▁which ▁the ▁positions ▁associated ▁with ▁the ▁same ▁connected ▁component ▁of ▁the ▁binary ▁input ▁image ▁have ▁a ▁unique ▁label .” ▁Sh api ro ▁et ▁al . ▁define ▁C CL ▁as ▁an ▁operator ▁whose ▁“ input ▁is ▁a ▁binary ▁image ▁and ▁[...] ▁output ▁is ▁a ▁symbol ic ▁image ▁in ▁which ▁the ▁label ▁assigned ▁to ▁each ▁pixel ▁is ▁an ▁integer ▁uniqu ely ▁ident ifying ▁the ▁connected ▁component ▁to ▁which ▁that ▁pixel ▁belongs .” ▁ ▁There ▁is ▁no ▁cons ensus ▁on ▁the ▁definition ▁of ▁C CA ▁in ▁the ▁academic ▁literature . ▁It ▁is ▁often ▁used ▁inter change ably ▁with ▁C CL . ▁A ▁more ▁extensive ▁definition ▁is ▁given ▁by ▁Sh api ro ▁et ▁al .: ▁“ Conne cted ▁component ▁analysis ▁consists ▁of ▁connected ▁component ▁label ing ▁of ▁the ▁black ▁pixels ▁followed ▁by ▁property ▁measurement ▁of ▁the ▁component ▁regions ▁and ▁decision ▁making .” ▁The ▁definition ▁for ▁connected - component ▁analysis ▁presented ▁here ▁is ▁more ▁general , ▁taking ▁the ▁thoughts ▁expressed ▁in ▁ ▁into ▁account . ▁ ▁Alg orithms ▁The ▁algorithms ▁discussed ▁can ▁be ▁generalized ▁to ▁arbitrary ▁dimensions , ▁al beit ▁with ▁increased ▁time ▁and ▁space ▁complexity . ▁ ▁One ▁component ▁at ▁a ▁time ▁This ▁is ▁a ▁fast ▁and ▁very ▁simple ▁method ▁to ▁implement ▁and ▁understand . ▁It ▁is ▁based ▁on ▁graph ▁travers al ▁methods ▁in ▁graph ▁theory . ▁In ▁short , ▁once ▁the ▁first ▁pixel ▁of ▁a ▁connected ▁component ▁is ▁found , ▁all ▁the ▁connected ▁pixels ▁of ▁that ▁connected ▁component ▁are ▁label led ▁before ▁going ▁onto ▁the ▁next ▁pixel ▁in ▁the ▁image . ▁This ▁algorithm ▁is ▁part ▁of