Sibson (Natural Neighbour) and Non-Sibsonian Interpolation for Digital Elevation Model (Dem)

Yanalak, Mustafa

doi:10.1179/sre.2004.37.291.360

Cited by 5 publications

(2 citation statements)

References 19 publications

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“…The inverse distance to a power (IDP) method predicts the value for any test point by interpolating the measured values in the neighboring reference location (Franke and Nielson, 1980). The weight of a reference point is a function of the horizontal distance from the test point (Yanalak, 2004). The weighting function is assigned to the data using the weighting power (k).…”

Section: Inverse Distance To a Powermentioning

confidence: 99%

Geoid undulation prediction using Gaussian Processes Regression: A case study in a local region in Turkey

Konakoǧlu¹

2021

Acta Geodynamica Et Geomaterialia

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In order to convert ellipsoidal heights obtained by the Global Navigation Satellite System (GNSS) to orthometric heights, it is necessary to know the distance between the ellipsoidal and geoid surface, called the geoid undulation. The geoid undulation can be predicted using emerging mathematics tools and algorithms. The objective of this study was to develop a model for predicting the geoid undulation using Gaussian Process Regression (GPR), one of the soft machine learning algorithms having different covariance functions. This method was then compared with the radial basis function neural network (RBFNN), generalized regression neural network (GRNN), and the interpolation method of inverse distance to a power (IDP) with the power of 1, 2, 3, 4, and 5. First, 70 % of GNSS/leveling data (422 points) were used in the training phase. The remaining 185 points were used as testing data to check the effectiveness of the constructed model. In the GPR modeling, ten covariance functions (Materniso d= 1, 3, 5; Maternard d= 1, 3, 5; SEiso; SEard; RQiso; and RQard) were tested for prediction on this dataset. The GPR based on the Materniso (d = 1) covariance function model was introduced as an effective method for predicting geoid undulation and provided the best results (RMSE = 8.32 cm, MAE = 5.51 cm, R 2 = 0.98968) when compared with the other developed GPR models. In addition, the statistical findings showed that the accuracy of all the GPR models was also better in predicting geoid undulation than the RBFNN, GRNN, and IDP with the power of 1, 2, 3, 4, and 5.

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Section: Inverse Distance To a Powermentioning

confidence: 99%

Geoid undulation prediction using Gaussian Processes Regression: A case study in a local region in Turkey

Konakoǧlu¹

2021

Acta Geodynamica Et Geomaterialia

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“…• Deterministic interpolation methods include nearest (natural) neighbour (NN) [25], inverse distance weighting (IDW) [26], or trend surface mapping (TS) [27]. These methods often work better with homogeneous distributions of data points.…”

Section: Introductionmentioning

confidence: 99%

Multigrid/Multiresolution Interpolation: Reducing Oversmoothing and Other Sampling Effects

Rodríguez‐Pérez

Sánchez-Carnero

2022

Geomatics

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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.

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Investigation of landslide detection using radial basis functions: a case study of the Taşkent landslide, Turkey

Zeybek

Şanlıoğlu

2020

Environ Monit Assess

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Sibson (Natural Neighbour) and Non-Sibsonian Interpolation for Digital Elevation Model (Dem)

Cited by 5 publications

References 19 publications

Geoid undulation prediction using Gaussian Processes Regression: A case study in a local region in Turkey

Geoid undulation prediction using Gaussian Processes Regression: A case study in a local region in Turkey

Multigrid/Multiresolution Interpolation: Reducing Oversmoothing and Other Sampling Effects

Investigation of landslide detection using radial basis functions: a case study of the Taşkent landslide, Turkey

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