數(shù)字圖像處理第四專題報(bào)告

中國(guó)地質(zhì)大學(xué)（武漢）數(shù)字圖像處理上機(jī)實(shí)習(xí)（第四專題）姓名：班級(jí)序號(hào)：學(xué)號(hào)：指導(dǎo)老師：傅華明一、實(shí)驗(yàn)題目一、圖象復(fù)原3，已知p03-03-01為原圖象，p03-03-02為經(jīng)過高通濾波以后的退化圖象，請(qǐng)采用逆濾波方法，假設(shè)高通濾波器為（1）高斯濾波器（2）巴特沃茨濾波器。每組濾波器采用3組高通截止頻率。并計(jì)算均方誤差最小，說明那一組參數(shù)復(fù)原的圖象復(fù)原效果最好？二、幾何校正1，將圖象p03-06-01修正為菱形三、圖象重建（根據(jù)傅立葉反變換實(shí)施圖象重建）000000000000000000000000000000000111111110000001111111111000001100000011000001100000000000001101111111100001101111111100001100000110000001100110110000001100110110000001111100110000000111000110000000000000000000000000000000000

圖3實(shí)驗(yàn)內(nèi)容一、圖象復(fù)原：已知p03-03-01為原圖象，p03-03-02為經(jīng)過高通濾波以后的退化圖象，請(qǐng)采用逆濾波方法，假設(shè)高通濾波器為（1）高斯濾波器（2）巴特沃茨濾波器。每組濾波器采用3組高通截止頻率。并計(jì)算均方誤差最小，說明那一組參數(shù)復(fù)原的圖象復(fù)原效果最好？算法設(shè)計(jì)先進(jìn)行傅立葉變換后低通濾波，再傅立葉反變換得到退化圖象，再傅立葉變換，最后逆濾波。逆濾波：

1/H(u，v)稱為逆濾波器。對(duì)上式再進(jìn)行傅立葉反變換可得到f(x，y)。但實(shí)際上碰到的問題都是有噪聲的，因而只能求F(u，v)的估計(jì)值：然后再作傅立葉逆變換，得

