@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",
}