## Abstract

The set of all surface tensors of a convex body K (Minkowski tensors derived from the surface area measure of K) determine K up to translation, and hereby, the surface tensors of K contain all information on the shape of

K. Here, shape means the equivalence class of all convex bodies that are translates of each other. An algorithm for reconstructing an unknown convex body in R 2 from its surface tensors up to a certain rank is presented.

Using the reconstruction algorithm, the shape of an unknown convex body can be approximated when only a finite number s of surface tensors are available. The output of the reconstruction algorithm is a polytope P, where the surface tensors of P and K are identical up to rank s. We establish a stability result based on a generalization of Wirtinger’s inequality that shows that for large s, two convex bodies are close in shape when they have identical surface tensors up to rank s. This is used to establish consistency of the developed

reconstruction algorithm.

K. Here, shape means the equivalence class of all convex bodies that are translates of each other. An algorithm for reconstructing an unknown convex body in R 2 from its surface tensors up to a certain rank is presented.

Using the reconstruction algorithm, the shape of an unknown convex body can be approximated when only a finite number s of surface tensors are available. The output of the reconstruction algorithm is a polytope P, where the surface tensors of P and K are identical up to rank s. We establish a stability result based on a generalization of Wirtinger’s inequality that shows that for large s, two convex bodies are close in shape when they have identical surface tensors up to rank s. This is used to establish consistency of the developed

reconstruction algorithm.

Originalsprog | Engelsk |
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Publikationsdato | 2015 |

Antal sider | 1 |

Status | Udgivet - 2015 |

Begivenhed | GPSRS Conference - Bad Herrenalb, Tyskland Varighed: 6 sep. 2015 → 11 sep. 2015 |

### Konference

Konference | GPSRS Conference |
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Land/Område | Tyskland |

By | Bad Herrenalb |

Periode | 06/09/2015 → 11/09/2015 |