# regionprops circularity value >1 and 0 ?

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Lightisthenight on 22 Apr 2019
Commented: Steve Eddins on 24 Mar 2023
Hello,
I calculated for a binary image the circularity using the regionprops function with this formula:
allCircularities1 = allPerimeters1.^2 ./ (4* pi*allAreas1);
I got the following circularity values : 2.933 ; 1.5260 ; 3.4890 ; 0.5380 ; 1.1568 0 ; 0 ; 0.5591.
I know that a circle has a circularity of nearly 1. As i understand the circularity is the roundness of an object / blob ? So my question is what the values greater 1 implicate? There isn't an object available that is 'rounder' than a circle.
My second question is the circularity value = 0. I checked the perimeter for that small blob. It also has the value 0. Why is that so ? Is the blob too small for the regionprops perimeter function ?
Steve Eddins on 22 Mar 2023
See this updated answer regarding circularity values greater than 1.

Image Analyst on 22 Apr 2019
It seems like you're getting circularities less than 1 for perfectly rectangular blocks. The formula is not that accurate for small blobs due to digitization errors and you might need to filter on something in addition to circularity, such as area. Try the attached program to see. Be sure to change the filename if you need to.
Steve Eddins on 22 Mar 2023

Steve Eddins on 22 Mar 2023
R2023a Update: Correcting regionprops Circularity Measurements That Are Greater Than 1.0
Image Processing Toolbox R2023a or Later
In releases R2023a or later, the Circularity computation in regionprops has been revised to correct a bias towards higher values, and it no longer returns values greater than 1.0.
See this 21-Mar-2023 blog post for a detailed explanation.
if verLessThan("images","11.7")
error("Use this code with releases R2023a or later.")
end
props = regionprops("table",A,"Circularity");
Image Processing Toolbox R2019a to R2022b
In earlier releases, you can apply the same correction that was introduced in R2023a by adapting the following example. Note that the call to regionprops below uses the form that returns a table because it makes the correction steps easier.
if verLessThan("images","10.4") || ~verLessThan("images","11.7")
error("Use this code with releases R2019a through R2022b.")
end
props = regionprops("table",A,["Circularity" "Perimeter"]);
c = props.Circularity;
p = props.Perimeter;
r_eq = p/(2*pi) + 0.5;
correction = (1 - (0.5./r_eq)).^2;
props.Circularity = min(c .* correction, 1);
Image Processing Toolbox R2018b or Earlier
In these older releases, the function regionprops did not compute Circularity. You can compute it by adapting the following example.
if ~verLessThan("images","10.4")
error("Use this code with releases R2018b or earlier.")
end
props = regionprops("table",A,["Area" "Perimeter"]);
a = props.Area;
p = props.Perimeter;
c = 4*pi*a ./ (p.^2);
r_eq = p/(2*pi) + 0.5;
correction = (1 - (0.5./r_eq)).^2;
props.Circularity = min(c .* correction, 1);
##### 2 CommentsShow 1 older commentHide 1 older comment
Steve Eddins on 24 Mar 2023
Adrián, did you call regionprops with "table" as the first argument? Like this:
props = regionprops("table",A,["Circularity" "Perimeter"]);

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