Matlab实现 理想低通、巴特沃斯低通、高斯低通、理想高通、巴特沃斯高通、高斯高通（d=10,50,150）

数字图像处理第二次编程课后作业

理想低通（d=10,50,150）:

close all;clear all;%% ---------Ideal Lowpass Filters (Fre. Domain)------------f = imread('D:/testData/cameraman.tif');f = mat2gray(f,[0 255]);[M,N] = size(f);P = 2*M;Q = 2*N;fc = zeros(M,N);for x = 1:1:M    for y = 1:1:N        fc(x,y) = f(x,y) * (-1)^(x+y);    endendF = fft2(fc,P,Q);H_0 = zeros(P,Q);H_1 = zeros(P,Q);H_2 = zeros(P,Q);for x = (-P/2):1:(P/2)-1     for y = (-Q/2):1:(Q/2)-1        D = (x^2 + y^2)^(0.5);        if(D <= 10)  H_0(x+(P/2)+1,y+(Q/2)+1) = 1; end            if(D <= 50)  H_1(x+(P/2)+1,y+(Q/2)+1) = 1; end            if(D <= 150)  H_2(x+(P/2)+1,y+(Q/2)+1) = 1; end     endendG_0 = H_0 .* F;G_1 = H_1 .* F;G_2 = H_2 .* F;g_0 = real(ifft2(G_0));g_0 = g_0(1:1:M,1:1:N);g_1 = real(ifft2(G_1));g_1 = g_1(1:1:M,1:1:N);g_2 = real(ifft2(G_2));g_2 = g_2(1:1:M,1:1:N);         for x = 1:1:M    for y = 1:1:N        g_0(x,y) = g_0(x,y) * (-1)^(x+y);        g_1(x,y) = g_1(x,y) * (-1)^(x+y);        g_2(x,y) = g_2(x,y) * (-1)^(x+y);    endend%% -----show-------figure();subplot(1,2,1);imshow(f,[0 1]);xlabel('1).原图');subplot(1,2,2);imshow(log(1 + abs(F)),[ ]);xlabel('2).1图的傅里叶光谱');figure();subplot(1,2,1);imshow(H_0,[0 1]);xlabel('3).理想低通滤波(D=10)');subplot(1,2,2);h = mesh(1:20:P,1:20:Q,H_0(1:20:P,1:20:Q));set(h,'EdgeColor','k');axis([0 P 0 Q 0 1]);xlabel('u');ylabel('v');zlabel('|H(u,v)|');figure();subplot(1,2,1);imshow(log(1 + abs(G_0)),[ ]);xlabel('4).3得到的滤波结果');subplot(1,2,2);imshow(g_0,[0 1]);xlabel('5).效果图(D=10)');figure();subplot(1,2,1);imshow(H_1,[0 1]);xlabel('6).理想低通滤波(D=50)');subplot(1,2,2);h = mesh(1:20:P,1:20:Q,H_1(1:20:P,1:20:Q));set(h,'EdgeColor','k');axis([0 P 0 Q 0 1]);xlabel('u');ylabel('v');zlabel('|H(u,v)|');figure();subplot(1,2,1);imshow(log(1 + abs(G_1)),[ ]);xlabel('7).6得到的滤波结果');subplot(1,2,2);imshow(g_1,[0 1]);xlabel('8).效果图(D=50)');figure();subplot(1,2,1);imshow(H_2,[0 1]);xlabel('9).理想低通滤波(D=150)');subplot(1,2,2);h = mesh(1:20:P,1:20:Q,H_2(1:20:P,1:20:Q));set(h,'EdgeColor','k');axis([0 P 0 Q 0 1]);xlabel('u');ylabel('v');zlabel('|H(u,v)|');figure();subplot(1,2,1);imshow(log(1 + abs(G_2)),[ ]);xlabel('10).9得到的滤波结果');subplot(1,2,2);imshow(g_2,[0 1]);xlabel('11).效果图(D=150)');

