橢圓擬合

結合師兄寫的程序加上自己的修改

橢圓擬合

同時可參考http://mathworld.wolfram.com/Ellipse.html

function [Re, center, vertex]= MyEllipseDirectFit(XY)
%  Direct ellipse fit, proposed in article
%    A. W. Fitzgibbon, M. Pilu, R. B. Fisher
%     "Direct Least Squares Fitting of Ellipses"
%     IEEE Trans. PAMI, Vol. 21, pages 476-480 (1999)
%
%  Our code is based on a numerically stable version
%  of this fit published by R. Halir and J. Flusser
%
%     Input:  XY(n,2) is the array of coordinates of n points x(i)=XY(i,1), y(i)=XY(i,2)
%
%     Output: A = [a b c d e f]' is the vector of algebraic 
%             parameters of the fitting ellipse:
%             ax^2 + bxy + cy^2 +dx + ey + f = 0
%             the vector A is normed, so that ||A||=1
%
%  This is a fast non-iterative ellipse fit.
%
%  It returns ellipses only, even if points are
%  better approximated by a hyperbola.
%  It is somewhat biased toward smaller ellipses.
%
centroid = mean(XY); % the centroid of the data set
warning off;
D1 = [(XY(:,1)-centroid(1)).^2, (XY(:,1)-centroid(1)).*(XY(:,2)-centroid(2)),...
      (XY(:,2)-centroid(2)).^2];
D2 = [XY(:,1)-centroid(1), XY(:,2)-centroid(2), ones(size(XY,1),1)];
S1 = D1'*D1;
S2 = D1'*D2;
S3 = D2'*D2;
T = -inv(S3)*S2';
M = S1 + S2*T;
M = [M(3,:)./2; -M(2,:); M(1,:)./2];
[evec,eval] = eig(M);
cond = 4*evec(1,:).*evec(3,:)-evec(2,:).^2;
A1 = evec(:,find(cond>0));
A = [A1; T*A1];
A4 = A(4)-2*A(1)*centroid(1)-A(2)*centroid(2);
A5 = A(5)-2*A(3)*centroid(2)-A(2)*centroid(1);
A6 = A(6)+A(1)*centroid(1)^2+A(3)*centroid(2)^2+...
     A(2)*centroid(1)*centroid(2)-A(4)*centroid(1)-A(5)*centroid(2);
A(4) = A4;  A(5) = A5;  A(6) = A6;
% if A(1)<0
%     A=-A;
% end
Re=A;

%長軸傾角
%ellipse equation: a*x^2 + b*x*y + c*y^2 +d*x + e*y + 1 = 0;
% Refer to：http://blog.csdn.net/ningyaliuhebei/article/details/46327681
B=Re(2)/Re(6); A=Re(1)/Re(6);C=Re(3)/Re(6); D=Re(4)/Re(6);E=Re(5)/Re(6);
if B==0
     if A<C/2
    theta1=0; 
    else
      theta1= pi/2;
    end  
else
    if A<C/2
    theta1=0.5*atan(B/(A-C)); 
    else
      theta1= pi/2 + 0.5*atan(B/(A-C));
    end
end
K1= tan(theta1); %長軸斜率
if (abs(K1)<1e-8) 
    K1=0;
end
%橢圓的中心點
xc=(B*E-2*C*D)/(4*A*C-B^2);
yc=(B*D-2*A*E)/(4*A*C-B^2);
%橢圓的長、短半軸長度
la=sqrt(2*(A*xc^2+C*yc^2+B*xc*yc-1)/(A+C-sqrt((A-C)^2+B^2)));
lb=sqrt(2*(A*xc^2+C*yc^2+B*xc*yc-1)/(A+C+sqrt((A-C)^2+B^2)));
%長、短軸頂點座標
n1=[1,K1]; n1=n1/norm(n1);
center = [xc, yc];
va1=center+la*n1;  %長軸頂點1, 座標軸正向
va2=center-la*n1;  %長軸頂點2，座標軸負向

if(K1 == 0)
    n2=[0,1];
else
    n2=[1,-1/K1];
end
n2=n2/norm(n2);
if n2(2) >= 0
    vb1=center+lb*n2;  %短軸頂點1，座標軸正向
    vb2=center-lb*n2;  %短軸頂點2，座標軸負向
else
    vb1=center-lb*n2;  %短軸頂點1，座標軸正向
    vb2=center+lb*n2;  %短軸頂點2，座標軸負向
end

center = [xc, yc];
vertex = [va1;va2;vb1;vb2];

end  %  EllipseDirectFit

長短軸計算

結合上文函數

function [aa,bb]=getab(re)
a=re(1);
b=re(2)/2;
c=re(3);
d=re(4)/2;
f=re(5)/2;
g=re(6);
aa=sqrt((2*(a*f^2+c*d^2+g*b^2-2*b*d*f-a*c*g))/((b^2-a*c)*(sqrt((a-c)^2+4*b^2)-(a+c))));
bb=sqrt((2*(a*f^2+c*d^2+g*b^2-2*b*d*f-a*c*g))/((b^2-a*c)*(-sqrt((a-c)^2+4*b^2)-(a+c))));
if abs(aa)>abs(bb)
    temp=aa;
    aa=bb;
    bb=temp;
end
end