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Zhang_InAndOut.m
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function Zhang_InAndOut
% 本m文件用来求解内参数和外参数并优化。
% 求解过称共用六幅图像，每幅图像取10个点。先求出每个图像的单应矩阵，然后把六个单应矩阵和在一起，
% 由V*b=0解出b。再然后用b分解出内参数矩阵A，最后由A和单应矩阵求出外参数矩阵
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 以下从文本中读出世界坐标和对应的图像坐标 %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
n = 24;
M=load('board.txt'); %读取世界坐标
M=[M';ones(1,49)];
m_all=load('speckle_150_20_snd_100.txt'); %读取关键点坐标
m_one=ones(3,49,n);
for i=1:1:n
m_temp = m_all((i-1)*49+1:i*49,:);
m_one(:,:,i) = [m_temp';ones(1,49)];
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 以下求解单应矩阵并解出b %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
H = ones(3,3,n); %每幅图一个单应矩阵
for i=1:1:n
H(:,:,i)=homography(m_one(:,:,i),M);
end
V=ones(2*n,6); %V*b=0
for i=1:n %求V
V(2*i-1,:)=[H(1,1,i)*H(1,2,i) H(1,1,i)*H(2,2,i)+H(2,1,i)*H(1,2,i) H(2,1,i)*H(2,2,i) ...
H(3,1,i)*H(1,2,i)+H(1,1,i)*H(3,2,i) H(3,1,i)*H(2,2,i)+H(2,1,i)*H(3,2,i) H(3,1,i)*H(3,2,i)];
p1=[H(1,1,i)^2 H(1,1,i)*H(2,1,i)+H(2,1,i)*H(1,1,i) H(2,1,i)^2 H(3,1,i)*H(1,1,i)+H(1,1,i)*H(3,1,i) H(3,1,i)*H(2,1,i)+H(2,1,i)*H(3,1,i) H(3,1,i)^2];
p2=[H(1,2,i)^2 H(1,2,i)*H(2,2,i)+H(2,2,i)*H(1,2,i) H(2,2,i)^2 H(3,2,i)*H(1,2,i)+H(1,2,i)*H(3,2,i) H(3,2,i)*H(2,2,i)+H(2,2,i)*H(3,2,i) H(3,2,i)^2];
V(2*i,:)=p1-p2;
end;
[u s v]=svd(V); %用正交分解解出b
b=v(:,6);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 以下分解内参数矩阵 %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
cy=(b(2)*b(4)-b(1)*b(5))/(b(1)*b(3)-b(2)^2);
lamda=b(6)-(b(4)^2+(b(2)*b(4)-b(1)*b(5))/(b(1)*b(3)-b(2)^2)*(b(2)*b(4)-b(1)*b(5)))/b(1);
kx=sqrt(lamda/b(1));
ky=sqrt((lamda*b(1))/(b(1)*b(3)-b(2)^2));
gama=-(b(2)*kx^2*ky)/lamda;
cx=(gama*cy)/kx-(b(4)*kx^2)/lamda;
%A=[kx gama cx;0 ky cy;0 0 1]; %求出内参数矩阵
A=[kx 0 cx;0 ky cy;0 0 1] %求出内参数矩阵
mp=ones(3,49,n); %图像坐标矩阵（合成三维形式，方便循环操作）
mp = m_one;
%para1=[kx gama cx ky cy ];
%A = [15037.6, 0, 1393.4; 0, 15085.2, 1153.8; 0, 0, 1]
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 以下求解外参数矩阵 %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
inv(A)*H(:,1,1);
inv(A)*H(:,2,1);
q1=(norm(inv(A)*H(:,1,1))+norm(inv(A)*H(:,2,1)))/2;
q1=(norm(inv(A)*H(:,1,1),2)+norm(inv(A)*H(:,2,1),2))/2;