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巴特沃斯低通（d=10,50,150）:

close all;clear all;%% ---------Butterworth Lowpass Filters (Fre. Domain)------------f = imread('D:/testData/cameraman.tif');f = mat2gray(f,[0 255]);[M,N] = size(f);P = 2*M;Q = 2*N;fc = zeros(M,N);for x = 1:1:M    for y = 1:1:N        fc(x,y) = f(x,y) * (-1)^(x+y);    endendF = fft2(fc,P,Q);H_0 = zeros(P,Q);H_1 = zeros(P,Q);H_2 = zeros(P,Q);for x = (-P/2):1:(P/2)-1     for y = (-Q/2):1:(Q/2)-1        D = (x^2 + y^2)^(0.5);        %n=1        D_0 = 10;        H_0(x+(P/2)+1,y+(Q/2)+1) = 1/(1+(D/D_0)^2);        D_0 = 50;        H_1(x+(P/2)+1,y+(Q/2)+1) = 1/(1+(D/D_0)^2);           D_0 = 150;        H_2(x+(P/2)+1,y+(Q/2)+1) = 1/(1+(D/D_0)^2);        %H_2(x+(P/2)+1,y+(Q/2)+1) = 1/(1+(D/D_0)^6);     endendG_0 = H_0 .* F;G_1 = H_1 .* F;G_2 = H_2 .* F;g_0 = real(ifft2(G_0));g_0 = g_0(1:1:M,1:1:N);g_1 = real(ifft2(G_1));g_1 = g_1(1:1:M,1:1:N);g_2 = real(ifft2(G_2));g_2 = g_2(1:1:M,1:1:N);         for x = 1:1:M    for y = 1:1:N        g_0(x,y) = g_0(x,y) * (-1)^(x+y);        g_1(x,y) = g_1(x,y) * (-1)^(x+y);        g_2(x,y) = g_2(x,y) * (-1)^(x+y);    endend%% -----show-------figure();subplot(1,2,1);imshow(f,[0 1]);xlabel('1).原图');subplot(1,2,2);imshow(log(1 + abs(F)),[ ]);xlabel('2).1图的傅里叶光谱');figure();subplot(1,2,1);imshow(H_0,[0 1]);xlabel('3).巴特沃斯低通滤波(D=10)');subplot(1,2,2);h = mesh(1:20:P,1:20:Q,H_0(1:20:P,1:20:Q));set(h,'EdgeColor','k');axis([0 P 0 Q 0 1]);xlabel('u');ylabel('v');zlabel('|H(u,v)|');figure();subplot(1,2,1);imshow(log(1 + abs(G_0)),[ ]);xlabel('4).3得到的滤波结果');subplot(1,2,2);imshow(g_0,[0 1]);xlabel('5).效果图(D=10)');figure();subplot(1,2,1);imshow(H_1,[0 1]);xlabel('6).巴特沃斯低通滤波(D=50)');subplot(1,2,2);h = mesh(1:20:P,1:20:Q,H_1(1:20:P,1:20:Q));set(h,'EdgeColor','k');axis([0 P 0 Q 0 1]);xlabel('u');ylabel('v');zlabel('|H(u,v)|');figure();subplot(1,2,1);imshow(log(1 + abs(G_1)),[ ]);xlabel('7).6得到的滤波结果');subplot(1,2,2);imshow(g_1,[0 1]);xlabel('8).效果图(D=50)');figure();subplot(1,2,1);imshow(H_2,[0 1]);xlabel('9).巴特沃斯低通滤波(D=150)');subplot(1,2,2);h = mesh(1:20:P,1:20:Q,H_2(1:20:P,1:20:Q));set(h,'EdgeColor','k');axis([0 P 0 Q 0 1]);xlabel('u');ylabel('v');zlabel('|H(u,v)|');figure();subplot(1,2,1);imshow(log(1 + abs(G_2)),[ ]);xlabel('10).9得到的滤波结果');subplot(1,2,2);imshow(g_2,[0 1]);xlabel('11).效果图(D=150)');

