Given a bounded open set Ω ⊂ ℝ 2 , we study the relaxation of nonparametric area functional in strict topology BV (Ω; ). and compute it for vortex-type maps, more generally maps W 1,1 (Ω;S 1 ) having finite number topological singularities. We also extend analysis to some specific piecewise constant ), including symmetric triple junction map.

Features such as photon rings, jets, or hot. spots can leave particular topological signatures in a black hole image. As such, data analysis be used to characterize images resulting from high resolution observations (synthetic real) of holes the electromagnetic sector. We demonstrate that persistent homology allows for this characterization made automatically by counting number connected compon...