R=[];
Rm=[];
for i=1:n
q1=(norm(inv(A)*H(:,1,i))+norm(inv(A)*H(:,2,i)))/2; %下面求解外参数矩阵
r1=(1/q1)*inv(A)*H(:,1,i);
r2=(1/q1)*inv(A)*H(:,2,i);
r3=cross(r1,r2);
RL=[r1 r2 r3];
[u s v]=svd(RL);
RL=u*v'; %旋转矩阵正交化
p=(1/q1)*inv(A)*H(:,3,i);
RT=[r1 r2 p];
R=[R;RT];
% rotationVectors = vision.internal.calibration.rodriguesMatrixToVector(RL)
% p;
% (RL-RL')/2
sq = sqrt(RL(3,2)^2+RL(3,3)^2);
Q1 = atan2(RL(3,2),RL(3,3));
Q2 = atan2(-RL(3,1),sq);
Q3 = atan2(RL(2,1),RL(1,1));
% r=[cos(Q2)*cos(Q3) sin(Q1)*sin(Q2)*cos(Q3)-cos(Q1)*sin(Q3) cos(Q1)*sin(Q2)*cos(Q3)+sin(Q1)*sin(Q3); %旋转矩阵
% cos(Q2)*sin(Q3) sin(Q1)*sin(Q2)*sin(Q3)+cos(Q1)*cos(Q3) cos(Q1)*sin(Q2)*sin(Q3)-sin(Q1)*cos(Q3);
% -sin(Q2) sin(Q1)*cos(Q2) cos(Q1)*cos(Q2)];
% r13=RL(1,3);
% r12=RL(1,2);
% r23=RL(2,3);
% Q1=-asin(r13); %分解出旋转矩阵中的独立变量，即三个转角
% Q2=asin(r12/cos(Q1));
% Q3=asin(r23/cos(Q1));
[Q1 Q2 Q3]';
p;
R_new=[Q1,Q2,Q3,p'];
% R_new=[rotationVectors',p'];
Rm=[Rm , R_new];
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 闭式解的重投影误差 %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% R=[];
%
% for i=1:n %下面用来恢复出外参数矩阵
% R_new=Rm([(i-1)*6+1 : (i-1)*6+6] );
% Q1=R_new(1);
% Q2=R_new(2);
% Q3=R_new(3);
% TL=R_new([4:6])';
% RL=[ cos(Q2)*cos(Q1) sin(Q2)*cos(Q1) -sin(Q1) ; %旋转矩阵
% -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)];
% RT=[RL(:,1:2) , TL];
% R=[R;RT];
% end
res = ones(3,49,n);
for i=1:n
RT=R([(i-1)*3+1 : (i-1)*3+3],:);
x=A*RT*M;
x=[x(1,:)./x(3,:) ; x(2,:)./x(3,:); x(3,:)./x(3,:)]; % 保证最后一列为1
res(:,:,i) = mp(:,:,i)-x;
end
res_sum = zeros(1,98*n);
for i = 1:n
for j = 1:49
res_sum(1,2*((i-1)*49+j)-1) = res(1,j,i);
res_sum(1,2*((i-1)*49+j)) = res(2,j,i);
end
end
res_sum.*res_sum;
xxx=sum(res_sum.*res_sum);
initres = sqrt(sum(res_sum.*res_sum,2)/(n*49))
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 下面进行最终的优化（包括内参数，三个旋转角度，平移向量和畸变系数） %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
para=[Rm,A(1,1),A(1,3),A(2,2),A(2,3)];%优化畸变系数，内参数，外参数（平移矩阵和三个转角）
options = optimset('LargeScale','off','Algorithm','levenberg-marquardt','Display','iter');
%options = optimoptions(@lsqnonlin,'Algorithm','levenberg-marquardt',...
% 'TolFun',1.0e-8,...
% 'StepTolerance',1.0e-8,...
% 'Display','iter');
% 'FiniteDifferenceStepSize',2,...