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高斯低通（d=10,50,150）:

close all;clear all;clc;%% ---------Gaussian Lowpass Filters (Fre. Domain)------------f = imread('D:/testData/cameraman.tif');f = mat2gray(f,[0 255]);[M,N] = size(f);P = 2*M;Q = 2*N;fc = zeros(M,N);for x = 1:1:M    for y = 1:1:N        fc(x,y) = f(x,y) * (-1)^(x+y);    endendF = fft2(fc,P,Q);H_0 = zeros(P,Q);H_1 = zeros(P,Q);H_2 = zeros(P,Q);for x = (-P/2):1:(P/2)-1     for y = (-Q/2):1:(Q/2)-1        D = (x^2 + y^2)^(0.5);        D_0 = 10;        H_0(x+(P/2)+1,y+(Q/2)+1) = exp(-(D*D)/(2*D_0*D_0));         D_0 = 50;        H_1(x+(P/2)+1,y+(Q/2)+1) = exp(-(D*D)/(2*D_0*D_0));           D_0 = 150;        H_2(x+(P/2)+1,y+(Q/2)+1) = exp(-(D*D)/(2*D_0*D_0));     endendG_0 = H_0 .* F;G_1 = H_1 .* F;G_2 = H_2 .* F;g_0 = real(ifft2(G_0));g_0 = g_0(1:1:M,1:1:N);g_1 = real(ifft2(G_1));g_1 = g_1(1:1:M,1:1:N);g_2 = real(ifft2(G_2));g_2 = g_2(1:1:M,1:1:N);         for x = 1:1:M    for y = 1:1:N        g_0(x,y) = g_0(x,y) * (-1)^(x+y);        g_1(x,y) = g_1(x,y) * (-1)^(x+y);        g_2(x,y) = g_2(x,y) * (-1)^(x+y);    endend%% -----show-------close all;figure();subplot(1,2,1);imshow(f,[0 1]);xlabel('1).原图');subplot(1,2,2);imshow(log(1 + abs(F)),[ ]);xlabel('2).1图的傅里叶光谱');figure();subplot(1,2,1);imshow(H_0,[0 1]);xlabel('3).高斯低通滤波(D=10)');subplot(1,2,2);h = mesh(1:20:P,1:20:Q,H_0(1:20:P,1:20:Q));set(h,'EdgeColor','k');axis([0 P 0 Q 0 1]);xlabel('u');ylabel('v');zlabel('|H(u,v)|');figure();subplot(1,2,1);imshow(log(1 + abs(G_0)),[ ]);xlabel('4).3得到的滤波结果');subplot(1,2,2);imshow(g_0,[0 1]);xlabel('5).效果图(D=10)');figure();subplot(1,2,1);imshow(H_1,[0 1]);xlabel('6).高斯低通滤波(D=50)');subplot(1,2,2);h = mesh(1:20:P,1:20:Q,H_1(1:20:P,1:20:Q));set(h,'EdgeColor','k');axis([0 P 0 Q 0 1]);xlabel('u');ylabel('v');zlabel('|H(u,v)|');figure();subplot(1,2,1);imshow(log(1 + abs(G_1)),[ ]);xlabel('7).6得到的滤波结果');subplot(1,2,2);imshow(g_1,[0 1]);xlabel('8).效果图(D=50)');figure();subplot(1,2,1);imshow(H_2,[0 1]);xlabel('9).高斯低通滤波(D=150)');subplot(1,2,2);h = mesh(1:20:P,1:20:Q,H_2(1:20:P,1:20:Q));set(h,'EdgeColor','k');axis([0 P 0 Q 0 1]);xlabel('u');ylabel('v');zlabel('|H(u,v)|');figure();subplot(1,2,1);imshow(log(1 + abs(G_2)),[ ]);xlabel('10).9得到的滤波结果');subplot(1,2,2);imshow(g_2,[0 1]);xlabel('11).效果图(D=150)');

