Using Daugmans Rubber Sheet model, I am not able to get the correct normalized image of iris. Please help me out.

This is my input image, the output i am getting is:

I am sure the center coordinates , I have found them correctly because I am able to segment the iris from the image:

Below is my code for the same.

clc
clear all
close all

%Any image from CASIA Dataset
eyeimage_filename = "F:\8th SEM\Dataset\CASIA\file1.jpg";
eyeimage = imread(eyeimage_filename); 
I = eyeimage;

%%%%%%%%%%%%%%%%%%%%%%%%  CREATEIRISTEMPLATE  %%%%%%%%%%%%%%%%%%
%normalisation parameters
radial_res = 20;
angular_res = 240;

% with these settings a 9600 bit iris template is created
%feature encoding parameters
nscales=1;
minWaveLength=18;
mult=1; % not applicable if using nscales = 1
sigmaOnf=0.5;

%%%%%%%%%%%%%%%%%%%%%%%%  SEGMENTIRIS  %%%%%%%%%%%%%%%%%%
%CASIA
lpupilradius = 28;
upupilradius = 75;
lirisradius = 80;
uirisradius = 150;

% define scaling factor to speed up Hough transform
scaling = 0.4;

reflecthres = 240;

% find the iris boundary
[row, col, r] = findcircle(eyeimage, lirisradius, uirisradius, scaling, 2, 0.20, 0.19, 1.00, 0.00);

circleiris = [row col r];

rowd = double(row);
cold = double(col);
rd = double(r);

irl = round(rowd-rd);
iru = round(rowd+rd);
icl = round(cold-rd);
icu = round(cold+rd);

imgsize = size(eyeimage);

if irl < 1 
    irl = 1;
end

if icl < 1
    icl = 1;
end

if iru > imgsize(1)
    iru = imgsize(1);
end

if icu > imgsize(2)
    icu = imgsize(2);
end

% to find the inner pupil, use just the region within the previously
% detected iris boundary
imagepupil = eyeimage( irl:iru,icl:icu);

%find pupil boundary
[rowp, colp, r] = findcircle(imagepupil, lpupilradius, upupilradius,0.6,2,0.25,0.25,1.00,1.00);

rowp = double(rowp);
colp = double(colp);
r = double(r);

row = double(irl) + rowp;
col = double(icl) + colp;

row = round(row);
col = round(col);

circlepupil = [row col r];

% set up array for recording noise regions
% noise pixels will have NaN values
imagewithnoise = double(eyeimage);

%find top eyelid
topeyelid = imagepupil(1:(rowp-r),:);
lines = findline(topeyelid);

if size(lines,1) > 0
    [xl yl] = linecoords(lines, size(topeyelid));
    yl = double(yl) + irl-1;
    xl = double(xl) + icl-1;
    
    yla = max(yl);
    
    y2 = 1:yla;
    
    ind3 = sub2ind(size(eyeimage),yl,xl);
    imagewithnoise(ind3) = NaN;
    
    imagewithnoise(y2, xl) = NaN;
end

%find bottom eyelid
bottomeyelid = imagepupil((rowp+r):size(imagepupil,1),:);
lines = findline(bottomeyelid);

if size(lines,1) > 0
    
    [xl yl] = linecoords(lines, size(bottomeyelid));
    yl = double(yl)+ irl+rowp+r-2;
    xl = double(xl) + icl-1;
    
    yla = min(yl);
    
    y2 = yla:size(eyeimage,1);
    
    ind4 = sub2ind(size(eyeimage),yl,xl);
    imagewithnoise(y2, xl) = NaN;
    
end

imagewithnoise(ind4) = NaN;
%For CASIA, eliminate eyelashes by thresholding
ref = eyeimage < 100;
coords = find(ref==1);
imagewithnoise(coords) = NaN;
% figure,imshow(eyeimage);title('originalimage');
% figure,imshow(imagepupil);title('pupil');
% figure,imshow(imagewithnoise);title('image with noise');

% WRITE NOISE IMAGE
%

imagewithnoise2 = uint8(imagewithnoise);
imagewithcircles = uint8(eyeimage);

%get pixel coords for circle around iris
[xii,yii] = circlecoords([circleiris(2),circleiris(1)],circleiris(3),size(eyeimage));
ind2 = sub2ind(size(eyeimage),double(yii),double(xii)); 

%get pixel coords for circle around pupil
[xpp,ypp] = circlecoords([circlepupil(2),circlepupil(1)],circlepupil(3),size(eyeimage));
ind1 = sub2ind(size(eyeimage),double(ypp),double(xpp));

% Write noise regions
imagewithnoise2(ind2) = 255;
imagewithnoise2(ind1) = 255;
% Write circles overlayed
imagewithcircles(ind2) = 255;
imagewithcircles(ind1) = 255;
figure,subplot(1,3,1);imshow(imagewithnoise2);title('segmented');
subplot(1,3,2);imshow(imagewithcircles);title('circles');
subplot(1,3,3);imshow(eyeimage);title('original image');

%%%%%%%%%%%%%%%%%% MODEL2OUTPUT %%%%%%%%%%%%%%%%%
x=xii;
y=yii;
r1=ind2;
xp=xpp;
yp=ypp;
r2=ind1;
[nx,ny,d] = size(I) ;
[X,Y] = meshgrid(1:ny,1:nx) ;

th = linspace(0,2.*pi);
x=double(x);
y=double(y);
r1=double(r1);
xp=double(xp);
yp=double(yp);
r2=double(r2);

idx = inpolygon(X(:),Y(:),x,y) ;

for i = 1:d
    I1 = I(:,:,i) ;
    I1(~idx) = 255 ;
    I(:,:,i) = I1 ;
end
idx = inpolygon(X(:),Y(:),xp,yp) ;
for i = 1:d
    I1 = I(:,:,i) ;
    I1(idx) = 255 ;
    I(:,:,i) = I1 ;
end
figure,imshow(I);
title("INPOLYGON IRIS");

