### Literature Review
#### 1.2.2. Spatial Interpolation Methods  
Spatial interpolation can be categorized into point interpolation and areal interpolation [15]. While both methods are identical in that they both estimate unknown values on a location that is not sampled from spatiotemporally distributed observation data, they are used in completely different geographical problems [16]. Generally, areal interpolation uses simple areal weighting [17] or dasymetric mapping [18], and these are applied to reassign the spatial unit of the observed data [19]. On the other hand, the point interpolation can be further categorized into local neighborhood approach-based interpolation (i.e., IDW, Natural neighbor interpolation, TIN), geostatistical approach-based interpolation (i.e., Krig  
Figure 1: Neighborhood types in a grid system. ing), and variational approach-based interpolation (i.e., Spline), and as has been discussed, it can often perform spatial modeling through the estimation of an unknown value or resample the raster data resolution [20]. Since the aim of this study is the interpolation of 3D point data distributed in 3D space, the literature on areal interpolation is not reviewed additionally. The point interpolation that is most widely used in geographical information systems (GIS) these days applies to inverse distance weighting (IDW) and Kriging. By characteristics, there exist improved models of these methods (i.e., Multivariate blended IDW surfaces and volumes [20; 21; 22; 23], Co-Kriging [24], Empirical Bayesian Kriging [25; 26], but these are basically identical in that the closer the distance between a cell with an unknown value and neighborhoods with known values, the stronger the correlation that is assumed. The biggest difference between IDW and Kriging is that Kriging is a probabilistic interpolation method that determines the weighting value based not only on distance but on spatial autocorrelation toward observed data, and it produces an interpolation function based on a covariance or variogram model [27]. Due to such characteristics, it is effective in fields with a spatial arrangement from a geostatistical perspective, such as mining and petroleum, geochemistry, geology, and ecology [20]. In addition, as a new approach for voxel data processing and visualization in recent years, 3D search neighborhoods-based 3D Empirical Bayesian Kriging is being applied to GIS applications [28]. On the other hand, IDW is a deterministic interpolation method that determines weight based on the distance between neighborhoods and a location with unknown values and estimates unknown values by assigning the weighting value to neighboring observation data. As such, IDW has a simple basic assumption and offers efficient processing, but its disadvantage is that it generates local extrema on the estimation surface (Figure 2). Due to such characteristics, IDW is limited in topographic modeling that reproduces natural (or smooth) local shapes, rather than the quantitative evaluation of the interpolation predictive capabilities. These traditional interpolation methods could not satisfy the requirements that should be considered in 3D space since they were developed assuming 2D spatial modeling. Thus, many scholars suggested an improved method related to traditional interpolation  
Figure 2: Interpolation of a DEM: (**a**) Ordinary Kriging (spherical variogram); (**b**) IDW; (**c**) Regularized Spline; (**d**) Tension Spline. in terms of 3D search neighbors and an interpolation function. When considering the interpolation method, [PERSON] et al. proposed a Kriging approach based on a divide-and -conquer strategy through linear combination on multiple prediction results to improve the classical Co-Kriging method where all the input data are fitted at once [29]. Moreover, [PERSON] et al. proposed an effective method to recreate uniform meshes from point cloud data through improved interpolation based on the Radial Basis Function (RBF) [30], and it is similar to Dual Kriging [27].