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理想高通（d=10,50,150）:

close all;clear all;%% ---------Ideal Lowpass Filters (Fre. Domain)------------f = imread('D:/testData/cameraman.tif');f = mat2gray(f,[0 255]);[M,N] = size(f);P = 2*M;Q = 2*N;fc = zeros(M,N);for x = 1:1:M    for y = 1:1:N        fc(x,y) = f(x,y) * (-1)^(x+y);    endendF = fft2(fc,P,Q);H_0 = zeros(P,Q);H_1 = zeros(P,Q);H_2 = zeros(P,Q);for x = (-P/2):1:(P/2)-1     for y = (-Q/2):1:(Q/2)-1        D = (x^2 + y^2)^(0.5);        if(D > 10)  H_0(x+(P/2)+1,y+(Q/2)+1) = 1; end            if(D > 50)  H_1(x+(P/2)+1,y+(Q/2)+1) = 1; end            if(D > 150)  H_2(x+(P/2)+1,y+(Q/2)+1) = 1; end     endendG_0 = H_0 .* F;G_1 = H_1 .* F;G_2 = H_2 .* F;g_0 = real(ifft2(G_0));g_0 = g_0(1:1:M,1:1:N);g_1 = real(ifft2(G_1));g_1 = g_1(1:1:M,1:1:N);g_2 = real(ifft2(G_2));g_2 = g_2(1:1:M,1:1:N);         for x = 1:1:M    for y = 1:1:N        g_0(x,y) = g_0(x,y) * (-1)^(x+y);        g_1(x,y) = g_1(x,y) * (-1)^(x+y);        g_2(x,y) = g_2(x,y) * (-1)^(x+y);    endend%% -----show-------figure();subplot(1,2,1);imshow(f,[0 1]);xlabel('1).原图');subplot(1,2,2);imshow(log(1 + abs(F)),[ ]);xlabel('2).1图的傅里叶光谱');figure();subplot(1,2,1);imshow(H_0,[0 1]);xlabel('3).理想高通滤波(D=10)');subplot(1,2,2);h = mesh(1:20:P,1:20:Q,H_0(1:20:P,1:20:Q));set(h,'EdgeColor','k');axis([0 P 0 Q 0 1]);xlabel('u');ylabel('v');zlabel('|H(u,v)|');figure();subplot(1,2,1);imshow(log(1 + abs(G_0)),[ ]);xlabel('4).3得到的滤波结果');subplot(1,2,2);imshow(g_0,[0 1]);xlabel('5).效果图(D=10)');figure();subplot(1,2,1);imshow(H_1,[0 1]);xlabel('6).理想高通滤波(D=50)');subplot(1,2,2);h = mesh(1:20:P,1:20:Q,H_1(1:20:P,1:20:Q));set(h,'EdgeColor','k');axis([0 P 0 Q 0 1]);xlabel('u');ylabel('v');zlabel('|H(u,v)|');figure();subplot(1,2,1);imshow(log(1 + abs(G_1)),[ ]);xlabel('7).6得到的滤波结果');subplot(1,2,2);imshow(g_1,[0 1]);xlabel('8).效果图(D=50)');figure();subplot(1,2,1);imshow(H_2,[0 1]);xlabel('9).理想高通滤波(D=150)');subplot(1,2,2);h = mesh(1:20:P,1:20:Q,H_2(1:20:P,1:20:Q));set(h,'EdgeColor','k');axis([0 P 0 Q 0 1]);xlabel('u');ylabel('v');zlabel('|H(u,v)|');figure();subplot(1,2,1);imshow(log(1 + abs(G_2)),[ ]);xlabel('10).9得到的滤波结果');subplot(1,2,2);imshow(g_2,[0 1]);xlabel('11).效果图(D=150)');

