▁a ▁size ▁that ▁is ▁much ▁more ▁likely ▁to ▁fit ▁within ▁a ▁modern ▁computer ' s ▁memory . ▁ ▁E fficient ▁el lipse ▁detection ▁algorithm ▁▁ ▁Y ong h ong ▁X ie ▁and ▁Q i ang ▁Ji ▁give ▁an ▁efficient ▁way ▁of ▁implementing ▁the ▁H ough ▁transform ▁for ▁el lipse ▁detection ▁by ▁over coming ▁the ▁memory ▁issues . ▁As ▁discussed ▁in ▁the ▁algorithm ▁( on ▁page ▁ 2 ▁of ▁the ▁paper ), ▁this ▁approach ▁uses ▁only ▁a ▁one - dimensional ▁accum ulator ▁( for ▁the ▁minor ▁axis ) ▁in ▁order ▁to ▁detect ▁elli ps es ▁in ▁the ▁image . ▁The ▁complexity ▁is ▁O ( N 3 ) ▁in ▁the ▁number ▁of ▁non - zero ▁points ▁in ▁the ▁image . ▁ ▁Lim itations ▁The ▁H ough ▁transform ▁is ▁only ▁efficient ▁if ▁a ▁high ▁number ▁of ▁votes ▁fall ▁in ▁the ▁right ▁bin , ▁so ▁that ▁the ▁bin ▁can ▁be ▁easily ▁detected ▁amid ▁the ▁background ▁noise . ▁This ▁means ▁that ▁the ▁bin ▁must ▁not ▁be ▁too ▁small , ▁or ▁else ▁some ▁votes ▁will ▁fall ▁in ▁the ▁neighbor ing ▁b ins , ▁thus ▁reducing ▁the ▁visibility ▁of ▁the ▁main ▁bin . ▁ ▁Also , ▁when ▁the ▁number ▁of ▁parameters ▁is ▁large ▁( that ▁is , ▁when ▁we ▁are ▁using ▁the ▁H ough ▁transform ▁with ▁typically ▁more ▁than ▁three ▁parameters ), ▁the ▁average ▁number ▁of ▁votes ▁cast ▁in ▁a ▁single ▁bin ▁is ▁very ▁low , ▁and ▁those ▁b ins ▁corresponding ▁to ▁a ▁real ▁figure ▁in ▁the ▁image ▁do ▁not ▁necessarily ▁appear ▁to ▁have ▁a ▁much ▁higher ▁number ▁of ▁votes