Image Enhancement in Frequency Domain (i) Gaussian Low Pass Filter (ii) Butterworth Low Pass Filter (iii) Ideal High Pass Filter (iv) Ideal Low Pass Filter

1. IDEAL LPF:

clc;

close all;

clear all;

        a=imread('circuit.tif');  % reading an image X

        a=double(a);

        c=size(a);

       N=c(1);

        D0=input('Enter the cut-off frequency:  ');

        for u=1:1:c(1)

        for v=1:1:c(2)

        D=((u-N/2))^2+((v-(N/2))^2)^0.5;

         if D<D0;

             H(u,v)=1;

         else

             H(u,v)=0;

         end

        end

        end

       vv=fft2(a);

       vc=fftshift(vv);

       x=vc.*H;

       X=abs(ifft2(x));

        figure;

        imshow(uint8(a));

        title('original image'),

         figure;

        imshow(uint8(X));

       title('practical by shruti naik');

        figure;

        mesh(H);

      figure;

      imagesc(H),colormap(gray);

2. BUTTERWORTH LPF:

img=im2double(imread('circuit.tif'));

figure(1)

imshow(img)

title('ORIGINAL IMAGE');

[M N] = size(img); % Saving the the rows of image in M and columns in N

filter=zeros(M,N);

f_transform=fft2(img); %Fourier transformed of an image

f_shift=fftshift(f_transform);

d0=100; %10 %210            %Cutoff Frequency

n=2;                %Order of butterworth filter

    for i=1:M

        for j=1:N

            distance=(i-M/2)^2 + (j-N/2)^2;   %distance between pt.(m,n)

            low_filter(i,j)= ( 1 + (distance/d0)^(2*n))^(-1);  %butterworthlpf formula

        end

    end

filter_apply=f_shift.*low_filter;

image_orignal=ifftshift(filter_apply);

image_filter_apply=abs(ifft2(image_orignal));

figure(2)

imshow(image_filter_apply,[])

title('practical performed by shruti');

figure(3)

mesh(low_filter), figure(4)

imagesc(low_filter),colormap(gray);

3. GAUSSIAN LPF:

a=im2double(imread('circuit.tif'));

figure(1)

imshow(a)

title('original image')

[m n]=size(a); % Saving the the rows of image in M and columns in N

f_transform=fft2(a);

f_shift=fftshift(f_transform);  %Fourier transformed of an image

p=m/2;

q=n/2;

d0=25; %Cutoff Frequency and the sigma value

for i=1:m

for j=1:n

distance=sqrt((i-p)^2+(j-q)^2);  

low_filter(i,j)=exp(-(distance)^2/(2*(d0^2)));  

end

end

filter_apply=f_shift.*low_filter;

image_orignal=ifftshift(filter_apply);

image_filter_apply=abs(ifft2(image_orignal));

figure(2)

imshow(image_filter_apply,[])

title('practical performed by shruti')

figure(3)

mesh(low_filter)

figure(4)

imagesc(low_filter),colormap(gray);

4. IDEAL HPF:

clc;

a=imread('circuit.tif');

a=double (a);

[row col]=size(a);

set=input('Enter the value of the cut off frequency: ');

for u=1:1:row

for v =1:1:col

D=((u-(row/2))^2+(v-(col/2))^2)^0.5;

if D<set;

H(u,v)=0;

else

    H(u,v)=1;

end

end

end

vv=fft2(a);

vc=fftshift(vv);

x=(vc.*H);

X=abs(ifft2(x));

%Plotting%

figure(1)

imshow(uint8(a));

figure(2)

imshow(uint8(X));

figure(3)

imagesc(H),colormap(gray);

figure(4)

mesh(H);

5. BUTTERWORTH HPF:

img=im2double(imread('circuit.tif'));

figure(1)

imshow(img)

title('ORIGINAL IMAGE');

[M N] = size(img);

filter=zeros(M,N);

f_transform=fft2(img);

f_shift=fftshift(f_transform);

d0=150;             %Cutoff Frequency

n=2;                %Order of butterworth filter

    for i=1:M

        for j=1:N

            distance=(i-M/2)^2 + (j-N/2)^2;

            hf(i,j)= ( 1 + (d0/distance)^(2*n))^(-1);

        end

    end

filter_apply=f_shift.*hf;

image_orignal=ifftshift(filter_apply);

image_filter_apply=abs(ifft2(image_orignal));

figure(2)

imshow(image_filter_apply,[])

title('practical performed by shruti');

figure(3)

mesh(hf)

figure(4)

imagesc(hf),colormap(gray);

6. GAUSSIAN HPF:

a=im2double(imread('circuit.tif'));

figure(1)

imshow(a)

title('original image')

[m n]=size(a);

f_transform=fft2(a);

f_shift=fftshift(f_transform);

p=m/2;

q=n/2;

d0=25;

for i=1:m

for j=1:n

distance=sqrt((i-p)^2+(j-q)^2);

high_filter(i,j)=1-exp(-(distance)^2/(2*(d0^2)));

end

end

filter_apply=f_shift.*high_filter;

image_orignal=ifftshift(filter_apply);

image_filter_apply=abs(ifft2(image_orignal));

figure(2)

imshow(image_filter_apply,[])

title('practical performed by shruti')

figure(4)

imagesc(high_filter),colormap(gray);