# Detection of ellipses;

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Sibel Cakir on 7 Nov 2016
Answered: Image Analyst on 29 Sep 2021
I need to detect ellipses for example in the attached picture. Is there any tool, which can automatically
-detect ellipses or - bring parts of curves together and merge them into ellipses? (e.g.: forms which look like ellipses should be detetected and merged into an ellipse; fitting to an ellipse)
Thank you very much in advance! Hannes Daepp on 11 Nov 2016
I understand that you would like to detect ellipses in the figure using a MATLAB function. While MATLAB offers "imfindcircles" and "hough", it does not have any built-in tools to detect ellipses.
You could try using the "regionprops" function to measure properties of image regions, as done in the following blog post: http://blogs.mathworks.com/steve/2015/08/17/ellipse-visualization-and-regionprops/?s_tid=srchtitle
You may also find some relevant files by searching the File Exchange. For example, the following file uses a Hough transform to detect ellipses: http://www.mathworks.com/matlabcentral/fileexchange/33970-ellipse-detection-using-1d-hough-transform?s_tid=srchtitle
Finally, you can find a complete list of functions in the Image Processing Toolbox at the following link in the documentation: http://www.mathworks.com/help/images/functionlist.html
Sibel Cakir on 14 Nov 2016
Thank you very much for so many advices. I will read all of them.

Razeem Ahmad on 29 Sep 2021
This code should help.
function bestFits = ellipseDetection(img, params)
% ellipseDetection: Ellipse detection
% default values
if nargin==1; params=[]; end
% - parameters to contrain the search
if ~isfield(params,'minMajorAxis'); params.minMajorAxis = 10; end
if ~isfield(params,'maxMajorAxis'); params.maxMajorAxis = 200; end
if ~isfield(params,'rotation'); params.rotation = 0; end
if ~isfield(params,'rotationSpan'); params.rotationSpan = 0; end
if ~isfield(params,'minAspectRatio'); params.minAspectRatio = 0.1; end
if ~isfield(params,'randomize'); params.randomize = 2; end
% - others
if ~isfield(params,'numBest'); params.numBest = 3; end
if ~isfield(params,'uniformWeights'); params.uniformWeights = true; end
if ~isfield(params,'smoothStddev'); params.smoothStddev = 1; end
eps = 0.0001;
bestFits = zeros(params.numBest,6);
params.rotationSpan = min(params.rotationSpan, 90);
H = fspecial('gaussian', [params.smoothStddev*6 1], params.smoothStddev);
[Y,X]=find(img);
Y = single(Y); X = single(X);
N = length(Y);
fprintf('Possible major axes: %d * %d = %d\n', N, N, N*N);
% compute pairwise distances between points (memory intensive!) and filter
% TODO: do this block-wise, just appending the filtered results (I,J)
distsSq = bsxfun(@minus,X,X').^2 + bsxfun(@minus,Y,Y').^2;
[I,J] = find(distsSq>=params.minMajorAxis^2 & distsSq<=params.maxMajorAxis^2);
idx = I<J;
I = uint32(I(idx)); J = uint32(J(idx));
fprintf('..after distance constraint: %d\n', length(I));
% compute pairwise angles and filter
if params.rotationSpan>0
tangents = (Y(I)-Y(J)) ./ (X(I)-X(J));
tanLo = tand(params.rotation-params.rotationSpan);
tanHi = tand(params.rotation+params.rotationSpan);
if tanLo<tanHi
idx = tangents > tanLo & tangents < tanHi;
else
idx = tangents > tanLo | tangents < tanHi;
end
I = I(idx); J = J(idx);
fprintf('..after angular constraint: %d\n', length(I));
else
fprintf('..angular constraint not used\n');
end
npairs = length(I);
% compute random choice and filter
if params.randomize>0
perm = randperm(npairs);
pairSubset = perm(1:min(npairs,N*params.randomize));
clear perm;
fprintf('..after randomization: %d\n', length(pairSubset));
else
pairSubset = 1:npairs;
end
% check out all hypotheses
for p=pairSubset
x1=X(I(p)); y1=Y(I(p));
x2=X(J(p)); y2=Y(J(p));
%compute center & major axis
x0=(x1+x2)/2; y0=(y1+y2)/2;
aSq = distsSq(I(p),J(p))/4;
thirdPtDistsSq = (X-x0).^2 + (Y-y0).^2;
K = thirdPtDistsSq <= aSq;
%get minor ax propositions for all other points
fSq = (X(K)-x2).^2 + (Y(K)-y2).^2;
cosTau = (aSq + thirdPtDistsSq(K) - fSq) ./ (2*sqrt(aSq*thirdPtDistsSq(K)));
cosTau = min(1,max(-1,cosTau));
sinTauSq = 1 - cosTau.^2;
b = sqrt( (aSq * thirdPtDistsSq(K) .* sinTauSq) ./ (aSq - thirdPtDistsSq(K) .* cosTau.^2 + eps) );
%proper bins for b
idxs = ceil(b+eps);
if params.uniformWeights
weights = 1;
else
weights = img(sub2ind(size(img),Y(K),X(K)));
end
accumulator = accumarray(idxs, weights, [params.maxMajorAxis 1]);
accumulator = conv(accumulator,H,'same');
accumulator(1:ceil(sqrt(aSq)*params.minAspectRatio)) = 0;
[score, idx] = max(accumulator);
%keeping only the params.numBest best hypothesis (no non-maxima suppresion)
if (bestFits(end,end) < score)
bestFits(end,:) = [x0 y0 sqrt(aSq) idx atand((y1-y2)/(x1-x2)) score];
if params.numBest>1
[~,si]=sort(bestFits(:,end),'descend');
bestFits = bestFits(si,:);
end
end
end
end

Image Analyst on 29 Sep 2021
There is a paper I'm attaching on detecting ellipses.
I have not coded it up but if you do, please attach your code here.