our project is based on this method of eye detection. Wavelet
decomposition provides local information in both space domain and frequency domain. Despite the equal subband sizes, different subbands carry different amounts of
information. The letter ‘L’ stands fo r low frequency and the letter ‘H’ stands for high frequen cy. The left upper band is called LL band because it contains low frequency
information in both the row and column directions. The LL band is a coarser
approximation to the original image containing the overall information about the whole image. The LH subband is the result of applying the filter bank column wise and extracts
the facial features v ery well. The HL subband, which is the result of applying the filter bank row wise, extracts the outline of the face boundar y very well. While the HH band shows the high frequency component of the image in non-horizontal, non-vertical
directions it proved to be a redundant subband and was not considered having significant
information about the face. This observation was made at all resolutions of the image.This is the first level decomposition. Finally a fixed no. of maximum peaks are selected from LH subband, which are fed as inputs to the neural n etwork back propagation model
or RBF or neuro-fuzzy model is used to train that required network. According to the outputs of those peaks, after being passed through the updated weight and bias values, they are categorized into eye parts and non-eye parts. our project is based on this method
of eye detection.
WAVELET BASED METHOD FOR EYE DETECTION
5.1 INTRODUCTION:
The system consists mainly of two stages training and detection stage. A
block diagram of these two stages is shown in Figure 1.
5.2 Acquisition of Training Data:
The training data typically consists of 50 images of different persons with different hairstyles, different illumination conditions and varying facial
expressions. Some of the images have different states of the eye such as eyes closed. The size of the images varies from 64x64 to 256x256.
5.3 Discrete Wavelet Transform:
Wavelet decomposition provides local information in both space domain and frequency domain. Despite the equal subband sizes, different subbands carry
different amounts of information. The letter ‘L’ stands for low frequency and the letter ‘H’stands for high frequency. The left upper band is called LL band because it contains low frequency info rmation in both the row and column directions. The LL band is a
coarser app roximation to the original image containing the overall information about the whole image. The LH subband is the result of applying the filter bank column wise and extracts the facial features very well. The HL subband, which is the result of applying the
filter bank row wise, extracts the outline of the face boundary very well. While the HH band shows the high frequency component of th e image in non-horizontal, non-vertical directions it proved to be a redundant subband and was not considered having significant
information about the face. This observation was made at all resolutions of the image.This is the first level decomposition. A CDF (2, 2) biorthogonal wavelet is used. Gabor Wavelets seem to be the most probable candidate for feature ex traction. But they suffer
from certain limitations i.e. they cannot be implemented using Lifting Scheme and secondly th e Gabor Wavelets form a non-orthogonal set thus making the computation of
wavelet co efficients difficult and expensive. Special hardware is required to make the algorithm work in real time. Thus choosing a wavelet for eye detection depends on a lot of trial and error. Discrete Wavelet Transform is recursively applied to all the images in
the training data set until the lowest frequency subband is of size 32x 32 pixels i.e. the LH subband at a particular level or depth of DWT is of size 32x32. The original image’s
grayscale image is shown in figure 5.2. Th e LH subband at resolution 32x32 is shown in Figure 5.3.Here we have used HAAR wavelet instead of Gabor wavelet while calculating
wavelet transform.
fig-5.3 the LH sub-band figure We take the modulus of the wavelet coefficients in the LH subband. Experiments were performed to go to a resolution even coarser than 32x32. However, it was observed that in certain cases the features would be too close to each other and it was difficult even manually too to separate them. This would burden the Neural Network model and a small
error in locating the eyes at this low resolution would result in a large error in locating the eyes in the original image.
5.4 Detection of Wavelet Maxima:
Our approach to eye detection is based on the observation that, in intensity images eyes differ from the rest of the face because of their low intensity. Even if the eyes are closed, the darkness of the eye sockets is sufficient to extract the eye
regions. These intensity peaks are well captured by the wavelet coefficients. Thus, wavelet coefficients have a high value at the coordinates surrounding the eyes. We then
detect the wavelet maxima or the wavelet peaks in this LH subband of resolution 32x32. Note that several such peaks are detected, which can be the potential lo cations of th e
eyes. The intensity peaks are shown in Figure 5.4 and 5.5.
Fig-5.5 LH sub-band with peaks replaced by its 3 *3 neighborhood wavelet coefficient
5.5 Neural Network Training:
The wavelet peaks detected are the center of potential eye windows. We then feed 3x3 neighborhood wavelet coefficients of each of these local maxima’s in 32x32 LH
subbands of all training images to a Neural Network for training. The Neural Network has 9 input nodes, 4 hidden nodes, and 2 output nodes. A diagram of the Neural Network
architecture is shown in Figu re 5.6.. A (1,-1) at the output of Neural Network indicates an eye at the location of the wavelet maxima whereas (-1, 1) indicates a non-eye. Two output nodes instead of one were taken to improve the performance of the Neural
Network. MATLAB’s Neural Network Toolbox was used for simulation of the back propagation Neural Network. A conjugate gr adient learning rate of 0.4 was chosen while
training. This completes the training stages for neural networks b ack propagation model.
