MATLAB: Perimeter used by regionprops

Question

Hi all,

I am using the output of bwconncomp as an input to regionprops to calculate some values for blobs in a binary image. One of the values that I calculate is "solidity" which is a direct output of regionprops. However, I am also interested in calculating circularity, which I define as 4*pi*Area/Perimeter^2. However, I keep getting values that are greater than one, which is unexpected. From running bwconncomp and regionprops on some artificial binary images with some pixels arbitrarily set to 1 to represent particles I can tell that regionprops does not calculate perimeter in the way that I would normally think of it. Does anybody know if the perimeter calculation fails for very small clusters of "on" pixels, or is there some rationale behind what regionprops is doing, and I just don't understand it?

I'll post the code I use to troubleshoot this:

%make an empty matrix
a = zeros(5,5)
%put a small cross shaped particle onto it
a(2, 2:4) = 1    
a(1:3, 3) = 1
%call bwconncomp
cc = bwconncomp(a)
%call regionprops
blobFacts = regionprops(cc, 'Perimeter', 'Solidity', 'Area')
%report values
p = blobFacts.Perimeter
s = blobFacts.Solidity
a = blobFacts.Area
%manually calculate circularity
c = (4*pi*a)/p^2

This gives a circularity of 1.9865, which is higher than 1 (what I intuitively think of as the max possible circularity). The area of the particle is 5, which is expected, but the perimeter is 5.6240, and I can't seem to figure out how regionprops is getting that value. Thanks in advance,

Clay

Answer 1

The 'perimeter' calculation in "regionprops" is done based on a formula explained in the following paper:

A.M. Vossepoel, and A.W.M. Smeulders, "Vector code probability and metrication error in the representation of straight lines of finite length", Computer Graphics and Image Processing, Volume 20, Issue 4, December 1982, Pages 347–364.

You can also refer to the following blog post which gives a general overview of the algorithm used (please note that this is not an official documentation):

http://www.crisluengo.net/index.php/archives/310

You can see the perimeter is computed using a local function called "computePerimeterFromBoundary" in the "regionprops" function which corresponds to the formula discussed in the paper and blog post above:

perimeter = sum(isEven)*0.980 + sum(~isEven)*1.406 - sum(isCorner)*0.091;