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Inextensible Surface Reconstruction Under Small Relative Deformations from Distributed Angle Measurements

Talon, Thibaud and Pellegrino, Sergio (2022) Inextensible Surface Reconstruction Under Small Relative Deformations from Distributed Angle Measurements. International Journal of Computer Vision, 130 (2). pp. 594-614. ISSN 0920-5691. doi:10.1007/s11263-021-01552-x. https://resolver.caltech.edu/CaltechAUTHORS:20220126-901981200

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Abstract

A mathematical model to measure the shape of a 3D surface using angle measurements from embedded sensors is presented. The surface is known in a reference configuration and is assumed to have deformed inextensibly to its current shape. An inextensibility condition is enforced through a discretization of the metric tensor generating a finite number of constraints. This model allows to parameterize the shape of the surface using a small number of unknowns which leads to a small number of sensors. We study the singularities of the equations and derive necessary conditions for the problem to be well-posed as well as limitations of the algorithm. Simulations and experiments are performed on developable surfaces under relatively small deformations to analyze the performance of the method and to show the influence of the parameters used in our algorithm. Overall, the proposed method outperforms the current state-of-the-art by almost an order of magnitude.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/s11263-021-01552-xDOIArticle
https://rdcu.be/cFL9iPublisherFree ReadCube access
ORCID:
AuthorORCID
Talon, Thibaud0000-0002-8240-1101
Pellegrino, Sergio0000-0001-9373-3278
Additional Information:© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022. Received 29 August 2020; Accepted 18 November 2021; Published 11 January 2022. Financial support from the Space Solar Power Project at Caltech is gratefully acknowledged.
Group:GALCIT, Space Solar Power Project
Funders:
Funding AgencyGrant Number
Space Solar Power ProjectUNSPECIFIED
Subject Keywords:Inextensible; Surface; Reconstruction; Distributed sensors; Angle measurements; Metric tensor
Issue or Number:2
DOI:10.1007/s11263-021-01552-x
Record Number:CaltechAUTHORS:20220126-901981200
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20220126-901981200
Official Citation:Talon, T., Pellegrino, S. Inextensible Surface Reconstruction Under Small Relative Deformations from Distributed Angle Measurements. Int J Comput Vis 130, 594–614 (2022). https://doi.org/10.1007/s11263-021-01552-x
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:113118
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:28 Jan 2022 19:08
Last Modified:01 Mar 2022 23:04

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