Fit a least squares ellipse
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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)
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Alex Sha
2022년 4월 21일
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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Matt J
2022년 4월 21일
편집: Matt J
2022년 4월 21일
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,
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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