程序代碼I1=imread('E:\dip05-補(bǔ)3-上機(jī)4-圖象復(fù)原校正重建\DIP-13級(jí)上機(jī)3-圖象復(fù)原校正重建\p03-03-01.bmp');subplot(3,3,1),imshow(I1),title('原始圖像');I2=imread('E:\dip05-補(bǔ)3-上機(jī)4-圖象復(fù)原校正重建\DIP-13級(jí)上機(jī)3-圖象復(fù)原校正重建\p03-03-02.bmp');subplot(3,3,4),imshow(I2),title('退化圖像');double(I1);double(I2);I=imread('E:\dip05-補(bǔ)3-上機(jī)4-圖象復(fù)原校正重建\DIP-13級(jí)上機(jī)3-圖象復(fù)原校正重建\p03-03-01.bmp');k=I;I=fftshift(fft2(I));J=I;[m,n]=size(I);x=fix(m/2);y=fix(n/2);%圖象復(fù)原高斯濾波d=1d0=1;fori=1:mforj=1:nd=sqrt((i-x)^2+(j-y)^2);ifd~=0;h(i,j)=1./(1-1*exp((-d^2)/(2*d0^2)));I(i,j)=h(i,j).*I(i,j);elseI(i,j)=I(i,j);endendend;I=real(ifft2(ifftshift(I)));subplot(3,3,2);imshow(I,[]);title('高斯濾波d=1');I1=imread('E:\dip05-補(bǔ)3-上機(jī)4-圖象復(fù)原校正重建\DIP-13級(jí)上機(jī)3-圖象復(fù)原校正重建\p03-03-01.bmp');I=double(I1)-double(I);D1=std2(I);D1%圖象復(fù)原高斯濾波d=2d0=2;I=J;fori=1:mforj=1:nd=sqrt((i-x)^2+(j-y)^2);ifd~=0;h(i,j)=1./(1-1*exp((-d^2)/(2*d0^2)));I(i,j)=h(i,j).*I(i,j);elseI(i,j)=I(i,j);endendend;I=real(ifft2(ifftshift(I)));subplot(3,3,5);imshow(I,[]);title('高斯濾波d=2');I1=imread('E:\dip05-補(bǔ)3-上機(jī)4-圖象復(fù)原校正重建\DIP-13級(jí)上機(jī)3-圖象復(fù)原校正重建\p03-03-01.bmp');I=double(I1)-double(I);std2(I);D2=std2(I);D2%圖象復(fù)原高斯濾波d=3d0=3;I=J;fori=1:mforj=1:nd=sqrt((i-x)^2+(j-y)^2);ifd~=0;h(i,j)=1./(1-1*exp((-d^2)/(2*d0^2)));I(i,j)=h(i,j).*I(i,j);elseI(i,j)=I(i,j);endendend;I=real(ifft2(ifftshift(I)));subplot(3,3,8);imshow(I,[]);title('高斯濾波d=3');I1=imread('E:\dip05-補(bǔ)3-上機(jī)4-圖象復(fù)原校正重建\DIP-13級(jí)上機(jī)3-圖象復(fù)原校正重建\p03-03-01.bmp');I=double(I1)-double(I);std2(I);D3=std2(I);D3I=J;%圖象復(fù)原butterworth濾波D=1J=I;D0=1;foru=1:m;forv=1:n;D=sqrt((u-x)^2+(v-y)^2);ifD~=0;H1(u,v)=(1+D0/D)^(2*1.5);J(u,v)=J(u,v)*H1(u,v);elseJ(u,v)=0;end;end;end;J=real(ifft2(ifftshift(J)));subplot(3,3,3);imshow(J,[]);title('butterworth濾波D=1');I1=imread('E:\dip05-補(bǔ)3-上機(jī)4-圖象復(fù)原校正重建\DIP-13級(jí)上機(jī)3-圖象復(fù)原校正重建\p03-03-01.bmp');J=double(I1)-double(J);std2(J);J1=std2(J);J1%圖象復(fù)原butterworth濾波D=2J=I;D0=2;foru=1:m;forv=1:n;D=sqrt((u-x)^2+(v-y)^2);ifD~=0;H1(u,v)=(1+D0/D)^(2*1.5);J(u,v)=J(u,v)*H1(u,v);elseJ(u,v)=0;end;end;end;J=real(ifft2(ifftshift(J)));subplot(3,3,6);imshow(J,[]);title('butterworth濾波D=2');I1=imread('E:\dip05-補(bǔ)3-上機(jī)4-圖象復(fù)原校正重建\DIP-13級(jí)上機(jī)3-圖象復(fù)原校正重建\p03-03-01.bmp');J=double(I1)-double(J);std2(J);J2=std2(J);J2%圖象復(fù)原butterworth濾波D=3J=I;D0=3;foru=1:m;forv=1:n;D=sqrt((u-x)^2+(v-y)^2);ifD~=0;H1(u,v)=(1+D0/D)^(2*1.5);J(u,v)=J(u,v)*H1(u,v);elseJ(u,v)=0;end;end;end;J=real(ifft2(ifftshift(J)));I1=imread('E:\dip05-補(bǔ)3-上機(jī)4-圖象復(fù)原校正重建\DIP-13級(jí)上機(jī)3-圖象復(fù)原校正重建\p03-03-01.bmp');J=double(I1)-double(J);std2(J);J3=std2(J);J3subplot(3,3,9);imshow(J,[]);title('butterworth濾波D=3');運(yùn)行結(jié)果通過以上各圖以及方差值的比較，可以看出使用高斯濾波器還原時(shí)d=1視覺效果最好,d=1的標(biāo)準(zhǔn)差最?。捶讲钭钚。?，使用巴特沃斯濾波器還原時(shí)D=1時(shí)視覺效果和方差都是最佳，總體上說，使用高斯濾波器還原效果較好。