www.pudn.com > zhang.rar > Zhang.m
% function Zhang(M,m)
%
% ***********************************************************************************
% ******* A Flexible New Technique for Camera Calibration *******
% ***********************************************************************************
% 7/2004 Simon Wan
% simonwan@hit.edu.cn
%
% Note: M:2*N m:2*N
% M point on the model plane, when using M=[X,Y]' ---> M=[X,Y,1]'
% m M's image, when using m=[u,v]' ---> m=[u,v,1]' , so that
% s*m = H*M , with H=A*[r1,r2,t]; (2)
% H homography matrix
%
% REF: "A Flexible New Technique for Camera Calibration"
% - Zhengyou Zhang
% - Microsoft Research
%
function Zhang(M,m)
% M=[X,Y]' ---> M=[X,Y,1]' ; m=[u,v]' ---> m=[u,v,1]'
[rows,npts]=size(M);
matrixone=ones(1,npts);
M=[M;matrixone];
num=size(m,3);
for i=1:num
m(3,:,i)=matrixone;
end
% Estimate the H
for i=1:num
H(:,:,i)=homography2d1(M,m(:,:,i))';
end
% solve the intrinsic parameters matrix A
% A=[alpha_u skewness u0
% 0 alpha_v v0
% 0 0 1]
% see Appendix B "Extraction of the Intrisic Parameters from Matrix B", P18
V=[];
for flag=1:num
v12(:,:,flag)=[H(1,1,flag)*H(2,1,flag), H(1,1,flag)*H(2,2,flag)+H(1,2,flag)*H(2,1,flag), H(1,2,flag)*H(2,2,flag), H(1,3,flag)*H(2,1,flag)+H(1,1,flag)*H(2,3,flag), H(1,3,flag)*H(2,2,flag)+H(1,2,flag)*H(2,3,flag), H(1,3,flag)*H(2,3,flag)];
v11(:,:,flag)=[H(1,1,flag)*H(1,1,flag), H(1,1,flag)*H(1,2,flag)+H(1,2,flag)*H(1,1,flag), H(1,2,flag)*H(1,2,flag), H(1,3,flag)*H(1,1,flag)+H(1,1,flag)*H(1,3,flag), H(1,3,flag)*H(1,2,flag)+H(1,2,flag)*H(1,3,flag), H(1,3,flag)*H(1,3,flag)];
v22(:,:,flag)=[H(2,1,flag)*H(2,1,flag), H(2,1,flag)*H(2,2,flag)+H(2,2,flag)*H(2,1,flag), H(2,2,flag)*H(2,2,flag), H(2,3,flag)*H(2,1,flag)+H(2,1,flag)*H(2,3,flag), H(2,3,flag)*H(2,2,flag)+H(2,2,flag)*H(2,3,flag), H(2,3,flag)*H(2,3,flag)];
V=[V;v12(:,:,flag);v11(:,:,flag)-v22(:,:,flag)];
end
k=V'*V;
[u,v,d]=svd(k);
[e,d2]=eig(k);
b=d(:,6);
v0=(b(2)*b(4)-b(1)*b(5))/(b(1)*b(3)-b(2)^2);
s=b(6)-(b(4)^2+v0*(b(2)*b(4)-b(1)*b(5)))/b(1);
alpha_u=sqrt(s/b(1));
alpha_v=sqrt(s*b(1)/(b(1)*b(3)-b(2)^2));
skewness=-b(2)*alpha_u*alpha_u*alpha_v/s;
u0=skewness*v0/alpha_u-b(4)*alpha_u*alpha_u/s;
A=[alpha_u skewness u0
0 alpha_v v0
0 0 1];
% solve k1 k1 and all the extrisic parameters, P6
D=[];
d=[];
Rm=[];
for flag=1:num
s=(1/norm(inv(A)*H(1,:,flag)')+1/norm(inv(A)*H(2,:,flag)'))/2;
rl1=s*inv(A)*H(1,:,flag)';
rl2=s*inv(A)*H(2,:,flag)';
rl3=cross(rl1,rl2);
RL=[rl1,rl2,rl3];
%%%%%%%%%%%%%%%%%%%%
% see Appendix C "Approximating a 3*3 matrix by a Rotation Matrix", P19
[U,S,V] = svd(RL);
RL=U*V';
%%%%%%%%%%%%%%%%%%%%
TL=s*inv(A)*H(3,:,flag)';
RT=[rl1,rl2,TL];
XY=RT*M;
UV=A*XY;
UV=[UV(1,:)./UV(3,:); UV(2,:)./UV(3,:); UV(3,:)./UV(3,:)];
XY=[XY(1,:)./XY(3,:); XY(2,:)./XY(3,:); XY(3,:)./XY(3,:)];
for j=1:npts
D=[D; ((UV(1,j)-u0)*( (XY(1,j))^2 + (XY(2,j))^2 )) , ((UV(1,j)-u0)*( (XY(1,j))^2 + (XY(2,j))^2 )^2) ; ((UV(2,j)-v0)*( (XY(1,j))^2 + (XY(2,j))^2 )) , ((UV(2,j)-v0)*( (XY(1,j))^2 + (XY(2,j))^2 )^2) ];
d=[d; (m(1,j,flag)-UV(1,j)) ; (m(2,j,flag)-UV(2,j))];
end
r13=RL(1,3);
r12=RL(1,2);
r23=RL(2,3);
Q1=-asin(r13);
Q2=asin(r12/cos(Q1));
Q3=asin(r23/cos(Q1));
[cos(Q2)*cos(Q1) sin(Q2)*cos(Q1) -sin(Q1) ; -sin(Q2)*cos(Q3)+cos(Q2)*sin(Q1)*sin(Q3) cos(Q2)*cos(Q3)+sin(Q2)*sin(Q1)*sin(Q3) cos(Q1)*sin(Q3) ; sin(Q2)*sin(Q3)+cos(Q2)*sin(Q1)*cos(Q3) -cos(Q2)*sin(Q3)+sin(Q2)*sin(Q1)*cos(Q3) cos(Q1)*cos(Q3)];
R_new=[Q1,Q2,Q3,TL'];
Rm=[Rm , R_new];
end
% using function (13), P8
k=inv(D'*D)*D'*d;
% Complete Maximun Likelihood Estimation, using function (14), P8
para=[Rm,k(1),k(2),alpha_u,skewness,u0,alpha_v,v0];
options = optimset('LargeScale','off','LevenbergMarquardt','on');
[x,resnorm,residual,exitflag,output] = lsqnonlin( @simon_HHH, para, [],[],options, m, M);
% display the result
k1=x(num*6+1)
k2=x(num*6+2)
A=[x(num*6+3) x(num*6+4) x(num*6+5); 0 x(num*6+6) x(num*6+7); 0,0,1]