Semivariogram fitting based on SVM and GPR for DEM interpolation

Abstract

DEM (Digital Elevation Model) as a digital model of the earth’s surface elevation could be generated from remote sensing technology such as stereo imaging for various applications. To generate DEM from stereo imagery, interpolation or approximation process stage is required. Stochastic interpolation e.g. ordinary kriging uses semivariogram fitting to calculate weights of interpolation values based on known points. This research is applying regression types of machine learning for semivariogram fitting to interpolate DEM. Previous research conducted was LS-SVM (Least Square-Support Vector Machine) and SVR (Support Vector Regression) for semivariogram fitting process. Types of SVM and GPR (Gaussian Process Regression) are adopted for semivariogram fitting for ordinary kriging interpolation in this experiment. The result showed that in general SVM types could predict accuracy better than other types of regression, and GPR types produce better DEM accuracy based on the experiment.

Minimax Approach for Semivariogram Fitting in Ordinary Kriging

“…While the types of GPR being used are Gaussian process regression, Gaussian process regression rational quadratic (GPRRQ), Gaussian process regression squared exponential (GPRSE), Gaussian process regression matem 5/2 (GPRM), and Gaussian process regression exponential (GPRE). The machine learning technique has been conducted in previous experiments [15], [16].…”

“…Previously, support vector regression has been applied to variogram modeling [13] and the least squares support vector machine (LS-SVM), invented for optimal control of the SVM [14], has been used to interpolate missing oceanic data [12] and coal seam thickness [13]. SVM and gaussian process regression (GPR) can improve result accuracy compared to conventional methods for DEM interpolation [15]. LS-SVM can be used to improve the cokriging fusion process [16].…”

“…The results for dataset 1 show that several attempts of the minimax operation is able to improve accuracy compared to the weighted least-squares approach at a smaller number of γ * (h). The least residual error is produced by polynomial minimax at 50 γ * (h) of 0.45 m. This accuracy achievement is better than machine learning, which has the best accuracy of 0.46 m. In a machine learning experiment for semivariogram fitting conducted previously [15], machine learning regression processes are set at five-folds.…”

How Does Spatial Heterogeneity Affect Industrial Outputs? Literature Review and Research Prospects

“…Basile (2014) presented a semiparametric framework which allows us to relax the linearity assumption and, simultaneously, model spatial dependence and unobserved heterogeneity. In general, SVM types yield prediction accuracy that is better than other types of regression, and GPR types produce better DEM accuracy based on experiments (Setiyoko et al, 2019). For example, Srikhum and Simon (2010) used a non-stationary semivariogram to analyze real estate transaction data, and confirmed a degree of spatial autocorrelation (positive or very positive autocorrelation) between neighboring properties.…”

Simulation of DEM Based on ICESat-2 Data Using Openly Accessible Topographic Datasets

“…Interpolation is the process of estimating the value of attributes at unsampled si from measurements made at point locations within the same area or region, but it oft leads to over-smoothening [7]. Simulation technique can be defined as a statistical way generate data, where unavailable, based on the statistical models like linear regressi which correlates the input and output of the sample/training data and calculates the s tistical relationship between the two and implements the same for other input points generate their corresponding output.…”