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巴特沃斯高通（d=10,50,150）:

close all;clear all;%% ---------Butterworth Lowpass Filters (Fre. Domain)------------f = imread('D:/testData/cameraman.tif');f = mat2gray(f,[0 255]);[M,N] = size(f);P = 2*M;Q = 2*N;fc = zeros(M,N);for x = 1:1:M    for y = 1:1:N        fc(x,y) = f(x,y) * (-1)^(x+y);    endendF = fft2(fc,P,Q);H_0 = zeros(P,Q);H_1 = zeros(P,Q);H_2 = zeros(P,Q);for x = (-P/2):1:(P/2)-1     for y = (-Q/2):1:(Q/2)-1        D = (x^2 + y^2)^(0.5);        %n=1        D_0 = 10;        H_0(x+(P/2)+1,y+(Q/2)+1) = 1/(1+(D_0/D)^2);        D_0 = 50;        H_1(x+(P/2)+1,y+(Q/2)+1) = 1/(1+(D_0/D)^2);           D_0 = 150;        H_2(x+(P/2)+1,y+(Q/2)+1) = 1/(1+(D_0/D)^2);        %H_2(x+(P/2)+1,y+(Q/2)+1) = 1/(1+(D/D_0)^6);     endendG_0 = H_0 .* F;G_1 = H_1 .* F;G_2 = H_2 .* F;g_0 = real(ifft2(G_0));g_0 = g_0(1:1:M,1:1:N);g_1 = real(ifft2(G_1));g_1 = g_1(1:1:M,1:1:N);g_2 = real(ifft2(G_2));g_2 = g_2(1:1:M,1:1:N);         for x = 1:1:M    for y = 1:1:N        g_0(x,y) = g_0(x,y) * (-1)^(x+y);        g_1(x,y) = g_1(x,y) * (-1)^(x+y);        g_2(x,y) = g_2(x,y) * (-1)^(x+y);    endend%% -----show-------figure();subplot(1,2,1);imshow(f,[0 1]);xlabel('1).原图');subplot(1,2,2);imshow(log(1 + abs(F)),[ ]);xlabel('2).1图的傅里叶光谱');figure();subplot(1,2,1);imshow(H_0,[0 1]);xlabel('3).巴特沃斯高通滤波(D=10)');subplot(1,2,2);h = mesh(1:20:P,1:20:Q,H_0(1:20:P,1:20:Q));set(h,'EdgeColor','k');axis([0 P 0 Q 0 1]);xlabel('u');ylabel('v');zlabel('|H(u,v)|');figure();subplot(1,2,1);imshow(log(1 + abs(G_0)),[ ]);xlabel('4).3得到的滤波结果');subplot(1,2,2);imshow(g_0,[0 1]);xlabel('5).效果图(D=10)');figure();subplot(1,2,1);imshow(H_1,[0 1]);xlabel('6).巴特沃斯高通滤波(D=50)');subplot(1,2,2);h = mesh(1:20:P,1:20:Q,H_1(1:20:P,1:20:Q));set(h,'EdgeColor','k');axis([0 P 0 Q 0 1]);xlabel('u');ylabel('v');zlabel('|H(u,v)|');figure();subplot(1,2,1);imshow(log(1 + abs(G_1)),[ ]);xlabel('7).6得到的滤波结果');subplot(1,2,2);imshow(g_1,[0 1]);xlabel('8).效果图(D=50)');figure();subplot(1,2,1);imshow(H_2,[0 1]);xlabel('9).巴特沃斯高通滤波(D=150)');subplot(1,2,2);h = mesh(1:20:P,1:20:Q,H_2(1:20:P,1:20:Q));set(h,'EdgeColor','k');axis([0 P 0 Q 0 1]);xlabel('u');ylabel('v');zlabel('|H(u,v)|');figure();subplot(1,2,1);imshow(log(1 + abs(G_2)),[ ]);xlabel('10).9得到的滤波结果');subplot(1,2,2);imshow(g_2,[0 1]);xlabel('11).效果图(D=150)');

