Automatic Circle Detection on Images Based on an Evolutionary Algorithm That Reduces the Number of Function Evaluations

Table 4

𝑃 values produced by Wilcoxon’s test comparing APRE to GA and BFOA over the averaged ME from Table 2.

Image	𝑃 value
	APRE versus GA	APRE versus BFOA
Synthetic images
(a)	1.7345𝑒−004	1.5294𝑒−004
(b)	𝟏.𝟔𝟕𝟐𝟏𝐞−𝟎𝟎𝟒	𝟏.𝟒𝟖𝟑𝟐𝐞−𝟎𝟎𝟒
(c)	1.0463𝑒−004	1.9734𝑒−004
Natural images
(a)	1.5563𝑒−004	1.6451𝑒−004
(b)	𝟏.𝟐𝟕𝟒𝟖𝐞−𝟎𝟎𝟒	𝟏.𝟓𝟔𝟐𝟏𝐞−𝟎𝟎𝟒
(c)	1.0463𝑒−004	1.7213𝑒−004