Removing moire pattern from an image

Hi Guys,

I trying to remove The moiré pattern from an image using filters in frequency domain, specifically, NOTCH REJECT HIGH PASS FILTER,

But when I try to plot the filtered image, a black image appears,

Here is the code that i use to do that, Someone can help me please??

clc;clear all;
I=imread('img2.PNG');
I=im2double(I);
I=rgb2gray(I);
h=size(I,1);%ALTO (Y)
w=size(I,2);%ANCHO (X)
P=2*h;
Q=2*w;
I1=fft2(I,P,Q);% FFT NÃO CENTRALIZADA
Ia=abs(I1);
I2=fftshift(I1);%FFT CENTRALIZADA
I3=log(1+abs(I2));
f_max=max(I3(:));
I4=I3/f_max;%SPECTRUM IN FREQUENCY DOMAIN OF THE ORIGINAL IMAGE


[x,y]=meshgrid(-floor(Q/2):floor(Q-1)/2, -floor(P/2):floor(P-1)/2);
Do=15;n=5;fc=30; %
a1=x-110/2; b1=y-145/2;
a2=x-110/2; b2=y+145/2;
a3=x+110/2; b3=y+145/2;
a4=x+110/2; b4=y-145/2;
D1=sqrt(a1.^2+b1.^2);
D2=sqrt(a2.^2+b2.^2);
D3=sqrt(a3.^2+b3.^2
D4=sqrt(a4.^2+b4.^2);

B1=1./(1.+(Do.*(D1.^(-1))).^(2*n));
B2=1./(1.+(Do./D2).^(2*n));
B3=1./(1.+(Do./D3).^(2*n));
B4=1./(1.+(Do./D4).^(2*n));

I5=I4.*B1.*B2.*B3.*B4;
I6=abs(ifft2(I5));
I7=abs(I6);maxi=max(I6(:));
I8=im2uint8(I6/maxi);
%=========================================================================%
%=============================PLOT========================================%
%=========================================================================%
figure
subplot(1,2,1),imhist(I),title('Histograma Img. Original')
subplot(1,2,2),imhist(histeq(I)),title('Histograma Equalizado')
figure
subplot(2,3,1),imshow(I),title('Imagem Original')
subplot(2,3,2),imshow(I1),title('FFT nao centralizada')
subplot(2,3,3),imshow(I2),title('FFT centralizada')
subplot(2,3,4),imshow(I4),title('Spectrum')
subplot(2,3,5),imshow(I5),title('Notch Reject')
subplot(2,3,6),imshow(I8),title('Imagem filtrada')

[Walter Roberson]

The original image appears to be the same one as at https://www.mathworks.com/matlabcentral/answers/452551-removing-a-moire-pattern-from-a-bw-image

[Walter Roberson]

See https://www.mathworks.com/matlabcentral/answers/317402-how-to-create-a-notch-filter-for-the-image-to-remove-noise

Answer 1

[Walter Roberson]

filename = 'https://www.mathworks.com/matlabcentral/answers/uploaded_files/210517/MatlabThing.png';
I = imread(filename);
I=im2double(I);
I=rgb2gray(I);
h=size(I,1);%ALTO (Y)
w=size(I,2);%ANCHO (X)
P=2*h;
Q=2*w;
I1=fft2(I,P,Q);% FFT NÃO CENTRALIZADA
I2=fftshift(I1);%FFT CENTRALIZADA
I3=log(1+abs(I2));
f_max=max(I3(:));
I4=I3/f_max;%SPECTRUM IN FREQUENCY DOMAIN OF THE ORIGINAL IMAGE


[x,y]=meshgrid(-floor(Q/2):floor(Q-1)/2, -floor(P/2):floor(P-1)/2);
Do=15;n=5;fc=30; %
a1=x-110/2; b1=y-145/2;
a2=x-110/2; b2=y+145/2;
a3=x+110/2; b3=y+145/2;
a4=x+110/2; b4=y-145/2;
D1=sqrt(a1.^2+b1.^2);
D2=sqrt(a2.^2+b2.^2);
D3=sqrt(a3.^2+b3.^2);
D4=sqrt(a4.^2+b4.^2);

B1=1./(1.+(Do.*(D1.^(-1))).^(2*n));
B2=1./(1.+(Do./D2).^(2*n));
B3=1./(1.+(Do./D3).^(2*n));
B4=1./(1.+(Do./D4).^(2*n));

I5=I4.*B1.*B2.*B3.*B4;
I6=abs(ifft2(I5));
maxi=max(I6(:));
[min(I6(:)), max(I6(:)), min(maxi), max(maxi)]

ans = 1×4

0.0000 0.2581 0.2581 0.2581

I8=im2uint8(I6/maxi);
whos I8; min(I8(:)), max(I8(:)), nnz(I8)

  Name        Size              Bytes  Class    Attributes

  I8        948x652            618096  uint8              

ans = uint8 0

ans = uint8 255

ans = 920

%=========================================================================%
%=============================PLOT========================================%
%=========================================================================%
figure
subplot(1,2,1),imhist(I),title('Histograma Img. Original')
subplot(1,2,2),imhist(histeq(I)),title('Histograma Equalizado')

figure
subplot(2,3,1),imshow(I),title('Imagem Original')
subplot(2,3,2),imshow(real(I1)),title('FFT nao centralizada')
subplot(2,3,3),imshow(real(I2)),title('FFT centralizada')
subplot(2,3,4),imshow(I4),title('Spectrum')
subplot(2,3,5),imshow(I5),title('Notch Reject')
subplot(2,3,6),imshow(I8),title('Imagem filtrada')

figure;
imshow(~I8)

This tells us that after the filtering, the only places that are non-zero are some near the corner, and difficult to see.

Notice that you did not fftshift() back after the notch filter.