# An Improved Skewness Balancing Filtering Algorithm Based on Thin Plate Spline Interpolation
## 3 Experimental Results  
To evaluate the performance of the proposed method, the datasets provided by the ISPRS Commission III were employed [43]. The datasets are selected from seven sites located in the Vaihingen/Enz test field and Stuttgart city center. This paper chose one sample datum from each site. These selected samples (samp12, samp21, samp31, samp41, samp54, samp61 and samp71) cover different terrain features as shown in Table 1. These samples were classified correctly using semiautomatic filtering and subsequent manual editing. Thus, these samples are convenient for performing quantitative calculations.  
The filtering results of the seven samples are shown in Figure 6. Three accuracy metrics, namely Type I error, Type II error, and total error, are were adopted for the quantitative analysis. The Type I error is the proportion of ground points misclassified as nonground points, while the Type II error is the proportion of nonground points that the method fails to reject. The total error is the entire set of erroneous points. The filtering accuracy of the proposed method is shown in Table 2. In terms of the total error, the proposed method performs the best for samp21. Moreover, samp21 also has the smallest Type I error, which means that almost all the ground points are correctly classified. From samp12 (a) and samp12 (b) in Figure 6, it can be observed that the terrain in this sample is not too complicated. The main filtering challenge is the bridge, which has been removed effectively. samp41 has the largest total error since both its Type I error and Type II error are larger. In the area of samp41, there are some complex buildings and low outliers. In particular, certain low outliers are dense enough to be hard to remove. These points are wrongly selected as ground seeds, which affects the accuracy of the interpolated surface. Therefore, the proposed method does not perform well in this area. From Table 2, it can be concluded that the proposed method is biased in favor of minimizing Type I errors because the average Type II error (9.94%) is more than two times the average Type I error (4.17%). That result occurs because samp71 and samp41 have larger Type II errors. Because Type II errors are easily modified, most filtering algorithms tend to suppress Type I errors at the expense of larger Type II errors.  
\begin{table}
\begin{tabular}{c c} \hline
**Samples** & **Terrain Features** \\ \hline samp12 & Small objects, mixed vegetation and buildings \\ samp21 & Attached objects, narrow bridge, and low vegetation \\ samp31 & Dense buildings, data gaps, and mixture of high and low objects \\ samp41 & Data gaps, complex buildings, and low outliers \\ samp54 & Gentle sloped terrains, dense objects \\ samp61 & Buildings, embankments, data gaps, and roads \\ samp71 & Bridges, embankments, underpasses, and roads \\ \hline \end{tabular}
\end{table}
Table 1: Terrain features of the selected seven samples.  
Figure 6: _Cont._  
Figure 6: Filtering results: (**a**) the DSMs before filtering; (**b**) the filtered DEMs generated from the ground points derived by the proposed filtering algorithm.