第七章圖像的空間變換

1、第七章 圖像的空間變換,,空間變換,MATLAB空間變換方法,MATLAB的圖像匹配,MATLAB的圖像投影,一.空間變換 空間變換主要是用來保持圖像中的連續(xù)性和物體的連通性,一般都用數(shù)學(xué)函數(shù)形式來描述輸入輸出圖像相應(yīng)像素間的空間關(guān)系。空間變換的一般表達式為： g(x,y)=f(x’,y’)=f[a(x’,y’),b(x,y)] g(x,y)

2、 輸出圖像 (x’,y’) 空間變換后的坐標(biāo) a(x’,y’),b(x,y) 空間變換函數(shù),,,,§7.1 空間變換,,,二.簡單變換,簡單變換用來實現(xiàn)圖像的平移、旋轉(zhuǎn)、剪切等簡單操作。如：,a(x,y)=x+x0,b(x,y)=y+y0,2)旋轉(zhuǎn)變換,3)平移放大,水平變換,a(x,y)=xcosθ-ysinθ,垂直變換,b(x,y)

3、=y,a(x,y)=x,b(x,y)=（xsinθ+y）/cosθ,1)平移變換,a(x,y)=xcosθ-ysinθ,b(x,y)=xsinθ+ycosθ,,,,,,,,,,,,,,,1）多項式卷繞 利用控制點序列為a(x,y)和b(x,y)找到一個近似的多項式描述。該多項式的參數(shù)能夠使多項式的取值與控制點及其位移量吻合。,三.利用控制點進行變換：,2）圖像分割卷繞 將控制點形成一個矩形輸入柵格，通過映射將柵格變換為輸

4、出圖像中連同的水平輸出柵格，控制點為每一個輸出柵格對應(yīng)的頂點，輸入柵格內(nèi)的各點影射為相應(yīng)輸出柵格內(nèi)的點。 通常采用的柵格插值方法是雙線性空間變換方法，其一般表達式為： G(x,y)=F(ax+by+cxy+d,e+fy+gxy+h),%%7_3_aI=imread('flowers.tif');subplot(331),imshow(I);%%7_3_bI=imread(

5、9;flowers.tif');scale=1.2;angle=20*pi/180;tx=0;ty=0;sc=scale*cos(angle);ss=scale*sin(angle);T=[sc ss; ss sc; tx ty];,t_lc=maketform('affine',T);I_linearconformal=imtransform(I,t_lc,'FillVa

6、lues',.3);%%subplot(332),imshow(I_linearconformal);imshow(I_linearconformal);%%7_3_cI=imread('flowers.tif');T=[1 0.1 ;1 1;0 0 ];t_aff=maketform('affine',T);I_affine=imtransform(I,t_aff,'Fil

7、lValues',.3);%%subplot(333),imshow(I_affine)imshow(I_affine);%%7_3_dI=imread('flowers.tif');T=[1 0 0.008; 1 1 0.01; 0 0 1];,t_proj=maketform('projective',T);I_projective=imtransform(I,t_proj,

8、9;FillValues',.3);%%subplot(334),imshow(I_projective)iptsetpref('ImshowTruesize','manual');imshow(I_projective);%%7_3_eI=imread('flowers.tif');xybase=reshape(randn(12,1),6,2);t_poly=cp2

9、tform(xybase,xybase,'polynomial',2);T=[0 0;1 0;0 1;0.001 0;0.02 0;0.01 0];t_poly.tdata=T;I_polynomial=imtransform(I,t_poly,'FillValues',.3);%%subplot(335),imshow(I_polynomial);iptsetpref('ImshowT

10、ruesize','manual');,imshow(I_polynomial);%%7_3_fI=imread('flowers.tif');imid=round(size(I,2)/2);I_left=I(:,1:imid);stretch=1.5;size_right=[size(I,1)round(stretch*imid)];I_right=I(:,imid+1:end);

11、I_right_stretched=imresize(I_right,size_right);I_piecewiselinear=[I_left I_right_stretched];%%subplot(336),imshow(I_piecewiselinear);iptsetpref('ImshowTruesize','manual');imshow(I_piecewiselinear);%

