Anisotropic Third-Order Regularization for Sparse Digital Elevation Models

Handle URI:
http://hdl.handle.net/10754/597575
Title:
Anisotropic Third-Order Regularization for Sparse Digital Elevation Models
Authors:
Lellmann, Jan; Morel, Jean-Michel; Schönlieb, Carola-Bibiane
Abstract:
We consider the problem of interpolating a surface based on sparse data such as individual points or level lines. We derive interpolators satisfying a list of desirable properties with an emphasis on preserving the geometry and characteristic features of the contours while ensuring smoothness across level lines. We propose an anisotropic third-order model and an efficient method to adaptively estimate both the surface and the anisotropy. Our experiments show that the approach outperforms AMLE and higher-order total variation methods qualitatively and quantitatively on real-world digital elevation data. © 2013 Springer-Verlag.
Citation:
Lellmann J, Morel J-M, Schönlieb C-B (2013) Anisotropic Third-Order Regularization for Sparse Digital Elevation Models. Scale Space and Variational Methods in Computer Vision: 161–173. Available: http://dx.doi.org/10.1007/978-3-642-38267-3_14.
Publisher:
Springer Science + Business Media
Journal:
Scale Space and Variational Methods in Computer Vision
KAUST Grant Number:
KUK-I1-007-43
Issue Date:
2013
DOI:
10.1007/978-3-642-38267-3_14
Type:
Book Chapter
ISSN:
0302-9743; 1611-3349
Sponsors:
The authors would like to thank Andrea Bertozzi andAlex Chen for helpful discussions. This publication is based on work supportedby Award No. KUK-I1-007-43, made by King Abdullah University of Scienceand Technology (KAUST), EPSRC first grant No. EP/J009539/1, EPSRC/IsaacNewton Trust Small Grant, and Royal Society International Exchange AwardNo. IE110314. J.-M. Morel was supported by MISS project of Centre Nationald’Etudes Spatiales, the Office of Naval Research under Grant N00014-97-1-0839and by the European Research Council, advanced grant “Twelve labours”.
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Full metadata record

DC FieldValue Language
dc.contributor.authorLellmann, Janen
dc.contributor.authorMorel, Jean-Michelen
dc.contributor.authorSchönlieb, Carola-Bibianeen
dc.date.accessioned2016-02-25T12:42:21Zen
dc.date.available2016-02-25T12:42:21Zen
dc.date.issued2013en
dc.identifier.citationLellmann J, Morel J-M, Schönlieb C-B (2013) Anisotropic Third-Order Regularization for Sparse Digital Elevation Models. Scale Space and Variational Methods in Computer Vision: 161–173. Available: http://dx.doi.org/10.1007/978-3-642-38267-3_14.en
dc.identifier.issn0302-9743en
dc.identifier.issn1611-3349en
dc.identifier.doi10.1007/978-3-642-38267-3_14en
dc.identifier.urihttp://hdl.handle.net/10754/597575en
dc.description.abstractWe consider the problem of interpolating a surface based on sparse data such as individual points or level lines. We derive interpolators satisfying a list of desirable properties with an emphasis on preserving the geometry and characteristic features of the contours while ensuring smoothness across level lines. We propose an anisotropic third-order model and an efficient method to adaptively estimate both the surface and the anisotropy. Our experiments show that the approach outperforms AMLE and higher-order total variation methods qualitatively and quantitatively on real-world digital elevation data. © 2013 Springer-Verlag.en
dc.description.sponsorshipThe authors would like to thank Andrea Bertozzi andAlex Chen for helpful discussions. This publication is based on work supportedby Award No. KUK-I1-007-43, made by King Abdullah University of Scienceand Technology (KAUST), EPSRC first grant No. EP/J009539/1, EPSRC/IsaacNewton Trust Small Grant, and Royal Society International Exchange AwardNo. IE110314. J.-M. Morel was supported by MISS project of Centre Nationald’Etudes Spatiales, the Office of Naval Research under Grant N00014-97-1-0839and by the European Research Council, advanced grant “Twelve labours”.en
dc.publisherSpringer Science + Business Mediaen
dc.titleAnisotropic Third-Order Regularization for Sparse Digital Elevation Modelsen
dc.typeBook Chapteren
dc.identifier.journalScale Space and Variational Methods in Computer Visionen
dc.contributor.institutionUniversity of Cambridge, Cambridge, United Kingdomen
dc.contributor.institutionEcole Normale Superieure de Cachan, Cachan, Franceen
kaust.grant.numberKUK-I1-007-43en
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