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Ellipse Detection Using 1D Hough Transform

version (25.2 KB) by Martin Simonovsky
An efficient ellipse detector based on Hough voting


Updated 26 Jul 2013

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Fits an ellipse by examining all possible major axes (all pairs of points) and getting the minor axis using Hough transform. The algorithm complexity depends on the number of valid non-zero points, therefore it is beneficial to provide as many restrictions in the "params" input arguments as possible if there is any prior
knowledge about the problem.

The code is reasonably fast due to (optional) randomization and full code vectorization. However, as the algorithm needs to compute pairwise point distances, it can be quite memory intensive. If you get out of memory errors, either downsample the input image or somehow decrease the number of non-zero points in it. It can deal with big amount of noise but can have severe problem with occlusions (major axis end points need to be visible)

Input arguments:
- One-channel input image (greyscale or binary).
- Parameters of the algorithm:
* minMajorAxis: Minimal length of major axis accepted.
* maxMajorAxis: Maximal length of major axis accepted.
rotation, rotationSpan: Specification of restriction on the angle of the major axis in degrees. If rotationSpan is in (0,90), only angles within [rotation-rotationSpan, rotation+rotationSpan] are accepted.
* minAspectRatio: Minimal aspect ratio of an ellipse (in (0,1))
* randomize: Subsampling of all possible point pairs. Instead of examining all N*N pairs, runs only on N*randomize pairs. If 0, randomization is turned off.
* numBest: Top numBest to return
* uniformWeights: Used to prefer some points over others. If false, accumulator points are weighted by their grey intensity in the image. If true, the input image is regarded as binary.
* smoothStddev: In order to provide more stability of the solution, the accumulator is convolved with a gaussian kernel. This parameter specifies its standard deviation in pixels.

Return value:
Returns a matrix of best fits. Each row (there are params.numBest of them) contains six elements: [x0 y0 a b alpha score] being the center of the ellipse, its major and minor axis, its angle in degrees and score.

Based on:
- "A New Efficient Ellipse Detection Method" (Yonghong Xie Qiang , Qiang Ji / 2002)
- random subsampling inspired by "Randomized Hough Transform for Ellipse Detection with Result Clustering" (CA Basca, M Talos, R Brad / 2005)

Update log:
1.1: More memory efficient code, better documentation, more parameters, more solutions possible, example code.
1.0: Initial version

Cite As

Martin Simonovsky (2021). Ellipse Detection Using 1D Hough Transform (, MATLAB Central File Exchange. Retrieved .

Comments and Ratings (37)

Dmitrii Mishutin

Raphael Kriegl

Jhajaira Sanchez

Nicolas Pinon

Ramon Gonzalez

Hi! Nice code. Could you please specifically explain how to detect several ellipses in the image. Thanks!

Andrea Manjarres

Pappu Murthy

if you want more than one ellipse, you could apply the same method. after finding one ellipse, substitute edges of the ellipse to zeros. now among the remaining ellipses it will find another one based on the params . It is going to be iterative.


Great code!!

Leah Buck

Are the min and max major axis in units of pixels? Is the angle in units of degrees?

Zoran Cenev

Is there any way to detect more ellipses, maybe 2 will be good start.

Hi. I'm trying to use ellipseDetection to find six ellipses in an image. Unfortunatelly, I am unable to do that. Is it possible to send the image to anybody, via email, so he/she could try to find the correct parameters? Thanks in advance

guangwei wu

Agustin Trujillo-Pino

Good detection in most of cases!

But I have a question: the minor axis seems to be always an integer value. Is it possible to obtain more accuracy in this parameter?

shanhu yijiao

??? Subscript indices must either be real positive integers or logicals

Error in ==> example at 18

Can you help me please to fix this...

shanhu yijiao

shanhu yijiao

i have download the code from for drawing an ellipse.
it runs out of memory due to index size!
Error using bsxfun
Out of memory. Type HELP MEMORY for your options.

Any fix???


great code

Javeria Farooq

hii,I am working on head detection using hough transform, I am trying to implement this algorithm for head detection but I am unable to achieve the required result....can u please help me regarding this...

it runs out of memory due to index size!

Error using bsxfun
Out of memory. Type HELP MEMORY for your options.

Any fix???

Nitay Megides

Good work! I'm getting an "Out of memory" error when I try to use uniformWeights as false


Antonio Scrima

Good Job!!!

Omar Al Okashi

Dear Sir, Thank you very much for your valuable work... when I run your example I got this error message:

??? Subscript indices must either be real positive integers or logicals

Error in ==> example at 18

Can you help me please to fix this...

Nicole Kovacs

Really liked it! Congratulations!

Hemo khalifa

it's not working


Can you please tell me what to change to detect more than one ellipse in one image(for example 3 ellipses)
It's very important!
Thank you in advance


I am talking about the hough matrix.
Is it possible to dispay it and if it is possible which is the code?


Hello again,
i handle with the 1 fit.
But is it possible to get the graphic of the Hough transform and if it is,what is the code?
Thanks in advance




first.congratulation for the excellent work!
I have a question,how to change the code to have 1 fit at the picture at the end,only one draw of the ellipse, not 3(the best fit)


Hi Martin Simonovsky,

can you teach me how to use the coding to ellipse detect the image below. I really need your help, i had try many method but cannot ellipse detect the i had out of time. really need your help,your help waill be appreciated.
Thank you.

Andri Pranata

heres my email if you please :)

Andri Pranata

hey martin, im andri from indonesia. your code maybe is a modified form of old ellipse detection method, maybe :p before you create this code, is there any old ellipse detector you have? could you send me that code to my email? thank you martin :)


High speed, but not very satisfactory result.

Martin Simonovsky

Hao zheng Yan: See e.g. for drawing an ellipse.

Hao zheng Yan

Hao zheng Yan

The code is very Concise!But the function of drawing ellipse is not submited.Can you submit a testing image?

MATLAB Release Compatibility
Created with R2010b
Compatible with any release
Platform Compatibility
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