find the circularity of diamond, inverted triangle and octagon shape

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Tulips 2012-10-15

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hi,currently I working with road sign sign detection, based on the observations from regionprops of matlab value, to detect circular shape, the circularities should be < 1.2, for square shape, circularities <1.6 and triangle shape should be <1.8

Can I know what is the circularities values for diamond , inverted triangle and octagon shapes respectively?

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Answer 1

Image Analyst 2012-10-15

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Circularity is obtained by solving for the radius in terms of both the perimeter and area for a circle:

P = 2*pi*r
r = P/(2*pi)
A = pi*r^2
r = sqrt(A/pi) = P/(2*pi)
A/pi = P^2 / (4*pi^2)
1 = p^2 / (4*pi*A) = circularity
circularity = Perimeter^2 / (4 * pi * Area)