Anisotropic Third-Order Regularization for Sparse Digital Elevation Models

Jan Lellmann; Jean-Michel Morel; Carola-Bibiane Schönlieb

doi:10.1007/978-3-642-38267-3_14

Anisotropic Third-Order Regularization for Sparse Digital Elevation Models

Jan Lellmann, Jean-Michel Morel, Carola-Bibiane Schönlieb

Research output: Chapter in Book/Report/Conference proceeding › Chapter

7 Scopus citations

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.

Original language	English (US)
Title of host publication	Scale Space and Variational Methods in Computer Vision
Publisher	Springer Nature
Pages	161-173
Number of pages	13
ISBN (Print)	9783642382666
DOIs	https://doi.org/10.1007/978-3-642-38267-3_14
State	Published - 2013
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-I1-007-43
Acknowledgements: 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”.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

Access to Document

10.1007/978-3-642-38267-3_14

Cite this

@inbook{cdedea546110442e85a775eca84eaa85,

title = "Anisotropic Third-Order Regularization for Sparse Digital Elevation Models",

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. {\textcopyright} 2013 Springer-Verlag.",

author = "Jan Lellmann and Jean-Michel Morel and Carola-Bibiane Sch{\"o}nlieb",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUK-I1-007-43 Acknowledgements: 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{\textquoteright}Etudes Spatiales, the Office of Naval Research under Grant N00014-97-1-0839and by the European Research Council, advanced grant “Twelve labours”. This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

year = "2013",

doi = "10.1007/978-3-642-38267-3_14",

language = "English (US)",

isbn = "9783642382666",

pages = "161--173",

booktitle = "Scale Space and Variational Methods in Computer Vision",

publisher = "Springer Nature",

}

TY - CHAP

T1 - Anisotropic Third-Order Regularization for Sparse Digital Elevation Models

AU - Lellmann, Jan

AU - Morel, Jean-Michel

AU - Schönlieb, Carola-Bibiane

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUK-I1-007-43 Acknowledgements: 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”. This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/597575

UR - http://link.springer.com/10.1007/978-3-642-38267-3_14

UR - http://www.scopus.com/inward/record.url?scp=84884389464&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-38267-3_14

DO - 10.1007/978-3-642-38267-3_14

M3 - Chapter

SN - 9783642382666

SP - 161

EP - 173

BT - Scale Space and Variational Methods in Computer Vision

PB - Springer Nature

ER -

Anisotropic Third-Order Regularization for Sparse Digital Elevation Models

Abstract

Bibliographical note

Access to Document

Other files and links

Fingerprint

Cite this