ellipse fitting with matlab using fittype

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Johannes Tischer 2020-8-25

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评论： Matt J 2020-8-27

Hello,

I want to use fitoptions and fittype for a staistical nonlinear least squares fitting approach. The problem is, I cant find the correct equation for my model (ellipse). I tried multiple like:

to fittype ('sqrt(b^2*(1-(x^2/a^2)))' ). In this example, the square root has to be positive. I tried to tightening the upper and lower bounderies, but it doesnt work.

Can someone make an example of the following form:

fo = fitoptions('Method','NonLinearLeastSquares')

ft = fittype('ellipse equation')

[myfit, gof] = fit(x_data, y_data, ft, fo)

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Answer 1

Matt J 2020-8-26

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编辑：Matt J 2020-8-26

You could use fit() if you convert your data to polar cooridnates. In polar coordinates, an ellipse is given by an explicit function,

https://en.wikipedia.org/wiki/Ellipse#Polar_form_relative_to_center

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Johannes Tischer 2020-8-27

After this I converted it back to cartesian coordinates and plotted the data with my original data.

The pictures shows the original data (blue) and the ellipse fit (red).

Thank you Matt !

Matt J 2020-8-27

The problem with this method, of course, is that it assumes that the ellipse is centered at the origin. In general, that may not be true or known to be true.

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Answer 2

Alan Stevens 2020-8-25

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https://ww2.mathworks.cn/matlabcentral/answers/584243-ellipse-fitting-with-matlab-using-fittype#answer_484757

Have a look here: https://uk.mathworks.com/help/curvefit/fittype.html?s_tid=srchtitle

It shows you how to construct your own function correctly.

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Johannes Tischer 2020-8-26

Data.mat

This is the basic data. I want to use fittype because it has so many different options to fit and compare.

Alan Stevens 2020-8-26

在 MATLAB Online 中打开

Hmm. I'm struggling to see your basic data as elliptical. Nevertheless, the code below tries to fit them using an ellipse (I've deleted a few obvious non-elliptical outliers below; however, you could easily retain them if you wish):

load('EllipseData.mat')
% The next three lines remove outliers that are obviously not part of an
% ellipse!  Delete the three lines if you wish to retain the outliers.
ix = find(data_x<-600); data_x(ix) = [];data_y(ix) = [];
iylo = find(data_y<-220); data_x(iylo) = [];data_y(iylo) = [];
iyhi = find(data_y>220); data_x(iyhi) = [];data_y(iyhi) = [];
% Set the origin at the means of the x and y data
x = data_x - mean(data_x);
y = data_y - mean(data_y);
% "Linearise" and do a straightforward least-squares fit
N = length(x);
X = x.^2; Y = y.^2;
M = [N  -sum(X); sum(X) -sum(X.^2)];
V = [sum(Y); sum(X.*Y)];
AB = M\V;  % AB = [A; B]
% Extract constants
A = AB(1);
B = AB(2);
% Create ellipse semimajor axes from "linear" constants
a = sqrt(A/B);
b = sqrt(A);
% Separate upper and lower halves of "elliptical" values.
xhi = x(x>=0); xlo = x(x<0);
yhi = b*sqrt(1 - (xhi/a).^2);
ylo = -b*sqrt(1 - (xlo/a).^2);
% Put them back together and shift the origin back
xf = [xhi xlo] + mean(data_x);
yf = [yhi ylo] + mean(data_y);
% Plot and compare Data and fit.
plot(data_x,data_y,'o',x,yf,'*'), grid
xlabel('x'),ylabel('y')
legend('Data','"Elliptical" fit')