%%%%%%%%%%%%%%%% RUBBER SHEET MODEL%%%%%%%%%%%%%%%%%%%%%%%%%%

xp = rowp;
yp = colp; 
rp = r;
xi = rowd;
yi = cold;
ri = rd;
% Initialize samples 

 angleSamples = 360;
    RadiusSamples = 360;
    debug =0;
    interpolateQ =1;
    angles = (0:pi/angleSamples:pi-pi/angleSamples) + pi/(2*angleSamples);%avoiding infinite slope
    r = 0:1/RadiusSamples:1;
    nAngles = length(angles);
    
    % Calculate pupil points and iris points that are on the same line
    x1 = ones(size(angles))*xi;
    y1 = ones(size(angles))*yi;
    x2 = xi + 10*sin(angles);
    y2 = yi + 10*cos(angles);
    dx = x2 - x1;
    dy = y2 - y1;
    slope = dy./dx;
    intercept = yi - xi .* slope;
    
    xout = zeros(nAngles,2);
    yout = zeros(nAngles,2);
    for i = 1:nAngles
        [xout(i,:),yout(i,:)] = linecirc(slope(i),intercept(i),xp,yp,rp);
    end
       
    % Get samples on limbus boundary
    xRightIris = yi + ri * cos(angles);
    yRightIris = xi + ri * sin(angles);
    xLeftIris = yi - ri * cos(angles);
    yLeftIris = xi - ri * sin(angles);
    
    
   % Get samples in radius direction
    xrt = (1-r)' * xout(:,1)' + r' * yRightIris;
    yrt = (1-r)' * yout(:,1)' + r' * xRightIris;
    xlt = (1-r)' * xout(:,2)' + r' * yLeftIris;
    ylt = (1-r)' * yout(:,2)' + r' * xLeftIris;
    
    % Create Normalized Iris Image
    if interpolateQ
        image = uint8(reshape(interp2(double(I),[yrt(:);ylt(:)],[xrt(:);xlt(:)]),length(r), 2*length(angles))');
    else
        image = reshape(I(sub2ind(size(I),round([xrt(:);xlt(:)]),round([yrt(:);ylt(:)]))),length(r), 2*length(angles));
    end
    figure,imshow(image);
    title("normalized image")
    
    %%Show all points on original input image
    if debug
        
        img = insertShape(eyeimage, 'circle', [yrt(:),xrt(:),2*ones(size(xrt(:)))],'Color','r');
        img = insertShape(eyeimage, 'circle', [ylt(:),xlt(:),2*ones(size(xrt(:)))],'Color','r');
        
        figure('name','Sample scheme of the rubber sheet normalization');
        imshow(img);
        drawnow;
        
    end

Answer 1

[Aditya]

Hi Ridhima,

If you're looking to normalize an iris region using Daugman's Rubber Sheet Model, you can refer to the following resources which can help you in resolving the issue. Here's how you can utilize them:

1] MATLAB Central File Exchange Resource: https://in.mathworks.com/matlabcentral/fileexchange/51246-pupil-limbus-detection-and-daugman-normalization

This submission includes a function for detecting the pupil and limbus (iris boundary) and a function for performing the normalization.

Below is an example code snippet using that resource which demonstrates how to detect the iris and pupil boundaries and then normalize the iris region:

% Read the eye image 
img = imread('example.jpg'); 

% Find the Limbus boundary without GUI 
[yPosIris, xPosIris, rIris, image] = daugmanCircleDetection(img); 

% Find the Pupil boundary 
[yPosPupil, xPosPupil, rPupil, image] = daugmanCircleDetection(img, 'Feature','pupil'); 

% Normalize the iris region according to Daugman's model 
irisRegion = rubberSheetNormalisation(img, xPosPupil, yPosPupil, rPupil, xPosIris, yPosIris, rIris, 'DebugMode', 1); 

% Show the resulting image 
figure(2); 
imshow(irisRegion); 

You can adjust the DebugMode, RadiusSamples, UseInterpolation, and AngleSamples parameters to control the visualization and resolution of the normalization process.

2] GitHub Repository: https://github.com/shubhamagarwal269/iris_recognition/blob/master/src/createiristemplate.m

This repository includes code for creating an iris template, which is part of the iris recognition pipeline. The normalization step is also included within this process.

You can review the “createiristemplate.m” script to understand how it integrates the normalization step within the broader context of iris recognition.

If you continue to face difficulties with your code, please provide all the related files, including the image and any custom functions. So that, I can run a test on my side to better diagnose the issue and assist you in resolving it.

Hope this helps!

[Ridhima Chopra]

Thanks a lot for your response.

I debugged the error. To get the pupil, we are cropping the image and getting the centre coordinates of the pupil with respect to that cropped image. This was where i went wrong.

rowp = double(rowp);

colp = double(colp);

r = double(r);

row = double(irl) + rowp;

col = double(icl) + colp;

Instead of rowp and colp I had to use row and col.

Thus for the rubber sheet model, variables will be initialized like this:

xp = row;

yp = col;

rp = r;

xi = rowd;

yi = cold;

ri = rd;

I appreciate your help. Thanks again @Aditya! :)