▁associated ▁with ▁them . ▁ ▁Given ▁a ▁single ▁point ▁in ▁the ▁plane , ▁then ▁the ▁set ▁of ▁ ▁all ▁straight ▁lines ▁going ▁through ▁that ▁point ▁corresponds ▁to ▁a ▁sin us oid al ▁curve ▁in ▁the ▁( r , θ ) ▁plane , ▁which ▁is ▁unique ▁to ▁that ▁point . ▁A ▁set ▁of ▁two ▁or ▁more ▁points ▁that ▁form ▁a ▁straight ▁line ▁will ▁produce ▁sin us oid s ▁which ▁cross ▁at ▁the ▁ ▁( r , θ ) ▁for ▁that ▁line . ▁Thus , ▁the ▁problem ▁of ▁detect ing ▁col linear ▁points ▁can ▁be ▁converted ▁to ▁the ▁problem ▁of ▁finding ▁concurrent ▁curves . ▁ ▁Im plementation ▁ ▁The ▁linear ▁H ough ▁transform ▁algorithm ▁uses ▁a ▁two - dimensional ▁array , ▁called ▁an ▁accum ulator , ▁to ▁detect ▁the ▁existence ▁of ▁a ▁line ▁described ▁by ▁. ▁ ▁The ▁dimension ▁of ▁the ▁accum ulator ▁equals ▁the ▁number ▁of ▁unknown ▁parameters , ▁i . e ., ▁two , ▁considering ▁quant ized ▁values ▁of ▁r ▁and ▁ θ ▁in ▁the ▁pair ▁( r , θ ). ▁ ▁For ▁each ▁pixel ▁at ▁( x , y ) ▁and ▁its ▁neighborhood , ▁the ▁H ough ▁transform ▁algorithm ▁determ ines ▁if ▁there ▁is ▁enough ▁evidence ▁of ▁a ▁straight ▁line ▁at ▁that ▁pixel . ▁ ▁If ▁so , ▁it ▁will ▁calculate ▁the ▁parameters ▁( r , θ ) ▁of ▁that ▁line , ▁and ▁then ▁look ▁for ▁the ▁accum ulator ' s ▁bin ▁that ▁the ▁parameters ▁fall ▁into , ▁and ▁increment ▁the ▁value ▁of ▁that ▁bin . ▁By ▁finding ▁the ▁b ins ▁with