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Article

Multigrid/Multiresolution Interpolation: Reducing Oversmoothing and Other Sampling Effects

1
Departamento de Física Matemática y de Fluidos, Facultad de Ciencias, UNED, Avda. Esparta s/n, 28232 Las Rozas, Madrid, Spain
2
Centro para el Estudio de Sistemas Marinos (CESIMAR), CCT CONICET-CENPAT, Bv. Almirante Brown 2915, Puerto Madryn U9120ACD, Chubut, Argentina
3
Grupo de Ocenografia Fisica (GOFUVI), Facultade de Ciencias do Mar, Campus de Vigo, Lagoas-Marcosende, Illa de Toralla s/n, 36331 Vigo, Pontevedra, Spain
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Academic Editors: Giuseppe Masetti, Ian Church, Anand Hiroji and Ove Andersen
Geomatics 2022, 2(3), 236-253; https://doi.org/10.3390/geomatics2030014
Received: 25 May 2022 / Revised: 14 June 2022 / Accepted: 18 June 2022 / Published: 22 June 2022
(This article belongs to the Special Issue Advances in Ocean Mapping and Nautical Cartography)
Traditional interpolation methods, such as IDW, kriging, radial basis functions, and regularized splines, are commonly used to generate digital elevation models (DEM). All of these methods have strong statistical and analytical foundations (such as the assumption of randomly distributed data points from a gaussian correlated stochastic surface); however, when data are acquired non-homogeneously (e.g., along transects) all of them show over/under-smoothing of the interpolated surface depending on local point density. As a result, actual information is lost in high point density areas (caused by over-smoothing) or artifacts appear around uneven density areas (“pimple” or “transect” effects). In this paper, we introduce a simple but robust multigrid/multiresolution interpolation (MMI) method which adapts to the spatial resolution available, being an exact interpolator where data exist and a smoothing generalizer where data are missing, but always fulfilling the statistical requirement that surface height mathematical expectation at the proper working resolution equals the mean height of the data at that same scale. The MMI is efficient enough to use K-fold cross-validation to estimate local errors. We also introduce a fractal extrapolation that simulates the elevation in data-depleted areas (rendering a visually realistic surface and also realistic error estimations). In this work, MMI is applied to reconstruct a real DEM, thus testing its accuracy and local error estimation capabilities under different sampling strategies (random points and transects). It is also applied to compute the bathymetry of Gulf of San Jorge (Argentina) from multisource data of different origins and sampling qualities. The results show visually realistic surfaces with estimated local validation errors that are within the bounds of direct DEM comparison, in the case of the simulation, and within the 10% of the bathymetric surface typical deviation in the real calculation. View Full-Text
Keywords: multiresolution interpolation; bathymetry; SRTM; Gulf of San Jorge; Patagonia; Argentina; Atlantic Ocean multiresolution interpolation; bathymetry; SRTM; Gulf of San Jorge; Patagonia; Argentina; Atlantic Ocean
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Figure 1

  • Externally hosted supplementary file 1
    Link: https://github.com/daniel-rperez/mrinterp
    Description: The code implementing the algorithms described and some sample data can be found in the GitHub public repository https://github.com/daniel-rperez/mrinterp.
MDPI and ACS Style

Rodriguez-Perez, D.; Sanchez-Carnero, N. Multigrid/Multiresolution Interpolation: Reducing Oversmoothing and Other Sampling Effects. Geomatics 2022, 2, 236-253. https://doi.org/10.3390/geomatics2030014

AMA Style

Rodriguez-Perez D, Sanchez-Carnero N. Multigrid/Multiresolution Interpolation: Reducing Oversmoothing and Other Sampling Effects. Geomatics. 2022; 2(3):236-253. https://doi.org/10.3390/geomatics2030014

Chicago/Turabian Style

Rodriguez-Perez, Daniel, and Noela Sanchez-Carnero. 2022. "Multigrid/Multiresolution Interpolation: Reducing Oversmoothing and Other Sampling Effects" Geomatics 2, no. 3: 236-253. https://doi.org/10.3390/geomatics2030014

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