二、幾何校正：將圖象p03-06-01修正為菱形算法設(shè)計(jì)導(dǎo)入原圖像導(dǎo)入原圖像統(tǒng)計(jì)四邊形左右兩邊的橫坐標(biāo)平均值(X1，X2)統(tǒng)計(jì)四邊形左右兩邊的橫坐標(biāo)平均值(X1，X2)統(tǒng)計(jì)四邊形上下兩邊的縱坐標(biāo)坐標(biāo)平均值(Y1，Y2)統(tǒng)計(jì)四邊形上下兩邊的縱坐標(biāo)坐標(biāo)平均值(Y1，Y2)根據(jù)X1,X2,Y1,Y2確定四邊形四個(gè)頂點(diǎn)根據(jù)X1,X2,Y1,Y2確定四邊形四個(gè)頂點(diǎn)根據(jù)四個(gè)頂點(diǎn)對(duì)原圖四個(gè)邊緣下進(jìn)行一維擬合，使之處于正菱形邊上根據(jù)四個(gè)頂點(diǎn)對(duì)原圖四個(gè)邊緣下進(jìn)行一維擬合，使之處于正菱形邊上輸出圖像輸出圖像程序代碼統(tǒng)計(jì)圖像邊緣坐標(biāo)，并確定四邊形頂點(diǎn)function[p1_x,p2_x,p3_y,p4_y]=Recover(img_in)%尋找頂點(diǎn)%[p1_x,p2_x,p3_y,p4_y,img_out]=Recover(img_in);[C,R]=size(img_in);k=0;p1_x=0;p2_x=0;p3_y=0;p4_y=0;fori=50:(C-50)%統(tǒng)計(jì)左邊緣橫坐標(biāo)平均值forj=1:Rifimg_in(i,j)~=0p1_x=j+p1_x;k=k+1;break;endendendp1_x=round(p1_x/k);k=0;fori=50:(C-50)%統(tǒng)計(jì)右邊緣橫坐標(biāo)平均值forj=R:-1:1ifimg_in(i,j)~=0p2_x=j+p2_x;k=k+1;break;endendendp2_x=round(p2_x/k);k=0;forj=50:(R-50)%統(tǒng)計(jì)上邊緣縱坐標(biāo)平均值fori=1:Cifimg_in(i,j)~=0p3_y=i+p3_y;k=k+1;break;endendendp3_y=round(p3_y/k);k=0;forj=50:(R-50)%統(tǒng)計(jì)下邊緣縱坐標(biāo)平均值fori=C:-1:1ifimg_in(i,j)~=0p4_y=i+p4_y;k=k+1;break;endendendp4_y=round(p4_y/k);end2.水平方向的擬合：function[img_out]=Processor_1(img_in,t1_x,t2_x,t3_y,t4_y)%圖像矯正%img_out=Processor_1(img_in,t1_x,t2_x,t3_y,t4_y);[C,R]=size(img_in);img_out=img_in;fori=t3_y:t4_yforj=1:t1_ximg_out(i,j)=0;endendfori=t3_y:t4_yforj=R:-1:t2_ximg_out(i,j)=0;endendforj=t1_x:t2_xfori=1:t3_yimg_out(i,j)=0;endendforj=t1_x:t2_xfori=R:-1:t4_yimg_out(i,j)=0;endendend3.豎直方向的擬合：function[img_out]=Processor_2(img_in,t1_x,t2_x,t3_y,t4_y)%圖像矯正%img_out=Processor_2(img_in,t1_x,t2_x,t3_y,t4_y);[C,R]=size(img_in);img_out=img_in;fori=t3_y:t4_yforj=R/2:-1:t1_ximg_out(i,j)=1;endendfori=t3_y:t4_yforj=R/2:1:t2_ximg_out(i,j)=1;endendend主程序：clear;p03_10_02=imread('E:\dip05-補(bǔ)3-上機(jī)4-圖象復(fù)原校正重建\DIP-13級(jí)上機(jī)3-圖象復(fù)原校正重建\p03-10-02.tif');[t1_x,t2_x,t3_y,t4_y]=Recover(p03_10_02);f1=Processor_1(p03_10_02,t1_x,t2_x,t3_y,t4_y);f2=Processor_2(f1,t1_x,t2_x,t3_y,t4_y);subplot(2,2,1);imshow(p03_10_02);title('原圖像');subplot(2,2,2);imshow(f1);title('水平處理后的效果');subplot(2,2,3);imshow(f2);title('垂直處理后的效果');運(yùn)行結(jié)果三、圖象重建（根據(jù)傅立葉反變換實(shí)施圖象重建）：000000000000000000000000000000000111111110000001111111111000001100000011000001100000000000001101111111100001101111111100001100000110000001100110110000001100110110000001111100110000000111000110000000000000000000000000000000000

圖3算法設(shè)計(jì)創(chuàng)建原始圖像創(chuàng)建原始圖像確定采樣角度間隔確定采樣角度間隔利用系統(tǒng)自帶radon函數(shù)進(jìn)行投影利用系統(tǒng)自帶radon函數(shù)進(jìn)行投影利用系統(tǒng)自帶iradon函數(shù)完成重建利用系統(tǒng)自帶iradon函數(shù)完成重建比較各種濾波性能比較各種濾波性能程序代碼clear;Img_Init=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0];dit=0.1;thetal=0:dit:180-dit;[R1,xp]=radon(Img_Init,thetal);g01s=iradon(R1,thetal,'Shepp-Logan');g01s=mat2gray(g01s);g01c=iradon(R1,thetal,'Cosine');g01c=mat2gray(g01c);g01h=iradon(R1,thetal,'Hamming');g01h=mat2gray(g01h);dit=1;thetal=0:dit:180-dit;[R1,xp]=radon(Img_Init,thetal);g1s=iradon(R1,thetal,'Shepp-Logan');g1s=mat2gray(g1s);g1c=iradon(R1,thetal,'Cosine');g1c=mat2gray(g1c);g1h=iradon(R1,thetal,'Hamming');g1h=mat2g