Anisotropic Third-Order Regularization for Sparse Digital Elevation Models

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

Research output: Chapter in Book/Report/Conference proceedingChapter

7 Scopus citations


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 languageEnglish (US)
Title of host publicationScale Space and Variational Methods in Computer Vision
PublisherSpringer Nature
Number of pages13
ISBN (Print)9783642382666
StatePublished - 2013
Externally publishedYes

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.


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