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