基于最小二乘解包裹附Matlab代码（Matlab最小二乘）

基于最小二乘解包裹附Matlab代码（Matlab最小二乘）

1 简介

2 完整代码

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%模拟球面 zernikeclcclear allclose allA=1000000000000000*ones([115 115]);zj=8;[M0 N0]=size(A);coef=zeros([1 zj]);RX = (M0+1)/2;RY = (N0+1)/2;R0 =min(RX,RY);fitted_ball=zeros([M0 N0]);r=0;k=0;z=0;wfront=0;for i = 1:M0 for j = 1:N0 rad = sqrt((i-RX)^2+(j-RY)^2);%椭圆的问题？ if rad <= R0;% &&A(i,j)~=0 r = rad/R0; if r~=0 theta = atan2(RX-i,j-RY); end k=k+1; wfront(k)=A(i,j); z(1,k)=1; z(2,k)=r*cos(theta); z(3,k)=r*sin(theta); z(4,k)=2*r^2-1; z(5,k)=r^2*cos(2*theta); z(6,k)=r^2*sin(2*theta); z(7,k)=(3*r^3-2*r)*cos(theta); z(8,k)=(3*r^3-2*r)*sin(theta); end endendorthop=zeros(zj,k);orthop(1,1:k)=z(1,:);bb(1)=wfront*orthop(1,:)'/(orthop(1,:)*orthop(1,:)');zterm=zj;for n=2:zterm orthop(n,:)=z(n,:); for m=1:n-1 aa(n,m)=z(n,:)*orthop(m,:)'/(orthop(m,:)*orthop(m,:)'); orthop(n,:)=orthop(n,:)-aa(n,m)*orthop(m,:); end bb(n)=wfront*orthop(n,:)'/(orthop(n,:)*orthop(n,:)');endcoef(zterm)=bb(zterm);for n=1:zterm-1 coef(zterm-n)=bb(zterm-n)-coef(zterm-n+1:zterm)*aa(zterm-n+1:zterm,zterm-n);endcoef_ball=coef;coef_ball(1:3)=0;coef_ball(5:zj)=0;% coef_qiumian(1)=0;coef_qiumian(4)=0;r=0;zz=zeros([1 zterm]);for i = 1:M0 for j = 1:N0 rad = sqrt((i-RX)^2+(j-RY)^2); if rad <= R0 r = rad/R0; if r~=0 theta = atan2(RX-i,j-RY); end zz(1)=1; zz(2)=r*cos(theta); zz(3)=r*sin(theta); zz(4)=2*r^2-1; zz(5)=r^2*cos(2*theta); zz(6)=r^2*sin(2*theta); zz(7)=(3*r^3-2*r)*cos(theta); zz(8)=(3*r^3-2*r)*sin(theta); fitted_ball(i,j)=coef_ball*zz'; end endendfigure(1),mesh(fitted_ball); title('三维面形图','FontSize',10); xlabel('x轴(pix)','FontSize',8); ylabel('y轴(pix)','FontSize',8); zlabel('面形','FontSize',8); gst0=255*cos(fitted_ball*20);gst1=imresize((gst0),[230 230],'bilinear');figure(2),imshow(uint8(gst1));%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 边界延拓B=gst1(65:180,65:180);figure(3),imshow(uint8(B));%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% FFT相位提取%%%%%%%%%%%%% %%%%%fft_lvbo%%%%%%%%%%%C=imresize(B,[128 128]);[m,n]=size(C);% Af=fft2(double(C));Af1=fft2(C); Af2=fftshift(Af1);figure(4),imshow(uint8(Af2));%%%%%%%lvbofilter0=ones([m n]);filter0(1:(m/2),:)=0;filter1=ones([m n]);filter1((m/2+1):m,:)=0;%%%+1filter2=ones([m n]);filter2(:,1:(n/2))=0;filter3=ones([m n]);filter3(:,(n/2+1):n)=0;%%%+1%Af2=abs(Af2);Af3_0=filter0.*Af2;Af3_1=filter1.*Af2;Af3_2=filter2.*Af2;Af3_3=filter3.