第七章 图像的空间变换

第七章 图像的空间变换,计算机图像处理,第七章 图像的空间变换,空间变换,MATLAB,空间变换方法,MATLAB,的图像匹配,MATLAB,的图像投影,一,.,空间变换,空间变换主要是用来保持图像中的连续性和物体的连通性,一般都用数学函数形式来描述输入输出图像相应像素间的空间关系。空间变换的一般表达式为：,g(x,y,)=,f(x,y,)=,fa(x,y),b(x,y,),g(x,y,),输出图像,(,x,y,),空间变换后的坐标,a(x,y),b(x,y,),空间变换函数,7.1,空间变换,二,.,简单变换,简单变换用来实现图像的平移、旋转、剪切等简单操作。如：,a(x,y,)=x+x0,b(x,y,)=y+y0,2),旋转变换,3),平移放大,水平变换,a(x,y,)=,xcos-ysin,垂直变换,b(x,y,)=y,a(x,y,)=x,b(x,y,)=,（,xsin+y,）,/,cos,1),平移变换,a(x,y,)=,xcos-ysin,b(x,y,)=,xsin+ycos,1,）多项式卷绕,利用控制点序列为,a(x,y,),和,b(x,y,),找到一个近似的多项式描述。该多项式的参数能够使,多项式的取值与控制点及其位移量吻合。,三,.,利用控制点进行变换：,2,）图像分割卷绕,将控制点形成一个矩形输入栅格，通过映,射将栅格变换为输出图像中连同的水平输出,栅格，控制点为每一个输出栅格对应的顶,点，输入栅格内的各点影射为相应输出栅格,内的点。,通常采用的栅格插值方法是双线性空间,变换方法，其一般表达式为：,G(x,y,)=,F(ax+by+cxy+d,e+fy+gxy+h,),%7_3_a,I=,imread(flowers.tif,);,subplot(331),imshow(I);,%7_3_b,I=,imread(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,FillValues,.3);,%subplot(332),imshow(I_linearconformal);,imshow(I_linearconformal,);,%7_3_c,I=,imread(flowers.tif,);,T=1 0.1;1 1;0 0;,t_aff,=,maketform(affine,T,);,I_affine,=imtransform(I,t_aff,FillValues,.3);,%subplot(333),imshow(I_affine),imshow(I_affine,);,%7_3_d,I=,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,FillValues,.3);,%subplot(334),imshow(I_projective),iptsetpref(ImshowTruesize,manual,);,imshow(I_projective,);,%7_3_e,I=,imread(flowers.tif,);,xybase,=reshape(randn(12,1),6,2);,t_poly,=cp2tform(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(ImshowTruesize,manual,);,imshow(I_polynomial,);,%7_3_f,I=,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);,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,);,%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,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,);,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,resamp,2 1,1 2,tmap_B,.3);,%subplot(338),imshow(I_barrel);,%,iptsetpref(ImshowTruesize,manual,);,imshow(I_barrel,);,%7_3_i,I=,imread(flowers.tif,);,xt,=xi(:)-,imid,;,yt,=,yi(:)-imid,;,theta,r,=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),imshow(I_pin);,iptsetpref(ImshowTruesize,manual,);,imshow(I_pin,),%7.5.6,orthophoto,=,imread(westconcordorthophoto.png,);,subplot(1,2,1),imshow(orthophoto),unregistered=,imread(westconcordaerial.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;,%,input_points_corr,=,cpcorr(input_points,base_points,.,unregistered(:,:,1),orthophoto),input_points_corr,=120.7086 93.9772,319.2222 78.9202,127.1064 289.8935,352.0729 281.1445;,%,mytform,=cp2tform(input_points,base_points,projective);,%,registered=,imtransform(unregistered,mytform,),%7.7,clc,Clear,%ch7_8_11,lily=,imread(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_flowers,=,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),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,=(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,+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,),end,%,recovered_lily,=uint8(zeros(size(flowers);,recovered_lily(ybegin:yend,xbegin: