▁is ▁ ▁used , ▁which ▁allows ▁a ▁feature ▁to ▁vote ▁for ▁a ▁particular ▁position , ▁orientation ▁and / or ▁scaling ▁of ▁the ▁shape ▁using ▁a ▁pre defined ▁look - up ▁table . ▁ ▁Circle ▁detection ▁process ▁▁ ▁Alter ing ▁the ▁algorithm ▁to ▁detect ▁circular ▁shapes ▁instead ▁of ▁lines ▁is ▁relatively ▁straightforward . ▁▁ ▁First , ▁we ▁create ▁the ▁accum ulator ▁space , ▁which ▁is ▁made ▁up ▁of ▁a ▁cell ▁for ▁each ▁pixel . ▁Initial ly ▁each ▁cell ▁is ▁set ▁to ▁ 0 . ▁ ▁For ▁each ▁edge ▁point ▁( i , ▁j ) ▁in ▁the ▁image , ▁increment ▁all ▁cells ▁which ▁according ▁to ▁the ▁equation ▁of ▁a ▁circle ▁ ▁could ▁be ▁the ▁center ▁of ▁a ▁circle . ▁These ▁cells ▁are ▁represented ▁by ▁the ▁letter ▁ ▁in ▁the ▁equation . ▁ ▁For ▁each ▁possible ▁value ▁of ▁ ▁found ▁in ▁the ▁previous ▁step , ▁find ▁all ▁possible ▁values ▁of ▁ ▁which ▁satisfy ▁the ▁equation . ▁ ▁Search ▁for ▁local ▁maxim a ▁in ▁the ▁accum ulator ▁space . ▁These ▁cells ▁represent ▁circles ▁that ▁were ▁detected ▁by ▁the ▁algorithm . ▁ ▁If ▁we ▁do ▁not ▁know ▁the ▁radius ▁of ▁the ▁circle ▁we ▁are ▁trying ▁to ▁locate ▁before hand , ▁we ▁can ▁use ▁a ▁three - dimensional ▁accum ulator ▁space ▁to ▁search ▁for ▁circles ▁with ▁an ▁arbitrary ▁radius . ▁Natur ally , ▁this ▁is ▁more ▁computation ally ▁expensive . ▁ ▁This ▁method ▁can ▁also ▁detect ▁circles ▁that ▁are ▁partially ▁outside ▁of ▁the ▁accum ulator ▁space , ▁as ▁long ▁as ▁enough ▁of ▁the ▁circle ' s ▁area ▁is ▁still