12、%7_3_g,I=imread('flowers.tif');[nrows,ncols]=size(I);[xi,yi]=meshgrid(1:ncols,1:nrows);a1=5;a2=3;u=xi+a1*sin(pi*xi/imid);v=yi-a2*sin(pi*yi/imid);tmap_B=cat(3,u,v);resamp=makeresampler('linear',

13、9;fill');I_sinusoid=tformarray(I,[ ],resamp,[2 1],[1 2],[ ],tmap_B,.3);%%subplot(337),imshow(I_sinusoid);iptsetpref('ImshowTruesize','manual');imshow(I_sinusoid);%%7_3_h,I=imread('flowers.tif

14、');xt=xi(:)-imid;yt=yi(:)-imid;[theta,r]=cart2pol(xt,yt);a=.00001;s=r+a*r.^3;[ut,vt]=pol2cart(theta,s);u=reshape(ut,size(xi))+imid;v=reshape(vt,size(yi))+imid;tmap_B=cat(3,u,v);I_barrel=tformarray(I,[ ],res

15、amp,[2 1],[1 2],[ ],tmap_B,.3);%%subplot(338),imshow(I_barrel);%%iptsetpref('ImshowTruesize','manual');imshow(I_barrel);,%%7_3_iI=imread('flowers.tif');xt=xi(:)-imid;yt=yi(:)-imid;[theta,r]

16、=cart2pol(xt,yt);a=-0.0005;s=r+a*r.^3;[ut,vt]=pol2cart(theta,s);u=reshape(ut,size(xi))+imid;v=reshape(vt,size(yi))+imid;tmap_B=cat(3,u,v);I_pin=tformarray(I,[ ],resamp,[2 1],[1 2],[ ],tmap_B,.3);%%subplot(339),im

17、show(I_pin);iptsetpref('ImshowTruesize','manual');,imshow(I_pin)%%7.5.6orthophoto=imread('westconcordorthophoto.png');subplot(1,2,1),imshow(orthophoto)unregistered=imread('westconcordaeri

18、al.png');subplot(1,2,2),imshow(unregistered)%%cpselect(unregistered(:,:,1),orthophoto)%%input_points=[120.7086 93.9772 319.2222 78.9202 127.9838 291.6312 352.0729 281.1445

19、];%%,input_points_corr=cpcorr(input_points,base_points,... unregistered(:,:,1),orthophoto) input_points_corr=[120.7086 93.9772 319.2222 78.9202

20、 127.1064 289.8935 352.0729 281.1445];%%mytform=cp2tform(input_points,base_points,'projective');%%registered=imtransform(unregistered,mytform)%%7.7clcClear%%ch7_8_11lily=imrea

21、d('lily.tif');flowers=imread('flowers.tif');,subplot(1,2,1),imshow(lily);subplot(1,2,2),imshow(flowers);%%rect_lily=[93 13 81 69];rect_flowers=[190 68 235 210];sub_lily=imcrop(lily,rect_lily);sub_f

22、lowers=imcrop(flowers,rect_flowers);[sub_lily1,rect_lily]=imcrop(lily);[sub_flowers1,rect_flowers]=imcrop(flowers);subplot(1,2,1),imshow(sub_lily1)subplot(1,2,2),imshow(sub_flowers1)%% c=normxcorr2(sub_lily(:,:,1),

23、sub_flowers(:,:,1));figure,surf(c),shading flat,%%[sub_lily,rect_lily]=imcrop(lily);[sub_flowers,rect_flowers]=imcrop(flowers);%%[max_c,imax]=max(abs(c(:)));[ypeak,xpeak]=ind2sub(size(c),imax(1));corr_offset=[(xpe

24、ak-size(sub_lily,2))(ypeak-size(sub_lily,1))];rect_offset=[(rect_flowers(1)-rect_lily(1)) (rect_flowers(2)-rect_lily(2))];offset=corr_offset+rect_offset;xoffset=offset(1);yoffset=offset(2);%%,xbegin=xo

25、ffset + 1;xend=xoffset + size(lily,2);ybegin=yoffset+1;yend=yoffset+size(lily,1);extracted_lily=flowers(ybegin:yend,xbegin:xend,:);if isequal(lily,extracted_lily) disp('lily.tif was extracted from flowers.ti

