Identification of an algebraic domain from a finite number of its generalized polarization tensors

The talk is related to the inverse problem  of  recovering the shape of a bounded domain from its generalized polarization tensors. I will first introduce the concept of using  infinitely many generalized polarization tensors as shape descriptors for general bounded domains.  Then, I will present recent results on identifying  an algebraic planar domain using only a finite number of its polarization tensors.  The density with respect to Hausdorff distance of algebraic domains among  all bounded domains invites to extend via approximation the obtained reconstruction procedure beyond its natural context.  Based on this, I will present a new algorithm for shape recognition  with a few numerical illustrations using synthetic data.

海报