How to fit an ellipse to an image in matlab.

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.

Answer 1

[Akira Agata]

How about the following?

% Read image
I = imread('diskimage1.jpeg');

% 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);
M = makehgtform('translate',[s.Centroid, 0],'zrotate',deg2rad(-1*s.Orientation));
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]

This is amazing! What if the image is poor in quality like the one below. There is still clearly a disk but how would you get rid of all the background stuff around it?

[Image Analyst]

I suggest you look for successful algorithms that have been developed and published. Click here.

• 20.5 Retinal Images, Analysis of Eye, etc.
• 20.5.1 Eye, Cornea, Corneal Images
• 20.5.2 Optic Disc Location, Optic Disc Detection
• 20.5.3 Retinal Images, Angiography, Blood Vessels in the Eye
• 20.5.4 Glaucoma Retinopathy, Retinal Analysis Application
• 20.5.5 Diabetic Retinopathy, Retinal Analysis Application
• 20.5.6 Macular Degeneration Detection, Retinal Analysis Application
• 20.5.7 Retinal Images, Optical Coherence Tomography, OCT

[Akira Agata]

Thank you Image Analyst-san for introducing many sophisticated algorithms!

These well-designed algorithms must be robust for many images. But, as far as this image, I think small modification for my previous code would be OK.

Please change the first half of my previous code as follows:

% Read image
I = imread('disk3.jpeg');

% Binarize
Igray = rgb2gray(I);
BW = Igray > 10; % <- Changed this line for this new image

% Extract the maximum area
BW = imclearborder(BW);
BW = bwareafilt(BW,1);
BW = imfill(BW,'holes'); % <- Added this line to fill holes

The remaining part is the same as previous one. If you run the code, the result will be like this:

[Hardit Singh]

Thank you so much for your help!

[UgiLishes]

Hi Akira,

Thank you very much for your code, I have found it to be very helpful!

can I ask you a follow up question?

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]

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 = bwboundaries(mask);
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)

[Sokratis Panagiotidis]

Hello Mr. @Akira Agata,

I looked into your code and would like to use it for my analysis of the area of certain objects in pictures - quite similar to Hardit Singh's case.

I have trouble understanding your code to its full core so I'd like to ask you wether your code takes into cosideration wether the ellipse is tilted or not? With my knowledge it would mean that if the ellipse is tilted by an angle φ, the points to use as Major- and MinorAxisLength are also tilted by φ.

If you'd like I asked this question about your code here, maybe it could help you understand my question a bit more: https://de.mathworks.com/matlabcentral/answers/1662750-getting-area-of-tilted-ellipse-with-regionprops?s_tid=prof_contriblnk, 08.03.2022, 3:16 pm.

Thank you for your time.

[Image Analyst]

You can get the angle of the tile in degrees by calling regionprops.

props = regionprops(BW, 'Orientation', 'MajorAxisLength', 'MinorAxisLength');
allAngles = [props.Orientation]

Of course the axis lengths do NOT depend on the angle. They are what they are, regardless of angle.

[Connor]

Hi, I'm trying to use your method to solve my own ellipse fitting problem, i have detected the edge of my shape in the image included and want to fit an ellipse to this to generate a function that i can use to perform the diff() function and get the tangent of the ellipse at the bottoms of the edge detected in the image.

I am having some trouble improving the fit of the ellipse here, this is my best attempt so far, any advice would be greatly appreciated:

[Image Analyst]

@Connor that is not a blob. Well it is but it's a very snake-like, line-like blob. So the fit is accurate. But I suspect what you want is to fit the (x,y) coordinates of the blob to an ellipse. So you need to get x and y from the binary image like this:

[y, x] = find(binaryImage);

and then use the ellipse fit in the FAQ: https://matlab.fandom.com/wiki/FAQ#How_can_I_fit_an_ellipse_or_other_shape_to_a_set_of_XY_data?

[Connor]

Thanks!

Answer 2

[Image Analyst]

See Steve's blog: Visualizing regionprops ellipse measurements

Answer 3

[Matt J]

You can use ellipticalFit from this FEX download

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

processImage('Connors_image.png')

ans = 
  ellipticalFit with properties:

    center: [196.4747 218.0069]
         a: 130.0274
         b: 119.1008
     angle: 3.0398

processImage('Hardits_image.png')

ans = 
  ellipticalFit with properties:

    center: [171.3735 173.6428]
         a: 112.7502
         b: 104.1636
     angle: 47.0771

function e=processImage(filename)
    I = imread(filename);
    % Binarize
    I = bwareafilt(imclearborder(imbinarize(rgb2gray(I))),1);
    b = bwboundaries(I);
    
    e=ellipticalFit(flipud(b{1}'));
    
    imshow(I,[]); hold on
    showfit(e,'LineWidth',1,'Color','r','LineStyle','--'); hold off
end

[Connor]

Thanks!