ps es ▁and ▁curves ▁can ▁also ▁be ▁found ▁this ▁way , ▁as ▁can ▁any ▁shape ▁easily ▁expressed ▁as ▁a ▁set ▁of ▁parameters . ▁ ▁The ▁general ization ▁of ▁the ▁H ough ▁transform ▁for ▁detect ing ▁analyt ical ▁shapes ▁in ▁spaces ▁having ▁any ▁dimensional ity ▁was ▁proposed ▁by ▁Fern and es ▁and ▁O live ira . ▁In ▁contrast ▁to ▁other ▁H ough ▁transform - based ▁approaches ▁for ▁analyt ical ▁shapes , ▁Fern and es ' ▁technique ▁does ▁not ▁depend ▁on ▁the ▁shape ▁one ▁wants ▁to ▁detect ▁nor ▁on ▁the ▁input ▁data ▁type . ▁The ▁detection ▁can ▁be ▁driven ▁to ▁a ▁type ▁of ▁analyt ical ▁shape ▁by ▁changing ▁the ▁assumed ▁model ▁of ▁geometry ▁where ▁data ▁have ▁been ▁encoded ▁( e . g ., ▁e uclidean ▁space , ▁project ive ▁space , ▁conform al ▁geometry , ▁and ▁so ▁on ), ▁while ▁the ▁proposed ▁form ulation ▁remains ▁un changed . ▁Also , ▁it ▁guarante es ▁that ▁the ▁intended ▁shapes ▁are ▁represented ▁with ▁the ▁smallest ▁possible ▁number ▁of ▁parameters , ▁and ▁it ▁allows ▁the ▁concurrent ▁detection ▁of ▁different ▁kinds ▁of ▁shapes ▁that ▁best ▁fit ▁an ▁input ▁set ▁of ▁entries ▁with ▁different ▁dimensional ities ▁and ▁different ▁geometric ▁definitions ▁( e . g ., ▁the ▁concurrent ▁detection ▁of ▁plan es ▁and ▁spher es ▁that ▁best ▁fit ▁a ▁set ▁of ▁points , ▁straight ▁lines ▁and ▁circles ). ▁ ▁For ▁more ▁complicated ▁shapes ▁in ▁the ▁plane ▁( i . e ., ▁shapes ▁that ▁cannot ▁be ▁represented ▁analyt ically ▁in ▁some ▁ 2 D ▁space ), ▁the ▁General ised ▁H ough ▁transform ▁