Here we hav e used the MLP (multi-layer p erceptions) back-propagation model for neural network training. It consists of having 9 neurons in the input layer. In the hidden layer or 2nd layer has 5 neuron for processing .In the 3rd or output layer h as the two nodes for
showing the output. We have taken two output node insists of one to get a better accuracy towards detecting eye. After this you have to find eye part & non-eye part in the figure
from neural network model. Where an output of (1, -1) indicates th e presence of an eye & output of (-1,1) indicates the presence of a non-eye.
EXPERIMENTATION & RESULTS
7.1 SOURCE CODE
Prog ram no.1
(Wavelet transform part)
function[inp]=aisT(a)
% clear all;
% close all;
% clc;
dwtmode('zpd');
% a=double(rgb2gray(imread('C:\MATLAB7\work\project\ais2.jpg') ));
imshow(uint8(a))
%figure
sizea=size(a)
[c,s]= wavedec2(a,4,'haar');
% ap_cf = appcoef2(c,s,'h aar',4);
% sizeAP_CF=size(ap_cf)
sizec=size(c)
h_cf2 = detcoef2('h ',c,s,4);
[m,n]=size(h_cf2); %n used later
sizehcf=size(h_cf2)
% sizevcf=size(v_cf2)
% sizedcf=size(d_cf2)
% imshow(uint8(ap_cf)) %for LL image
%figure %figure of LH
%imshow(uint8(h_cf2))
imview(h_cf2)
% % figure
% % imshow(uint8(v_cf2))
% % figure
% % imshow(uint8(d_cf2))
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%% DETECTION OF WAVELET
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%% MAXIMA
% LH=abs(h_cf2);
LH1=zeros(m*n,1); % LH1 just used for descending matrix h_cf....
%^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
k=1;
for i=1:m
for j=1:n
LH1(k)= abs(h_cf2(i,j)); %(h_cf2(i,j));
k=k+1;
end
end
LH=sort(LH1,'descend '); %all values h_cf2 r stored in LH1
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%max
peak wav elet
ln=25;
max_pk=zeros(ln,1);
for i=1:ln
max_pk(i)=LH(i); %the value of top ln=25 max wave coef.. in LH
figure(h_cf2)
end
% % % % % % % % % % % % % % % % % % % % % % % % % % % % % %
dhcf2=zeros(m,n);
for i=1:m
for j=1:n
if any( abs(h_ cf2(i,j))>=max_pk ) % (h_cf2(i,j))>=max_pk )
dhcf2(i,j)=h_cf2(i,j); % dchf is used for max peak detectiopn
& others zero
end
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%
% dhcf2
imview(dhcf2)
% figure
% imshow(uint8(dhcf2))
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% for
neighbourhood configuration
inp=zeros(ln,13);
size(inp)
l=1;k=1;
ph_cf2=[zeros(1,n+2);zeros(m,1),h_cf2,zeros(m,1);zeros(1,n+2)]; %2 avoid error
Attempted to access h_ cf2(13,51);
pdhcf2=[zeros(1,n+2);zeros(m,1),dhcf2,zeros(m,1);zeros(1,n+2)]; %index out of
bounds because size(h_cf2)=[38,50].
[size_LHx,size_LHy]=size(h_cf2);
for i=2:m+1
for j=2:n+1
if dhcf2(i-1,j-1)~=0
pdhcf2(i-1,j-1)=ph_cf2(i-1,j-1); p dhcf2(i-1,j) =ph_cf2(i-1,j); pdhcf2(i-
1,j+1)=ph_cf2(i-1,j+1);
pdhcf2(i,j-1)=ph_cf2(i,j-1); pdhcf2(i,j)=ph_cf2(i,j);
pdhcf2(i,j+1)=ph_cf2(i,j+1);
pdhcf2(i+1,j-1)=p h_cf2(i+1,j-1); pdhcf2(i+1,j)=ph_cf2(i+1,j);
pdhcf2(i+1,j+1)=ph_cf2(i+1,j+1);
inp(l,k) =ph_cf2(i-1,j-1); inp(l,k+1)=ph_cf2(i-1,j); inp(l,k+2)=ph_cf2(i-
1,j+1);
inp(l,k+3)=ph_cf2(i,j-1); inp(l,k+4)=ph_cf2(i,j);
inp(l,k+5)=ph_cf2(i,j+1);
inp(l,k+6)=ph_cf2(i+1,j-1); inp(l,k+7)=ph_cf2(i+1,j);
inp(l,k+8)=ph_cf2(i+1,j+1);
% inp(l,k+10)=i-1/size_LHx ; inp(l,k+9)=j-1/size_LHy;
inp(l,k+10)=i-1; inp(l,k+9)=j-1;
l=l+1; k=1;
end
end
end
inp(:,10:11)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
for i=1:m
for j=1:n
xdhcf2(i,j)=pdhcf2(i+1,j+1);
end
end
imview(xdhcf2)
% figure
% imshow(uint8(xdhcf2))
% max_pk
% pdhcf2
% ph_cf2
Prog ram no.2
(Neural network model part)
%for aiswariya
close all;
clear all;
clc;
a=double(rgb2gray(imread('C :\MATLAB7\work\project\ais2.jpg')));
pa=aisX(a);
pk=pa(:,1:9);
p=pk';
Tp=[1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1];
T=[Tp;-Tp];
net = newff( minmax(p),[5 2],{'tansig' 'purelin '});
Y = sim(net,p);
% plot(P,T,P,Y,'o');
% net.trainParam.show = 50;
net.trainParam.lr = 0.4;
net.trainParam.epo chs = 4000;
net.trainParam.goal = 1e-5;
[net,tr] = train(net,p,T);
Y = sim(net,p)
% plot(P,T,P,Y,'o')
% Y=sim(net,3.5)
b=double(rgb2gray(imread('C:\MATLAB7 \work \project\ais6.jpg')));
pb=aisT(b);
pbc=pb(:,1:9);
Y=sim(net,pbc')
Y1(output for training image) =
Columns 1 through 7
