Aarhus University Seal / Aarhus Universitets segl

Markus Kiderlen

Reconstruction of convex bodies from surface tensors

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review

We present two algorithms for reconstruction of the shape of convex bodies in the two-dimensional Euclidean space. The first reconstruction algorithm requires knowledge of the exact surface tensors of a convex body up to rank s for some natural number s. When only measurements subject to noise of surface tensors are available for reconstruction, we recommend to use certain values of the surface tensors, namely harmonic intrinsic volumes instead of the surface tensors evaluated at the standard basis. The second algorithm we present is based on harmonic intrinsic volumes and allows for noisy measurements. From a generalized version of Wirtinger's inequality, we derive stability results that are utilized to ensure consistency of both reconstruction procedures. Consistency of the reconstruction procedure based on measurements subject to noise is established under certain assumptions on the noise variables.
Original languageEnglish
JournalAdvances in Applied Mathematics
Pages (from-to)1-33
Number of pages33
Publication statusPublished - 2016

    Research areas

  • Generalized Wirtinger's inequality, Harmonic intrinsic volume, Surface tensor, Reconstruction algorithm, Convex body

See relations at Aarhus University Citationformats

ID: 96422546