Multigrid/Multiresolution Interpolation: Reducing Oversmoothing and Other Sampling Effects

RODRIGUEZ-PEREZ, DANIEL; SANCHEZ-CARNERO, NOELA

Geomatics

MDPI

Año: 2022 vol. 2 p. 236 - 253

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 methodshave strong statistical and analytical foundations (such as the assumption of randomly distributeddata points from a gaussian correlated stochastic surface); however, when data are acquired nonhomogeneously (e.g., along transects) all of them show over/under-smoothing of the interpolatedsurface depending on local point density. As a result, actual information is lost in high point densityareas (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 wheredata exist and a smoothing generalizer where data are missing, but always fulfilling the statisticalrequirement 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.