*Af2;%figure(5),imshow(uint8(Af3_0));Af4_0=fftshift(Af3_0);Af4_1=fftshift(Af3_1);Af4_2=fftshift(Af3_2);Af4_3=fftshift(Af3_3);Aiff5_0=ifft2(Af4_0);Aiff5_1=ifft2(Af4_1);Aiff5_2=ifft2(Af4_2);Aiff5_3=ifft2(Af4_3);%%%%%%%%%%%%%%%%%%%%J0=atan2(imag(Aiff5_0),real(Aiff5_0));J1=atan2(imag(Aiff5_1),real(Aiff5_1));J2=atan2(imag(Aiff5_2),real(Aiff5_2));J3=atan2(imag(Aiff5_3),real(Aiff5_3));%%%%%%%%%%%%%%%%%%%找中心x=0;r=ones([2 2]);tp=2;x0=0;for x=3:(m-3)% r=corrcoef(J0(x-1,:),J0(x,:))+corrcoef(J0(x,:),J0(x+1,:)); r=corrcoef(J0(x,:),J0(x+1,:)); if r(1,2)=pi k(h,j)=k(h-1,j)-1; elseif abs(J(h,j)-J(h-1,j))=pi k(h,p)=k(h,p-1)-1; elseif abs(J(h,p)-J(h,p-1))i j-->% if y==0% y=n;% end% if (x==0) && (y~=1&&y~=n)% F(w,w)=-3;% F(w,(x-1)*n+y)=F(w,(i+1)*n+j)% F(w,(x+1)*n+y)=1;% % F(w,(x-1)*n+y)=1;% F(w,x*n+y+1)=1;% F(w,x*n+y-1)=1;% end% if (x==m-1) && (y~=1&&y~=n)% F(w,w)=-3;% F(w,(x-1)*n+y)=F(w,(i+1)*n+j)% % F(w,(x+1)*n+y)=1;% F(w,(x-1)*n+y)=1;% F(w,x*n+y+1)=1;% F(w,x*n+y-1)=1;% end% if (y==1) && (x~=0&&x~=m-1)% F(w,w)=-3;% F(w,(x-1)*n+y)=F(w,(i+1)*n+j)% F(w,(x+1)*n+y)=1;% F(w,(x-1)*n+y)=1;% F(w,x*n+y+1)=1;% % F(w,x*n+y-1)=1;% end% if (y==n) && (x~=0&&x~=m-1) % F(w,w)=-3;% F(w,(x-1)*n+y)=F(w,(i+1)*n+j)% F(w,(x+1)*n+y)=1;% F(w,(x-1)*n+y)=1;% % F(w,x*n+y+1)=1;% F(w,x*n+y-1)=1;% end% if (x==0) && (y==1) % &&y~=n)% F(w,w)=-2;% F(w,(x-1)*n+y)=F(w,(i+1)*n+j)% F(w,(x+1)*n+y)=1;% % F(w,(x-1)*n+y)=1;% F(w,x*n+y+1)=1;% % F(w,x*n+y-1)=1;;% end% if (x==m-1) && (y==1)% &&y~=n)% F(w,w)=-2;% F(w,(x-1)*n+y)=F(w,(i+1)*n+j)% % F(w,(x+1)*n+y)=1;% F(w,(x-1)*n+y)=1;% F(w,x*n+y+1)=1;% % F(w,x*n+y-1)=1;;% end% if (x==m-1) && (y==n)% &&y~=n)% F(w,w)=-2;% F(w,(x-1)*n+y)=F(w,(i+1)*n+j)% % F(w,(x+1)*n+y)=1;% F(w,(x-1)*n+y)=1;% % F(w,x*n+y+1)=1;% F(w,x*n+y-1)=1;;% end% if (x==0) && (y==n)% &&y~=n)% F(w,w)=-2;% F(w,(x-1)*n+y)=F(w,(i+1)*n+j)% F(w,(x+1)*n+y)=1;% % F(w,(x-1)*n+y)=1;% % F(w,x*n+y+1)=1;% F(w,x*n+y-1)=1;;% end% if (x>0&&x1&&y=pi% bx(lx,ly)=0-1; % elseif J(lx+1,ly)-J(lx,ly)<-pi% bx(lx,ly)=0+1;% else% bx(lx,ly)=0;% end% dx(lx,ly)=J(lx+1,ly)-J(lx,ly)+2*pi*bx(lx,ly);%%NOTE: bb的形式！！！need to change% end% end% for lx=1:m% for ly=1:(n-1)% % dy(lx,ly)=J(lx,ly+1)-J(lx,ly);% !tongshang% if (J(lx,ly+1)-J(lx,ly))>=pi% by(lx,ly)=0-1; % elseif (J(lx,ly+1)-J(lx,ly))<-pi% by(lx,ly)=0+1;% else% by(lx,ly)=0;% end% dy(lx,ly)=J(lx,ly+1)-J(lx,ly)+2*pi*by(lx,ly);%%NOTE: bb的形式！！！need to change% end% end% dx(m,:)=0;% dy(:,n)=0;% R=zeros(m,n);% % R(1,2:n)=dx(1,2:n)-0+dy(1,2:n)-dy(1,1:(n-1)); % % R(2:m,1)=dx(2:m,1)-dx(1:(m-1),1)+dy(2:m,1)-0;% % R(1,1)=dx(lx,ly)+dy(lx,ly);% for lx=1:m% for ly=1:n% if (lx==1)&&(ly~=1) % R(lx,ly)=dx(lx,ly)+dy(lx,ly)-dy(lx,ly-1); % elseif (ly==1)&&(lx~=1)% R(lx,ly)=dx(lx,ly)-dx(lx-1,ly)+dy(lx,ly);% elseif (ly==1)&&(lx==1)% R(lx,ly)=dx(lx,ly)+dy(lx,ly);% else% R(lx,ly)=dx(lx,ly)-dx(lx-1,ly)+dy(lx,ly)-dy(lx,ly-1);% end% end% end% %%%%%%%%%%%%%解方程%%%%!!!!!!!!!!RR=wiener2(R,[10 10]);% for g=1:m% for t=1:n% GG((g-1)*n+t)=R(g,t);% end% end% GT=GG';% % TT=cgs(F,GT,1e-006,100);%300% X=zeros(m,n);% for g=1:m % for t=1:n% X(g,t)=TT((g-1)*n+t);%/2%%%%%2倍关系% end% end% figure(8),mesh(double(X));%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Zernike拟合%%%%%%A=imresize(X,[65 65],'bilinear');zj=16;[M0 N0]=size(A);coef(1:zj) = 0;RX = (M0+1)/2;RY = (N0+1)/2;R0 =min(RX,RY);% fitted(1:M0,1:N0) = 0;fitted_qulijiao=zeros([M0 N0]);% fitted_ball=zeros([M0 N0]);r=0;k=0;z=0;wfront=0;for i = 1:M0 for j = 1:N0 rad = sqrt((i-RX)^2+(j-RY)^2);%椭圆的问题？ if rad <= R0;% &&A(i,j)~=0 r = rad/R0; if r~=0 theta = atan2(RX-i,j-RY); end k=k+1; wfront(k)=A(i,j); z(1,k)=1; z(2,k)=r*cos(theta); z(3,k)=r*sin(theta); z(4,k)=2*r^2-1; z(5,k)=r^2*cos(2*theta); z(6,k)=r^2*sin(2*theta); z(7,k)=(3*r^3-2*r)*cos(theta); z(8,k)=(3*r^3-2*r)*sin(theta); z(9,k)=6*r^4-6*r^2+1; z(10,k)=r^3*cos(3*theta); z(11,k)=r^3*sin(3*theta); z(12,k)=(4*r^4-3*r^2)*cos(2*theta); z(13,k)=(4*r^4-3*r^2)*sin(2*theta); z(14,k)=(10*r^5-12*r^3+3*r)*cos(theta); z(15,k)=(10*r^5-12*r^3+3*r)*sin(theta); z(16,k)=20*r^6-30*r^4+12*r^2-1; end endendorthop=zeros(zj,k);orthop(1,1:k)=z(1,:);bb(1)=wfront*orthop(1,:)'/(orthop(1,:)*orthop(1,:)');zterm=zj;for n=2:zterm orthop(n,:)=z(n,:); for m=1:n-1 aa(n,m)=z(n,:)*orthop(m,:)'/(orthop(m,:)*orthop(m,:)'); orthop(n,:)=orthop(n,:)-aa(n,m)*orthop(m,:); end bb(n)=wfront*orthop(n,:)'/(orthop(n,:)*orthop(n,:)');endcoef(zterm)=bb(zterm);for n=1:zterm-1 coef(zterm-n)=bb(zterm-n)-coef(zterm-n+1:zterm)*aa(zterm-n+1:zterm,zterm-n);endcoef_qulijiao=coef;coef_qulijiao(1:4)=0;r=0;zz=zeros([1 zterm]);for i = 1:M0 for j = 1:N0 rad = sqrt((i-RX)^2+(j-RY)^2); if rad <= R0 r = rad/R0; if r~=0 theta = atan2(RX-i,j-RY); end zz(1)=1; zz(2)=r*cos(theta); zz(3)=r*sin(theta); zz(4)=2*r^2-1; zz(5)=r^2*cos(2*theta); zz(6)=r^2*sin(2*theta); zz(7)=(3*r^3-2*r)*cos(theta); zz(8)=(3*r^3-2*r)*sin(theta); zz(9)=6*r^4-6*r^2+1; zz(10)=r^3*cos(3*theta); zz(11)=r^3*sin(3*theta); zz(12)=(4*r^4-3*r^2)*cos(2*theta); zz(13)=(4*r^4-3*r^2)*sin(2*theta); zz(14)=(10*r^5-12*r^3+3*r)*cos(theta); zz(15)=(10*r^5-12*r^3+3*r)*sin(theta); zz(16)=20*r^6-30*r^4+12*r^2-1; % fitted(i,j) =coef*zz'; fitted_qulijiao(i,j)=coef_qulijiao*zz'; end endendif coef(4)>0 Result_qulijiao=fitted_qulijiao./(4*pi); else Result_qulijiao=(-1)*fitted_qulijiao./(4*pi);endfigure(9),mesh(double(Result_qulijiao));

3 仿真结果

4 参考文献

[1]钱晓凡, 饶帆, 李兴华,等. 精确最小二乘相位解包裹算法[J]. 中国激光, 2012, 39(2):5.

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