Fit a least squares ellipse

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B
B 2022-4-21
编辑： Matt J 2022-4-21
I am trying to fit a least square ellipse to to the 'ellipse' data set that i have attached
I feel like i have everything correct (i might not have) but i am struggling plottting the ellipse function 'f'. i keep getting the following error
Warning: Error updating ImplicitFunctionLine.
Arrays have incompatible sizes for this operation.
Any help would be appreciated, Thanks in advance
load ellipse % loads x and y
%least squares fit to an ellipse
% A x^2 + B xy + C y^2 + Dx + Ey = 1
% Returns coefficients A..F
%A x^2 + B xy + C y^2 + Dx + Ey + F = 0
% where F = -1
M = [x.^2 x.*y y.^2 x y]; % design matrix
b1=ones(size(x));
MTM=M'*M;MTb=M'*b1; %normal equation
R=rref([MTM MTb]); % the coefficent are found in the last collunm
A=R(1:6);
B=R(2,6);
C=R(3,6);
D=R(4,6);
E=R(5,6);
f= @(x,y) A.*x.^2 + B.*x.*y+C.*y.^2+D.*x+E.*y-1; % ellipse function
figure, plot(x, y, '.')
hold on
fimplicit(f)
  1 个评论
Alex Sha
Alex Sha 2022-4-21
Function: A*x^2 + B*x*y + C*y^2 + D*x + E*y + 1 = 0
Parameter:
A: -0.550741506585047
B: -0.46781995608367
C: -0.804115378029277
D: -0.163329836528614
E: 2.72555198327659

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采纳的回答

KSSV
KSSV 2022-4-21
编辑：KSSV 2022-4-21
Replace this line:
A=R(1:6);
with
A=R(1,6);
There is a typo error in getting A. A is a vector in your case, you arenot getting the ellipse.

更多回答（1 个）

Matt J
Matt J 2022-4-21
编辑：Matt J 2022-4-21
I feel like i have everything correct (i might not have)
Your ordinary least squares method is not ideal because your design matrix has stochastic errors in it (iterative total least squares is the gold standard). The method used by this toolbox is a bit better,
https://www.mathworks.com/matlabcentral/fileexchange/87584-object-oriented-tools-for-fitting-conics-and-quadrics
and also has utility functions to let you plot directly,
load ellipse
fitobj=ellipticalFit([x,y]')
fitobj =
ellipticalFit with properties:
center: [-0.9975 1.9968]
a: 3.0246
b: 1.9954
angle: -30.0868
plot(fitobj)

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