A boundary approach for set inversion. (April 2021) - Jaulin, Luc
Abstract: In the paper, we present a new interval-based set inversion algorithm which takes into account the continuity of the problem. In the case where the set Y to be inverted has some volume, we show that inverting the boundary ∂ Y of Y is sufficient to reconstruct the preimage X = f − 1 ( Y ) . The inversion of ∂ Y separates the domain of f into two regions : one inside X and one outside. To detect which part is inside or outside, we show that we can retro-propagate the information coming from Y at negligible cost. The efficiency of the approach is illustrated on a localization problem.