= Perimeter
{title2=$\operatorname{Per}(E;\Omega)=|D\chi_E|(\Omega)$}
The <perimeter> of a measurable set relative to an open domain is the <total variation seminorm> of its <indicator function> there. For a smooth region it equals the <Hausdorff measure> of the boundary lying inside the domain. Global <perimeter> uses the entire space as the domain; an internal interface shared by two regions appears in both relative perimeters and must be counted only once in a segmentation energy.
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