structuring element
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i:imagese:structuring elementi : image \\ se:structuring\ elementi:imagese:structuring element White top-hat transformTw(i)=i−(i∘se),(∘:opening)T_w(i) = i - (i \circ se), (\circ:opening)Tw(i)=i−(i∘se),(∘:opening) Black top-hat transformTb(i)=(i∙se)−i,(∙:closing)T_b(i) = (i \bullet se) - i, (\bullet:closing)Tb(i)=(i∙se)−i,(∙:closing)
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i−Tw(i)=i−(i−(i∘se))=i−i+(i∘se)=(i∘se)=opening\begin{aligned} i - T_w(i) &= i - ( i - (i \circ se ) )\\ &= i - i + (i \circ se ) \\ &= (i \circ se ) \\ &= opening \end{aligned}i−Tw(i)=i−(i−(i∘se))=i−i+(i∘se)=(i∘se)=opening