0.9090 0.9173 0.9187 0.8910 0.9654 0.9287 -0.8449
-0.9604 -0.9515 -0.8977 -1.1043 -0.9719 -0.9439 0.7588
Columns 8 through 14
-0.9669 -0.8692 -0.9752 -0.9505 -0.9779 -0.9481 -0.0072
0.8855 0.9132 0.7044 0.8979 0.7072 0.9427 0.8075
Columns 15 through 21
-0.9867 -0.8649 -0.9705 -0.9671 -0.9180 -0.8279 -0.9568
0.9640 0.9966 0.9099 0.8198 0.8876 0.9275 0.9610
Columns 22 through 25
-0.9707 -0.9030 -0.9872 -0.9412
0.9744 0.9312 0.9944 0.9187
Y2(output for test image)=
Columns 1 through 7
-0.9593 -0.8823 0.9363 0.9128 0.8900 0.9825 0.9067
0.8770 0.9303 -0.9011 -0.9900 -0.9881 -0.9614 - 0.9667
Columns 8 through 14
0.8744 -0.8321 -0.8557 -0.9644 -0.9089 -0.8669 -0.9586
-0.9106 0.9858 0.9368 0.9782 0.8298 0.9175 0.8018
Columns 15 through 21
-0.9604 -0.8081 -0.8315 -0.8783 -0.8116 -0.9650 -0.9011
0.8948 0.9015 0.9271 0.9845 0.9891 0.9533 0.8772
Columns 22 through 25
-0.8403 -0.8179 -0.9558 -0.9443
0.9556 0.9958 0.8170 1.0770
CONCLUSION
7.1. Performance
A number of experiments were done to test the robustness of the algorithm and to increase the accuracy of eye detection. Various architectures of Neural Networks with
different learning rates were tried and it was found that back propagation with conjugate gradient learning seemed to be the best choice. A very high learning rate of 0.8 was
Chosen because the learning algorithm was getting trapped in local minima while training the network. Final training was stopped when the error graph, as shown in Figure 7.1,
didn’t show any significant fluctuation.
An ex periment was done in which the face was analyzed using wavelet packets and it was found that most of the information was retained by the low frequency sub bands and the high frequency packets had no information. Images with different states of the eye
(closed, open, half open, looking sideways, head tilted etc.) and varying eye width were chosen. The eye positions found were compared with the positions that were pointed out
manually. The eyes were correctly located when its location is within two pixels, in both x and y directions, of the manually assigned point. The variation of 2 pix els is
deliberately allowed, to compensate for the inaccuracies in the location of eyes during training. An accuracy of 88% was observed in the final location of the eyes. A database
of 60 test images was evaluated for performan ce. All these test images were captured in totally different environment conditions and wer e not included while training the Neural Network. Most of the error cases occurred in images with complex background. Also
there was an error in accurately determining the exact location of the eyes since a 1-pixel shift at a resolution of 32x32 corresponded to a larger shift in the exact location of the
eye. In some cases the Neural Network classified only 1 peak as an eye in spite of the
presence of 2 eyes in the image. In a few cases observations were made in which regions of the face not belonging to the eyes were d etected as eyes. In other cases more than 2 eyes were indicated in the image. In contrast, the perfo rmance of this algorithm, which
uses wavelets as a preprocessor to Neural Networks, the algorithm with only Neural Networks, achieved an accuracy of 81% in d etecting the exact location of the eyes.
7.2 CONCLUSION:
This type of approach gives a n ew dimension to the existing eye detection algorithms. The present algorithm is robust and at par with the other existing methods but still has a lot of scope for improvement. In this type of approach a wavelet subband approach in
using Neural Networks for eye detection. Wavelet Transform is adopted to decompose an image into different sub bands with different frequency compon ents. A low frequency subband is selected for feature extraction. The proposed method is robust against
illumination, background, facial expression ch anges and also works for images of
different sizes. However, a combination of information in different frequency bands at different scales, or usin g multiple cues can even give better performance. Further studies
in using Fuzzy Logic fo r data fusion of multiple cues will give better results.
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