▁since ▁the ▁slope ▁can ▁go ▁to ▁infinity . ▁ ▁The ▁r ho - theta ▁paramet riz ation ▁univers ally ▁used ▁today ▁was ▁first ▁described ▁in ▁▁▁▁ ▁although ▁it ▁was ▁already ▁standard ▁for ▁the ▁Rad on ▁transform ▁since ▁at ▁least ▁the ▁ 1 9 3 0 s . ▁ ▁O ' G orm an ▁and ▁C low es ' ▁variation ▁is ▁described ▁in ▁▁▁▁ ▁The ▁story ▁of ▁how ▁the ▁modern ▁form ▁of ▁the ▁H ough ▁transform ▁was ▁invent ed ▁is ▁given ▁in ▁ ▁Theory ▁ ▁In ▁autom ated ▁analysis ▁of ▁digital ▁images , ▁a ▁sub problem ▁often ▁ar ises ▁of ▁detect ing ▁simple ▁shapes , ▁such ▁as ▁straight ▁lines , ▁circles ▁or ▁elli ps es . ▁In ▁many ▁cases ▁an ▁edge ▁det ector ▁can ▁be ▁used ▁as ▁a ▁pre - processing ▁stage ▁to ▁obtain ▁image ▁points ▁or ▁image ▁pixels ▁that ▁are ▁on ▁the ▁desired ▁curve ▁in ▁the ▁image ▁space . ▁Due ▁to ▁imper fe ctions ▁in ▁either ▁the ▁image ▁data ▁or ▁the ▁edge ▁det ector , ▁however , ▁there ▁may ▁be ▁missing ▁points ▁or ▁pixels ▁on ▁the ▁desired ▁curves ▁as ▁well ▁as ▁spatial ▁devi ations ▁between ▁the ▁ideal ▁line / circle / el lipse ▁and ▁the ▁no isy ▁edge ▁points ▁as ▁they ▁are ▁obtained ▁from ▁the ▁edge ▁det ector . ▁For ▁these ▁reasons , ▁it ▁is ▁often ▁non - t rivial ▁to ▁group ▁the ▁extracted ▁edge ▁features ▁to ▁an ▁appropriate ▁set ▁of ▁lines , ▁circles ▁or ▁elli ps es . ▁The ▁purpose ▁of ▁the ▁H ough ▁transform ▁is ▁to ▁address ▁this ▁problem ▁by ▁making