regionprops circularity value >1 and 0 ?

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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 ?
  3 Comments
Lightisthenight
Lightisthenight on 22 Apr 2019
Yes, sir. I did examine this discussion and others.
Steve Eddins
Steve Eddins on 22 Mar 2023
See this updated answer regarding circularity values greater than 1.

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Accepted Answer

Image Analyst
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.
0000 Screenshot.png
  6 Comments
Walter Roberson
Walter Roberson on 24 Apr 2019
allBB = vertcat(propied.BoundingBox);
[~, sortorder] = sort(allBB(:,3));
sorted_propied = propied(sortorder);
Now sorted_propied would be all of the properties that you asked for, sorted according to increasing width of the region.
Steve Eddins
Steve Eddins on 22 Mar 2023
See also this updated answer regarding circularity values greater than 1.

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More Answers (1)

Steve Eddins
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
A = imread("text.png");
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
A = imread("text.png");
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
A = imread("text.png");
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 Comments
Adrián G.
Adrián G. on 24 Mar 2023
Edited: Adrián G. on 24 Mar 2023
release: 2021b
When running this part:
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);
Returns error:
Scalar structure required for this assignment.
props.Circularity = min(c .* correction, 1);
Steve Eddins
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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