我想用MATLAB实现 将近似椭圆形的一些离散点 拟合成椭圆曲线

发布网友 发布时间：2022-04-23 09:15

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热心网友 时间：2023-06-28 16:49

以下为matlab采用最小二乘法的椭圆拟合程序：

function a = fitellipse(X,Y)

% FITELLIPSE Least-squares fit of ellipse to 2D points.
% A = FITELLIPSE(X,Y) returns the parameters of the best-fit
% ellipse to 2D points (X,Y).
% The returned vector A contains the center, radii, and orientation
% of the ellipse, stored as (Cx, Cy, Rx, Ry, theta_radians)
%
% Example: Run fitellipse without any arguments to get a demo
if nargin == 0
% Create an ellipse
t = linspace(0,2);

Rx = 300
Ry = 200
Cx = 250
Cy = 150
Rotation = .4 % Radians

x = Rx * cos(t);
y = Ry * sin(t);
nx = x*cos(Rotation)-y*sin(Rotation) + Cx;
ny = x*sin(Rotation)+y*cos(Rotation) + Cy;
% Draw it
plot(nx,ny,'o');
% Fit it
fitellipse(nx,ny)
% Note it returns (Rotation - pi/2) and swapped radii, this is fine.
return
end

% normalize data
mx = mean(X);
my = mean(Y);
sx = (max(X)-min(X))/2;
sy = (max(Y)-min(Y))/2;

x = (X-mx)/sx;
y = (Y-my)/sy;

% Force to column vectors
x = x(:);
y = y(:);

% Build design matrix
D = [ x.*x x.*y y.*y x y ones(size(x)) ];

% Build scatter matrix
S = D'*D;

% Build 6x6 constraint matrix
C(6,6) = 0; C(1,3) = -2; C(2,2) = 1; C(3,1) = -2;

% Solve eigensystem
[gevec, geval] = eig(S,C);

% Find the negative eigenvalue
I = find(real(diag(geval)) < 1e-8 & ~isinf(diag(geval)));

% Extract eigenvector corresponding to negative eigenvalue
A = real(gevec(:,I));

% unnormalize
par = [
A(1)*sy*sy, ...
A(2)*sx*sy, ...
A(3)*sx*sx, ...
-2*A(1)*sy*sy*mx - A(2)*sx*sy*my + A(4)*sx*sy*sy, ...
-A(2)*sx*sy*mx - 2*A(3)*sx*sx*my + A(5)*sx*sx*sy, ...
A(1)*sy*sy*mx*mx + A(2)*sx*sy*mx*my + A(3)*sx*sx*my*my ...
- A(4)*sx*sy*sy*mx - A(5)*sx*sx*sy*my ...
+ A(6)*sx*sx*sy*sy ...
]';

% Convert to geometric radii, and centers

thetarad = 0.5*atan2(par(2),par(1) - par(3));
cost = cos(thetarad);
sint = sin(thetarad);
sin_squared = sint.*sint;
cos_squared = cost.*cost;
cos_sin = sint .* cost;

Ao = par(6);
Au = par(4) .* cost + par(5) .* sint;
Av = - par(4) .* sint + par(5) .* cost;
Auu = par(1) .* cos_squared + par(3) .* sin_squared + par(2) .* cos_sin;
Avv = par(1) .* sin_squared + par(3) .* cos_squared - par(2) .* cos_sin;

% ROTATED = [Ao Au Av Auu Avv]

tuCentre = - Au./(2.*Auu);
tvCentre = - Av./(2.*Avv);
wCentre = Ao - Auu.*tuCentre.*tuCentre - Avv.*tvCentre.*tvCentre;

uCentre = tuCentre .* cost - tvCentre .* sint;
vCentre = tuCentre .* sint + tvCentre .* cost;

Ru = -wCentre./Auu;
Rv = -wCentre./Avv;

Ru = sqrt(abs(Ru)).*sign(Ru);
Rv = sqrt(abs(Rv)).*sign(Rv);

a = [uCentre, vCentre, Ru, Rv, thetarad];