▁present ▁within ▁it . ▁ ▁D ete ction ▁of ▁ 3 D ▁objects ▁( Pl anes ▁and ▁cyl ind ers ) ▁ ▁H ough ▁transform ▁can ▁also ▁be ▁used ▁for ▁the ▁detection ▁of ▁ 3 D ▁objects ▁in ▁range ▁data ▁or ▁ 3 D ▁point ▁clouds . ▁The ▁extension ▁of ▁classical ▁H ough ▁transform ▁for ▁plane ▁detection ▁is ▁quite ▁straightforward . ▁A ▁plane ▁is ▁represented ▁by ▁its ▁explicit ▁equation ▁ ▁for ▁which ▁we ▁can ▁use ▁a ▁ 3 D ▁H ough ▁space ▁corresponding ▁to ▁, ▁ ▁and ▁. ▁This ▁extension ▁suff ers ▁from ▁the ▁same ▁problems ▁as ▁its ▁ 2 D ▁counter part ▁i . e ., ▁near ▁horizontal ▁plan es ▁can ▁be ▁reli ably ▁detected , ▁while ▁the ▁performance ▁d eter ior ates ▁as ▁plan ar ▁direction ▁becomes ▁vertical ▁( big ▁values ▁of ▁ ▁and ▁ ▁ampl ify ▁the ▁noise ▁in ▁the ▁data ). ▁This ▁form ulation ▁of ▁the ▁plane ▁has ▁been ▁used ▁for ▁the ▁detection ▁of ▁plan es ▁in ▁the ▁point ▁clouds ▁acquired ▁from ▁air bor ne ▁las er ▁sc anning ▁ ▁and ▁works ▁very ▁well ▁because ▁in ▁that ▁domain ▁all ▁plan es ▁are ▁nearly ▁horizontal . ▁ ▁For ▁generalized ▁plane ▁detection ▁using ▁H ough ▁transform , ▁the ▁plane ▁can ▁be ▁paramet riz ed ▁by ▁its ▁normal ▁vector ▁ ▁( using ▁spher ical ▁coordinates ) ▁and ▁its ▁distance ▁from ▁the ▁origin ▁ ▁resulting ▁in ▁a ▁three ▁dimensional ▁H ough ▁space . ▁This ▁results ▁in ▁each ▁point ▁in ▁the ▁input ▁data ▁voting ▁for ▁a ▁sin us oid al ▁surface ▁in ▁the ▁H