26、f')end %%recovered_lily=uint8(zeros(size(flowers)));recovered_lily(ybegin:yend,xbegin:xend,:)=lily;[m,n,p]=size(flowers)mask=ones(m,n);i=find(recovered_lily(:,:,1)==0);,mask(i)=.2;figure,imshow(flowers(:,:

27、,1))hold onh=imshow(recovered_lily);set(h,'AlphaData',mask)%%ch7_8_11lily=imread('lily.tif');flowers=imread('flowers.tif');subplot(1,2,1),imshow(lily);subplot(1,2,2),imshow(flowers);%%re

28、ct_lily=[93 13 81 69];rect_flowers=[190 68 235 210];sub_lily=imcrop(lily,rect_lily);,sub_flowers=imcrop(flowers,rect_flowers);[sub_lily,rect_lily]=imcrop(lily);[sub_flowers,rect_flowers]=imcrop(flowers);subplot(1,2,

29、1),imshow(sub_lily)subplot(1,2,2),imshow(sub_flowers)%% c=normxcorr2(sub_lily(:,:,1),sub_flowers(:,:,1));figure,surf(c),shading flat%%[max_c,imax]=max(abs(c(:)));[ypeak,xpeak]=ind2sub(size(c),imax(1));corr_offset

30、=[(xpeak-size(sub_lily,2))(ypeak-size(sub_lily,1))];rect_offset=[(rect_flowers(1)-rect_lily(1)),(rect_flowers(2)-rect_lily(2))];offset=corr_offset+rect_offset;xoffset=offset(1);yoffset=offset(2);%%xbegin=xoffset +

31、 1;xend=xoffset + size(lily,2);ybegin=yoffset+1;yend=yoffset+size(lily,1);extracted_lily=flowers(ybegin:yend,xbegin:xend,:);if isequal(lily,extracted_lily) disp('lily.tif was extracted from flowers.tif')

32、end %%,recovered_lily=uint8(zeros(size(flowers)));recovered_lily(ybegin:yend,xbegin:xend,:)=lily;[m,n,p]=size(flowers)mask=ones(m,n);i=find(recovered_lily(:,:,1)==0);mask(i)=.2;figure,imshow(flowers(:,:,1))ho

33、ld onh=imshow(recovered_lily);set(h,'AlphaData',mask)%%ch7xiti%%7-1I=imread('greens.jpg');ring=maketform('affine',[1 0 0; .5 1 0; 0 0 1]);,%%J = imtransform(I,ring); %% imshow(I), fig

34、ure, imshow(J) uData =[0 1]; vData=[0 1]; D=imtransform(I,ring,'bicubic',... 'UData',uData,'VData',vData,... 'XData',[-2 2],'YData',[-2 2],...

35、 'Size',[400 400],'FillValues',255); imshow(I); figure, imshow(D); %%7-2 truesizewarning=iptgetpref('TruesizeWarning'); iptsetpref('TruesizeWarning&

36、#39;,'off'); load mri;,M1=D(:,64,:,:);size(M1); M2=reshape(M1,[128 27]);size(M2); T0=maketform('affine',[0 -2.5;1 0;0 0]); imtransform(M2,T0,'cubic') R2=makeresampler({'bicubic&#

37、39;,'nearest'},'fill'); M3=imfransform(M2,T0,R2); T1=makeform('affine',[-2.5 0;0 1;68.5 0]); T2=makeform('custom',3,2,[],@ipex003,64); T1=makeform('composite',T1,T2

38、); R3=makeresampler({'cubic','nearest','nearest'},'fill'); M4=tformarray(D,Tc,R3,[4 1 2],[1 2],[66 128],[],0); T3=maketform('affine',[-2.5 0 0;0 1 0;0 0 0.5;68.5 0 -14]

39、); S=tformarray(D,T3,R3,[4 1 2],[1 2 4],[66 128 35],[],0); figure;,immovie(S,map); S2=padarray(S,[6 0 0 0],0,'both'); montage(S2,map); functionU=ipex003(X,t) U=[X repmat(T.tdata,[size(X,1)