How to plot the best fitted ellipse or circle?

Question

Ashfaq Ahmed 2023-10-24

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2038016-how-to-plot-the-best-fitted-ellipse-or-circle

编辑： Matt J 2023-10-25

采纳的回答： Matt J

EllipseData.mat

在 MATLAB Online 中打开

Hi all,

I have a data set (attached here) that has two arrays. I want to plot them in a polar graph and want to find out the best fitted a) ellipse, and b) circle.

x(:,1) is the x and x(:,2) is the y for the plot.

If anyone can help me out here, I will be very grateful.

xy = load("EllipseData.mat");

x = xy.x(:,1);

y = xy.x(:,2);

plot(x,y,'o')

axis equal

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Ashfaq Ahmed 2023-10-25

编辑：Ashfaq Ahmed 2023-10-25

Hi @Image Analyst, the secoond option. It would be if they are plotted in the polarplot first and then creating the ellipsoid.

Image Analyst 2023-10-25

在 MATLAB Online 中打开

I see you accepted @Matt J's answer. You can adjust/control the approximate number of points within the ellipse by changing the 0.95 in this line of code:

b=boundary(XY,0.95);

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Answer 1

Matt J 2023-10-25

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2038016-how-to-plot-the-best-fitted-ellipse-or-circle#answer_1339901

编辑：Matt J 2023-10-25

在 MATLAB Online 中打开

EllipseData.mat

The code below uses ellipsoidalFit() from this FEX download,

https://www.mathworks.com/matlabcentral/fileexchange/87584-object-oriented-tools-for-fitting-conics-and-quadrics

Is this the kind of thing you are looking for?

xy=load('EllipseData.mat').x;

p=prunecloud(xy);

Warning: Polyshape has duplicate vertices, intersections, or other inconsistencies that may produce inaccurate or unexpected results. Input data has been modified to create a well-defined polyshape.

I=all(~isnan(p.Vertices),2);

e=ellipticalFit(p.Vertices(I,:)');

%Display -- EDITED

XY=e.sample(linspace(0,360,1000));

[t,r]=cart2pol(xy(:,1),xy(:,2));

[T,R]=cart2pol(XY{:});

polarplot(t,r,'ob',T,R,'r-')

function [p,XY]=prunecloud(xy)
 
    for i=1:3
      D2=max(pdist2(xy,xy,'euclidean','Smallest', 10),[],1);
    
      xy(D2>0.1,:)=[];
    end
 XY=xy;
 b=boundary(XY,0.95);
 p=polyshape(XY(b,:));
end

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Ashfaq Ahmed 2023-10-25

Hi @Matt J, thank you for the suggestion. I can see it is working now. I have a request. Can you please help me plot it on a polar plane?

Matt J 2023-10-25

编辑：Matt J 2023-10-25

See my edited answer.

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Answer 2

Image Analyst 2023-10-24

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https://ww2.mathworks.cn/matlabcentral/answers/2038016-how-to-plot-the-best-fitted-ellipse-or-circle#answer_1339686

See the FAQ:

https://matlab.fandom.com/wiki/FAQ#How_can_I_fit_a_circle_to_a_set_of_XY_data?

https://matlab.fandom.com/wiki/FAQ#How_can_I_fit_an_ellipse_or_other_shape_to_a_set_of_XY_data?

then you'll have the (x,y) data and you can simply use plot.

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Answer 3

Torsten 2023-10-24

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编辑：Torsten 2023-10-24

Compute the center of gravity of the point cloud. Call it (x',y').
Compute the point of your point cloud with the greatest distance to (x',y'). Call the distance R.
Define the circle that encloses the point cloud by (x-x')^2 + (y-y')^2 = R^2.

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Sam Chak 2023-10-25

在 MATLAB Online 中打开

EllipseData.mat

Hi @Ashfaq Ahmed

Circular fitting is way easier based on @Torsten's approach. Elliptical fitting is much harder, as you need to determine the semi-major and semi-minor axes. However, you can gradually decrease the length of the semi-minor axis until the farthest point in the y-direction is contained within the ellipse, or use @Matt J's approach.

% Load data

xy = load("EllipseData.mat");

x = xy.x(:,1);

y = xy.x(:,2);

% Find center of a single cluster based on Euclidean

xbar = sum(x)/length(x); % mean(x)

ybar = sum(y)/length(y); % mean(y)

center = [xbar ybar]

center = 1×2

0.0070 0.0271

% Find max distance of data from the center

radius = max(sqrt((x - xbar).^2 + (y - ybar).^2))

radius = 6.8125

% Plot data, the center, and a circle

plot(x, y, '.', 'markersize', 3), hold on

plot(xbar, ybar, 'xk', 'markersize', 12, 'linewidth', 3)

viscircles(center, radius, 'LineStyle', '--') % requires Image Processing Toolbox™

ans =

Group with properties: Children: [2×1 Line] Visible: on HitTest: on Use GET to show all properties

grid on, xlabel('x'), ylabel('y')

axis([-8 8 -8 8])

axis equal

Les Beckham 2023-10-25

@Sam Chak

Thanks

Image Analyst 2023-10-25

I moved @Les Beckham's comment to be an answer.

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Answer 4

Les Beckham 2023-10-25

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https://ww2.mathworks.cn/matlabcentral/answers/2038016-how-to-plot-the-best-fitted-ellipse-or-circle#answer_1340716

移动：Image Analyst 2023-10-25

在 MATLAB Online 中打开

EllipseData.mat

xy = load("EllipseData.mat");

x = xy.x(:,1);

y = xy.x(:,2);

rho = sqrt(x.^2 + y.^2);

theta = atan2(y,x); % <<< use 4 quadrant atan2

polarplot(theta, rho, '.', 'markersize', 3, 'Color', '#aa4488')

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