Image Processing - Matlab Homework II

Submitted By:

Adarsh Chandran (Student Id No: 3617720)
Ravishankar Sivalingam (Student Id No: 3617709)

Question Number 1
Question Number 2

Question Number 1

Morphology.

* Inbuilt Matlab functions have been made use of in implementing the
  below code.

clear all
close all
clc

% Initializing the Parameters
imageSize = 2000;
% number of 3x3 squares
num3s = 100;
% number of 5x5 squares
num5s = 20;

% Generating the image
I = uint8(zeros(imageSize));
% randomly generate the square centers
coords_3x3=randint(num3s,2,[3 imageSize+2]);
coords_5x5=randint(num5s,2,[3 imageSize+2]);
% zero-pad the image
padI=padarray(I,[2 2]);
% fill in the squares
for i=1:length(coords_3x3)
    padI(coords_3x3(i,1)-1:coords_3x3(i,1)+1,coords_3x3(i,2)-1:coords_3x3(i,2)+1)=255;
end
for i=1:length(coords_5x5)
    padI(coords_5x5(i,1)-2:coords_5x5(i,1)+2,coords_5x5(i,2)-2:coords_5x5(i,2)+2)=255;
end
% remove the zero-padding
I=padI(3:imageSize+2,3:imageSize+2);

% Defining the structure elements
%  1
%  1
se21 = strel('rectangle',[2 1]);
%  1  1
se12 = strel('rectangle',[1 2]);
% 0 0 1
% 0 0 0
% 1 0 0
serd101 = strel('arbitrary',[0 0 1; 0 0 0; 1 0 0]);
% 1 0 0
% 0 0 0
% 0 0 1
seld101 = strel('arbitrary',[1 0 0; 0 0 0; 0 0 1]);
% 0 1
% 1 0
serd11 = strel('arbitrary',[0 1; 1 0]);
% 1 0
% 0 1
seld11 = strel('arbitrary',[1 0; 0 1]);
% 0 1
% 0 0
% 1 0
serdstr = strel('arbitrary',[0 1; 0 0; 1 0]);
% 1 0
% 0 0
% 0 1
seldstr = strel('arbitrary',[1 0; 0 0; 0 1]);
% 0 0 1
% 1 0 0
serdstr1 = strel('arbitrary',[0 0 1; 1 0 0]);
% 1 0 0
% 0 0 1
seldstr1 = strel('arbitrary',[1 0 0; 0 0 1]);
% 3x3 square structuring element
se3=strel('square',3);
% 5x5 square structuring element
se5=strel('square',5);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% a.	 all the squares that are touching the image border
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% 5x5 squares touching the border
borders_5x5=0*I;
% create a border mask
borders_5x5([1:3 end-2:end],:)=1;
borders_5x5(:,[1:3 end-2:end])=1;
borderI5=imdilate((imerode(I,se5)).*borders_5x5,se5);

% 3x3 squares touching the border
borders_3x3=uint8(zeros(imageSize));
% create a border mask
borders_3x3([1 2 end-1 end],:)=1;
borders_3x3(:,[1 2 end-1 end])=1;
borderI3=imdilate((imerode(I,se3).*borders_3x3),se3);

% All the squares touching the image border
borderSquares = borderI5 + borderI3;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% b.	all the 3x3 squares that do not overlap with any other square
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Find all the 5x5 squares in the image
squares_5x5 = imdilate(imerode(I,se5),se5);

