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Astrid Kousholt

Reconstruction of convex bodies from surface tensors

Publikation: Konferencebidrag › Poster › Forskning

Standard

Reconstruction of convex bodies from surface tensors. / Kousholt, Astrid; Kiderlen, Markus.
2015. Poster session præsenteret ved GPSRS Conference, Bad Herrenalb, Tyskland.

Publikation: Konferencebidrag › Poster › Forskning

Harvard

Kousholt, A & Kiderlen, M 2015, 'Reconstruction of convex bodies from surface tensors', GPSRS Conference, Bad Herrenalb, Tyskland, 06/09/2015 - 11/09/2015.

APA

Kousholt, A., & Kiderlen, M. (2015). Reconstruction of convex bodies from surface tensors. Poster session præsenteret ved GPSRS Conference, Bad Herrenalb, Tyskland.

CBE

Kousholt A, Kiderlen M. 2015. Reconstruction of convex bodies from surface tensors. Poster session præsenteret ved GPSRS Conference, Bad Herrenalb, Tyskland.

MLA

Kousholt, Astrid og Markus Kiderlen Reconstruction of convex bodies from surface tensors. GPSRS Conference, 06 sep. 2015, Bad Herrenalb, Tyskland, Poster, 2015. 1 s.

Vancouver

Kousholt A, Kiderlen M. Reconstruction of convex bodies from surface tensors. 2015. Poster session præsenteret ved GPSRS Conference, Bad Herrenalb, Tyskland.

Author

Kousholt, Astrid ; Kiderlen, Markus. / Reconstruction of convex bodies from surface tensors. Poster session præsenteret ved GPSRS Conference, Bad Herrenalb, Tyskland.1 s.

Bibtex

@conference{288da80c875a465ab556f4331c33e337,
title = "Reconstruction of convex bodies from surface tensors",
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 ofK. 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{\textquoteright}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 developedreconstruction algorithm.",
author = "Astrid Kousholt and Markus Kiderlen",
year = "2015",
language = "English",
note = "GPSRS Conference ; Conference date: 06-09-2015 Through 11-09-2015",

}

RIS

TY - CONF

T1 - Reconstruction of convex bodies from surface tensors

AU - Kousholt, Astrid

AU - Kiderlen, Markus

PY - 2015

Y1 - 2015

N2 - 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 ofK. 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 developedreconstruction algorithm.

AB - 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 ofK. 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 developedreconstruction algorithm.

M3 - Poster

T2 - GPSRS Conference

Y2 - 6 September 2015 through 11 September 2015

ER -