# How to fit an ellipse to an image in matlab.

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Hardit Singh on 9 Dec 2019
Commented: Image Analyst on 29 Jun 2020
I have a image like this and I want to fit an ellipse around this disk image and get the info about the ellipse like its axis, center point, etc. I am unsure how to use the image proccessing toolbox to draw an ellipse to it and get info about the ellipse.

Akira Agata on 11 Dec 2019
% Binarize
Igray = rgb2gray(I);
BW = imbinarize(Igray);
% Extract the maximum area
BW = imclearborder(BW);
BW = bwareafilt(BW,1);
% Calculate centroid, orientation and major/minor axis length of the ellipse
s = regionprops(BW,{'Centroid','Orientation','MajorAxisLength','MinorAxisLength'});
% Calculate the ellipse line
theta = linspace(0,2*pi);
col = (s.MajorAxisLength/2)*cos(theta);
row = (s.MinorAxisLength/2)*sin(theta);
D = M*[col;row;zeros(1,numel(row));ones(1,numel(row))];
% Visualize the result
figure
imshow(Igray)
hold on
plot(D(1,:),D(2,:),'r','LineWidth',2)

Hardit Singh on 12 Dec 2019
Thank you so much for your help!
UgiLishes on 29 Jun 2020
Hi Akira,
Thank you very much for your code, I have found it to be very helpful!
I used your cade to fit an ellipse to my CT scan and I works really well but there is one more thing I'd like to do: find goodness of fit to my image. as you can see in the attached file the bottom of the image doesn't fit so well. what can I do to quantify how well the ellipse fits my image?
thank you very much
Image Analyst on 29 Jun 2020
You can get the boundary of your binary image with bwboundaries. Then use sqrt() to find the distance of every actual boundary point to the closest fit point. Find the closest one with min. Then take the mean or sum of those closest distances.
boundaries = boundaries{1}; % Extract from cell
xb = boundaries(:, 2);
yb = boundaries(:, 1);
closestDistances = zeros(1, length(xb));
for k = 1 : length(xb)
% Get distance of each actual boundary point to all points in your ellipse fit vectors.
distances = sqrt((xFit - xb(k)) .^ 2 + (yFit - yb(k)) .^ 2); % A vector of distances
closestDistances(k) = min(distances); % A single distance.
end
closenessOfFitMetric = mean(closestDistances)

Image Analyst on 11 Dec 2019

R2016b

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