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高斯高通（d=10,50,150）:

close all;clear all;clc;%% ---------Gaussian Lowpass Filters (Fre. Domain)------------f = imread('D:/testData/cameraman.tif');f = mat2gray(f,[0 255]);[M,N] = size(f);P = 2*M;Q = 2*N;fc = zeros(M,N);for x = 1:1:M    for y = 1:1:N        fc(x,y) = f(x,y) * (-1)^(x+y);    endendF = fft2(fc,P,Q);H_0 = zeros(P,Q);H_1 = zeros(P,Q);H_2 = zeros(P,Q);for x = (-P/2):1:(P/2)-1     for y = (-Q/2):1:(Q/2)-1        D = (x^2 + y^2)^(0.5);        D_0 = 10;        H_0(x+(P/2)+1,y+(Q/2)+1) = 1 - exp(-(D*D)/(2*D_0*D_0));         D_0 = 50;        H_1(x+(P/2)+1,y+(Q/2)+1) = 1 - exp(-(D*D)/(2*D_0*D_0));           D_0 = 150;        H_2(x+(P/2)+1,y+(Q/2)+1) = 1 - exp(-(D*D)/(2*D_0*D_0));     endendG_0 = H_0 .* F;G_1 = H_1 .* F;G_2 = H_2 .* F;g_0 = real(ifft2(G_0));g_0 = g_0(1:1:M,1:1:N);g_1 = real(ifft2(G_1));g_1 = g_1(1:1:M,1:1:N);g_2 = real(ifft2(G_2));g_2 = g_2(1:1:M,1:1:N);         for x = 1:1:M    for y = 1:1:N        g_0(x,y) = g_0(x,y) * (-1)^(x+y);        g_1(x,y) = g_1(x,y) * (-1)^(x+y);        g_2(x,y) = g_2(x,y) * (-1)^(x+y);    endend%% -----show-------close all;figure();subplot(1,2,1);imshow(f,[0 1]);xlabel('1).原图');subplot(1,2,2);imshow(log(1 + abs(F)),[ ]);xlabel('2).1图的傅里叶光谱');figure();subplot(1,2,1);imshow(H_0,[0 1]);xlabel('3).高斯高通滤波(D=10)');subplot(1,2,2);h = mesh(1:20:P,1:20:Q,H_0(1:20:P,1:20:Q));set(h,'EdgeColor','k');axis([0 P 0 Q 0 1]);xlabel('u');ylabel('v');zlabel('|H(u,v)|');figure();subplot(1,2,1);imshow(log(1 + abs(G_0)),[ ]);xlabel('4).3得到的滤波结果');subplot(1,2,2);imshow(g_0,[0 1]);xlabel('5).效果图(D=10)');figure();subplot(1,2,1);imshow(H_1,[0 1]);xlabel('6).高斯高通滤波(D=50)');subplot(1,2,2);h = mesh(1:20:P,1:20:Q,H_1(1:20:P,1:20:Q));set(h,'EdgeColor','k');axis([0 P 0 Q 0 1]);xlabel('u');ylabel('v');zlabel('|H(u,v)|');figure();subplot(1,2,1);imshow(log(1 + abs(G_1)),[ ]);xlabel('7).6得到的滤波结果');subplot(1,2,2);imshow(g_1,[0 1]);xlabel('8).效果图(D=50)');figure();subplot(1,2,1);imshow(H_2,[0 1]);xlabel('9).高斯高通滤波(D=150)');subplot(1,2,2);h = mesh(1:20:P,1:20:Q,H_2(1:20:P,1:20:Q));set(h,'EdgeColor','k');axis([0 P 0 Q 0 1]);xlabel('u');ylabel('v');zlabel('|H(u,v)|');figure();subplot(1,2,1);imshow(log(1 + abs(G_2)),[ ]);xlabel('10).9得到的滤波结果');subplot(1,2,2);imshow(g_2,[0 1]);xlabel('11).效果图(D=150)');