%options = optimoptions('lsqnonlin','FiniteDifferenceType','central');
[x,nor,res] = lsqnonlin( @fun2, para, [],[],options, mp, M, n);
A=[x(n*6+1) 0 x(n*6+2); 0 x(n*6+3) x(n*6+4); 0,0,1];
disp('最终优化过的内参数为');
disp(A);
sqrt(nor/(49*n))
% options = optimset('LargeScale','off','Algorithm','levenberg-marquardt');% 使用lsqnonlin进行非线性最小二乘求解
% [x,norm,res] = lsqnonlin( @fun2, para1 ,[],[],options, mp, M,H,n);
% A=[x(1) x(2) x(3);0 x(4) x(5);0 0 1]; % 得到优化后的内参数矩阵
% norm;
% res;
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % 以下求解畸变系数 %
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% D=[]; %D*K=d
% d=[];
% for i=1:6
% s=(1/norm(inv(A)*H(:,1,i))+1/norm(inv(A)*H(:,2,i)))/2;
% rl1=s*inv(A)*H(:,1,i);
% rl2=s*inv(A)*H(:,2,i);
% rl3=cross(rl1,rl2);
% RL=[rl1,rl2,rl3];
% [U,S,V] = svd(RL);
% RL=U*V'; %保证旋转矩阵为标准正交矩阵
% TL=s*inv(A)*H(:,3,i);
% RT=[rl1,rl2,TL]; %单应矩阵
% XY=RT*M; %得到Xc、Yc、Zc
% UV=A*XY; %计算出图像中的坐标
% UV=[UV(1,:)./UV(3,:); UV(2,:)./UV(3,:); UV(3,:)./UV(3,:)];%最后一行规‘1’
% XY=[XY(1,:)./XY(3,:); XY(2,:)./XY(3,:); XY(3,:)./XY(3,:)];%x=Xc/Zc,y=Yc/Zc,r=x^2+y^2
% for j=1:10
% 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; (mp(1,j,i)-UV(1,j)) ; (mp(2,j,i)-UV(2,j))];
% end
% end
% k=inv(D'*D)*D'*d; %求出畸变系数
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % 下面进行进一步的优化（包括内参数和畸变系数） %
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% para2=[k(1),k(2),A(1,1),A(1,2),u0,A(2,2),v0];%对畸变系数和内参数矩阵进行优化
% options = optimset('LargeScale','off','Algorithm','levenberg-marquardt');
% x= lsqnonlin( @fun3,para2,[],[],options,mp,M,H);
% k1=x(1);
% k2=x(2);
% K=[k1;k2];
% A=[x(3) x(4) x(5); 0 x(6) x(7); 0,0,1];
% disp(' ');
% disp('优化前的内参数矩阵为：');
% disp(A1);
% disp('优化前的畸变系数矩阵为：');
% disp(k);
% disp('优化后的内参数矩阵为：');
% disp(A);
% disp('优化后的畸变系数矩阵为：');
% disp(K);
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 下面进行最终的优化（包括内参数，三个旋转角度，平移向量和畸变系数） %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% D=[];
% d=[];
% Rm=[];
% for i=1:6 %共用了六幅图像
% s=(norm(inv(A)*H(:,1,i))+norm(inv(A)*H(:,2,i)))/2;
% rl1=(1/s)*inv(A)*H(:,1,i);
% rl2=(1/s)*inv(A)*H(:,2,i);
% rl3=cross(rl1,rl2);
% RL=[rl1,rl2,rl3];
% [U,S,V] = svd(RL);
% TL=(1/s)*inv(A)*H(:,3,i);
% 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=1:10 %每幅图取十个点
% 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; (mp(1,j,i)-UV(1,j)) ; (mp(2,j,i)-UV(2,j))];
% end
% r13=RL(1,3);
% r12=RL(1,2);
% r23=RL(2,3);
% Q1=-asin(r13); %分解出旋转矩阵中的独立变量，即三个转角
% Q2=asin(r12/cos(Q1));
% Q3=asin(r23/cos(Q1));
% R_new=[Q1,Q2,Q3,TL'];
% Rm=[Rm , R_new];
% end
% k=inv(D'*D)*D'*d;
% para3=[Rm,k(1),k(2),A(1,1),A(1,2),A(1,3),A(2,2),A(2,3)];%优化畸变系数，内参数，外参数（平移矩阵和三个转角）
% options = optimset('LargeScale','off','Algorithm','levenberg-marquardt');
% x = lsqnonlin( @fun4, para3, [],[],options, mp, M);
% k=[x(6*6+1);x(6*6+2)];
% A=[x(6*6+3) x(6*6+4) x(6*6+5); 0 x(6*6+6) x(6*6+7); 0,0,1];
% disp('最终优化过的畸变系数为');
% disp(k);
% disp('最终优化过的内参数为');
% disp(A);
%
%
%
%