Interpolation

Interpolation is necessary to produce digital models from Lidar point cloud. The simple idea of the interpolation is referred to the nearest neighbor interpolation method to estimate the elevation (Maune, 2007). It searches for the set of nearest points, thus the new elevation value is selected as the same value of the nearest point instead of taking the average of all points. An important problem here is the zigzag appearance of the surface. This is in fact due to the selecting of the nearest point method by defining Voroni diagrams or Theissen polygons. For this reason, some kinds of averaging methods should be applied to the set of known nearest elevation points. Therefore, a weighted average like inverse distance weighting (IDW) is introduced which is working with the distances between these points (Monnet et al, 2010; Bater and Coops, 2009).

In Lidar data especially in vegetated areas distances are not related to the elevations. In contrast, kriging or geostatistical approaches provide better results (Heritage and Large,

2009) . However, they require more mathematically complex and computationally intensive algorithms. Since dense data is always available, rapid interpolation methods such as the nearest neighbor are prefered to use for the rough surfaces in the forest areas (Fallah Vazirabad and Karslioglu, 2010).

Riano et al. (2003) investigated the performances of spline and nearest neighbor interpolation methods to generate DTM. Spline interpolation is a special form of piecewise polynomial. The interpolation error in the DTM can be small even applying the low degree polynomial. They concluded that there were no large differences between the spline and nearest neighbor results while the spline computation was three times slower. Hollaus et al. (2010) described the derivation of DSM employing the least square fitting method to compare it with kriging interpolation. They introduced a moving least square fitting technique which selects the highest points in the search window as surface points. This technique finds the best fitting surface to the set of points by minimizing the sum of squares of the residuals of the points from surface. The results of this study showed that the least square fitting technique produced high precision DSM on rough surfaces while it needs more computational time.