# Which one is best for calculating circularity ?

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Hi all, I need to calculate objects roundness.I am not sure about which of the below ones is the best choice for this purpose.

- R= 4*pi*A/P^2; where A is area in pixels, P is Perimeter.

-Eccentricity

Thank you for your opinions.particles I need to measure are like this :

##### 4 Comments

Image Analyst
on 15 Jun 2021

### Accepted Answer

Image Analyst
on 22 Aug 2013

Edited: Image Analyst
on 15 Jun 2021

I use circularity quite a bit. The formula I use is the inverse of the one you use:

props = regionprops(mask, 'Area', 'Perimeter');

allAreas = [props.Area];

allPerimeters = [props.Perimeter];

circularity = (allPerimeters .^ 2) ./ (4 * pi * allAreas);

so for me the circularity of a circle is 1 and the higher it goes, the less circular it it. For you the lower it goes (closer to zero) the less circular the blob is. You can do it either way.

I don't often use eccentricity because you can get the same eccentricity for a perfectly smooth ellipse as for some tortuous-shaped blob because it fits the perimeter shape to an ellipse. For example an asterisk and a disc might both have the same eccentricity but there is a dramatic difference in shape that is not picked up by eccentricity. Don't use eccentricity unless you know that your blobs are fairly close to ellipses.

##### 5 Comments

Image Analyst
on 15 Jun 2021

From what I see here: https://www.researchgate.net/publication/224112271_A_Measure_for_Circularity_of_Digital_Figures

it looks like it's the inverse of the coefficient of variation or the mean radius divided by the standard deviation of the radii = [(mean R) / (stddev R)]. So for a circle, the value is infinity since the standard deviation would be zero. He claims it's more accurate for small, digitized polygons, and that may be true.

I prefer the other definition - what he calls the Rosenfield formula P^2/(4*pi*Area). I like that it's simpler to compute plus it's nicely intuitive in that the value for a circle is 1, not some big undefined number. How big does the number need to be to be circular for Haralick? 10? 100? 1000? I don't know. I guess you could create randomly shaped blobs and compute it both ways and see what values each way produces.

But it comes down to whatever one you want to use. I don't think it's like one is better than another, though Haralick claims his is better for small circles where it's so quantized that it's more octagonal than circular. I mean a circle with a radius of 1 pixel would essentially be a cross + shape, not a circle. So if you have very small blobs then you might use Haralick's formula, though I might counter that comparing blobs based on circularity when the blobs are so tiny they can't really be circular in the first place is not a proper comparison.

### More Answers (2)

Amith Kamath
on 22 Aug 2013

I would do one of the following:

1. Use the 'solidity' option in REGIONPROPS to estimate how 'curvy' the blob is, and solidity is defined as the area/convexArea.

2. Use the 'MajorAxisLength' and 'MinorAxisLength' properties in REGIONPROPS and compare the two. If they are close to equal, the object would be more circular (in most cases).

3. Use 'Area' and 'Perimeter' from REGIONPROPS to estimate circularity in my custom code. http://www.mathworks.com/matlabcentral/newsreader/view_thread/292521 may be useful to see.

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