一、理想低通滤波器

T=rgb2gray(I);

figure(1);

subplot(1,2,1),imshow(uint8(I));

title('原图像');

subplot(1,2,2),imshow(uint8(T));

title('理想低通滤波所得图像');

[f1,f2]=freqspace(size(T),'meshgrid');

H=ones(size(T));

r=sqrt(f1.^2+f2.^2);

H(r>0.1)=0;

Y=fft2(double(T));

Y=fftshift(Y);

Ya=Y.*H;

Ya=ifftshift(Ya);

I=ifft2(Ya);

figure(2);

surf(H,'Facecolor','interp','Edgecolor','none','Facelighting','phong');

title('频谱图');

二、巴特沃斯低通滤波器

T=rgb2gray(I);

figure(1);

subplot(1,2,1),imshow(uint8(I));

title('原图像');

subplot(1,2,2),imshow(uint8(T));

title('巴特沃斯低通滤波所得图像');

[f1,f2]=freqspace(size(T),'meshgrid');

D=0.3;

r=f1.^2+f2.^2;

n=4;

for i=1:size(T,1)

    for j=1:size(T,2)

        t=r(i,j)/(D*D);

        H(i,j)=1/(t^n+1);

    end

end

Y=fft2(double(T));

Y=fftshift(Y);

Ya=Y.*H;

Ya=ifftshift(Ya);

I=real(ifft2(Ya));

figure(2);

surf(H,'Facecolor','interp','Edgecolor','none','Facelighting','phong');

title('频谱图');

三、梯形滤波器

T=rgb2gray(I);

figure(1);

subplot(1,2,1),imshow(uint8(I));

title('原图像');

subplot(1,2,2),imshow(uint8(T));

title('梯形低通滤波所得图像');

[f1,f2]=freqspace(size(T),'meshgrid');

D=100/size(I,1);

D0=0.1;

D1=0.4;

r=sqrt(f1.^2+f2.^2);

H=zeros(size(T));

H(rfor i=1:size(T,1)

    for j=1:size(I,2)

if r(i,j)>=D0 & r(i,j)<=D1

        H(i,j)=(D1-r(i,j))/(D1-D0);

        end

    end

end

Y=fft2(double(T));

Y=fftshift(Y);

Ya=Y.*H;

Ya=ifftshift(Ya);

I=real(ifft2(Ya));

figure(2);

surf(H,'Facecolor','interp','Edgecolor','none','Facelighting','phong');  

title('频谱图');

四、高斯低通滤波器

T=rgb2gray(I);

figure(1);

subplot(1,2,1),imshow(uint8(I));

title('原图像');

subplot(1,2,2),imshow(uint8(T));

title('高斯低通滤波所得图像');

[f1,f2]=freqspace(size(T),'meshgrid');

D=100/size(I,1);

r=f1.^2+f2.^2;

H=ones(size(T));

for i=1:size(T,1)

    for j=1:size(T,2)

        t=r(i,j)/(D*D);

        H(i,j)=exp(-t);

    end

end

Y=fft2(double(T));

Y=fftshift(Y);

Ya=Y.*H;

Ya=ifftshift(Ya);

I=real(ifft2(Ya));

figure(2);

surf(H,'Facecolor','interp','Edgecolor','none','Facelighting','phong');

title('频谱图');

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