▁of ▁the ▁image ▁size ▁orient ed ▁in ▁the ▁same ▁direction . ▁ ▁Red uc ing ▁the ▁range ▁of ▁a ▁and ▁b ▁in ▁this ▁fashion ▁reduces ▁the ▁accum ulator ▁array ▁to ▁ 5 7 ▁billion ▁values . ▁ ▁Trade ▁accuracy ▁for ▁space ▁in ▁the ▁estimation ▁of ▁the ▁center : ▁If ▁the ▁center ▁is ▁predicted ▁to ▁be ▁off ▁by ▁ 3 ▁on ▁both ▁the ▁x ▁and ▁y ▁axis ▁this ▁reduces ▁the ▁size ▁of ▁the ▁accum ulator ▁array ▁to ▁about ▁ 6 ▁billion ▁values . ▁ ▁Trade ▁accuracy ▁for ▁space ▁in ▁the ▁estimation ▁of ▁the ▁rad ii : ▁If ▁the ▁rad ii ▁are ▁estimated ▁to ▁each ▁be ▁off ▁by ▁ 5 ▁further ▁reduction ▁of ▁the ▁size ▁of ▁the ▁accum ulator ▁array ▁occurs , ▁by ▁about ▁ 2 5 6 ▁million ▁values . ▁ ▁C rop ▁the ▁image ▁to ▁areas ▁of ▁interest . ▁ ▁This ▁is ▁image ▁dependent , ▁and ▁therefore ▁un predict able , ▁but ▁imagine ▁a ▁case ▁where ▁all ▁of ▁the ▁edges ▁of ▁interest ▁in ▁an ▁image ▁are ▁in ▁the ▁upper ▁left ▁quadr ant ▁of ▁that ▁image . ▁ ▁The ▁accum ulator ▁array ▁can ▁be ▁reduced ▁even ▁further ▁in ▁this ▁case ▁by ▁const ra ining ▁all ▁ 4 ▁parameters ▁by ▁a ▁factor ▁of ▁ 2 , ▁for ▁a ▁total ▁reduction ▁factor ▁of ▁ 1 6 . ▁By ▁applying ▁just ▁the ▁first ▁three ▁of ▁these ▁constraints ▁to ▁the ▁example ▁stated ▁about , ▁the ▁size ▁of ▁the ▁accum ulator ▁array ▁is ▁reduced ▁by ▁almost ▁a ▁factor ▁of ▁ 1 0 0 0 , ▁bringing ▁it ▁down ▁to