% Find all the 3x3 squares in the image by subtracting from the original
% image
IbTemp = I;
% Determine the 3x3 squares which are not overlapping with any of the 3x3
% squares
IbTemp21 = imdilate(imdilate(imerode(imerode(IbTemp,se3),se21),se21),se3);
IbTemp12 = imdilate(imdilate(imerode(imerode(IbTemp,se3),se12),se12),se3);
IbTemprd101 = imdilate(imdilate(imerode(imerode(IbTemp,se3),serd101),serd101),se3);
IbTempld101 = imdilate(imdilate(imerode(imerode(IbTemp,se3),seld101),seld101),se3);
IbTemprd11 = imdilate(imdilate(imerode(imerode(IbTemp,se3),serd11),serd11),se3);
IbTempld11 = imdilate(imdilate(imerode(imerode(IbTemp,se3),seld11),seld11),se3);
IbTemprdstr = imdilate(imdilate(imerode(imerode(IbTemp,se3),serdstr),serdstr),se3);
IbTempldstr = imdilate(imdilate(imerode(imerode(IbTemp,se3),seldstr),seldstr),se3);
IbTemprdstr1 = imdilate(imdilate(imerode(imerode(IbTemp,se3),serdstr1),serdstr1),se3);
IbTempldstr1 = imdilate(imdilate(imerode(imerode(IbTemp,se3),seldstr1),seldstr1),se3);
ov3x3Squares = IbTemp21+IbTemp12+IbTemprd101+IbTempld101+IbTemprd11+IbTempld11+IbTemprdstr+IbTempldstr+IbTemprdstr1+IbTempldstr1;
for cnt = 1:(imageSize-2)
    if (ov3x3Squares(cnt:(cnt+2),(imageSize-2):imageSize) == [0 255 255; 0 255 255; 0 255 255])
        ov3x3Squares(cnt:(cnt+2),(imageSize-2):imageSize) = zeros(3);
    end
    if (ov3x3Squares((imageSize-2):imageSize, cnt:(cnt+2)) == [0 255 255; 0 255 255; 0 255 255]')
        ov3x3Squares((imageSize-2):imageSize, cnt:(cnt+2)) = zeros(3);
    end
end
notNonOv3x3Squares = ov3x3Squares + squares_5x5;
nonOv3x3Squares = I - notNonOv3x3Squares;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% c.	all the 5x5 squares, overlapping and non-overlapping
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
squares_5x5 = imdilate(imerode(I,se5),se5);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% d.    all the overlapping squares
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
ov3x3Squares;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Display the Results
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
figure;imagesc(I);colormap(gray)
title('Fig 1. Original Image')
figure;imagesc(borderSquares);colormap(gray)
title('Fig 1.A. All the squares that are touching the image border')
figure;imagesc(nonOv3x3Squares);colormap(gray)
title('Fig1.B. All the 3x3 squares that do not overlap with any other square')
figure;imagesc(squares_5x5);colormap(gray)
title('Fig1.C. All the 5x5 squares, overlapping and non-overlapping')
figure;imagesc(ov3x3Squares);colormap(gray)
title('Fig1.D. All the overlapping squares')

Question Number 2

Active Contours.

* Inbuilt Matlab functions have been made use of in implementing the
  below code.

close all
clear all
clc

% read the input image
inpImage =imread('coin_1.jpg');
% size of image
[rows cols dims] = size(inpImage);

if dims==3
    inpImage=double(rgb2gray(inpImage));
else
    inpImage=double(inpImage);
end

% Gaussian filter parameter
sigma=1.2;
% Gaussian filter
G=fspecial('gaussian',15,sigma);
% Gaussian smoothed image
inpImage=conv2(inpImage,G,'same');


% gradient of image
[gradIX,gradIY]=gradient(inpImage);
absGradI=sqrt(gradIX.^2+gradIY.^2);


% higher dimensional embedding function phi whose zero level set is our
% contour
% radius of circle - initial embedding function
% radius=min(floor(0.45*rows),floor(0.45*cols));
[u,v] = meshgrid(1:cols, 1:rows);
phi = ((u-cols/2)/(floor(0.45*cols))).^2+((v-rows/2)/(floor(0.45*rows))).^2-1;

% edge-stopping function
g = 1./(1+absGradI.^2);
% gradient of edge-stopping function
[gx,gy]=gradient(g);

% gradient descent step size
dt=.4;

% number of iterations after which we reinitialize the surface
num_reinit=10;

phiOld=zeros(rows,cols);

% number of iterations
iter=0;

while(sum(sum(abs(phi-phiOld)))~=0)
    % gradient of phi
    [gradPhiX gradPhiY]=gradient(phi);
    % magnitude of gradient of phi
    absGradPhi=sqrt(gradPhiX.^2+gradPhiY.^2);
    % normalized gradient of phi - eliminating singularities
    normGradPhiX=gradPhiX./(absGradPhi+(absGradPhi==0));
    normGradPhiY=gradPhiY./(absGradPhi+(absGradPhi==0));

    [divXnormGradPhiX divYnormGradPhiX]=gradient(normGradPhiX);
    [divXnormGradPhiY divYnormGradPhiY]=gradient(normGradPhiY);
    % curvature is the divergence of normalized gradient of phi
    K = divXnormGradPhiX + divYnormGradPhiY;
    % dPhiBydT
    dPhiBydT =( g.*K.*absGradPhi + g.*absGradPhi + (gx.*gradPhiX+gy.*gradPhiY) );
    phiOld=phi;
    % level set evolution equation
    phi = phi + ( dt * dPhiBydT );
    iter=iter+1;
    if mod(iter,num_reinit)==0
        % reinitialize the embedding function after num_reinit iterations
        phi=sign(phi);
        phi = double((phi > 0).*(bwdist(phi < 0)) - (phi < 0).*(bwdist(phi > 0)));
    end
    if mod(iter,10)==0
        pause(0.05)
        iter
        imagesc(inpImage)
        colormap(gray)
        hold on
        contour(phi,[0 0],'r')
        %         close all
        %         surf(phi)
        %         pause
    end
end

Image Processing - Matlab Homework II

Contents

Question Number 1

Question Number 2