# An Improved Skewness Balancing Filtering Algorithm Based on Thin Plate Spline Interpolation
## 4 Discussion  
To objectively evaluate the performance of the proposed method, this paper compared the total errors of the proposed method to the classic skewness balancing method and eight other algorithms tested by the ISPRS [44]. As shown in Figures 7 and 8, the improved method proposed in this paper performs much better than the classic skewness balancing method. The total errors of the seven samples are all smaller than those of skewness balancing. As a result, the average total error of the proposed method is much smaller than that of skewness balancing. Figure 8 shows that the proposed method outperforms most of the previous filtering methods except for the progressive triangulated irregular network densification (PTD) method proposed by [PERSON]. The average total error of the proposed method is only slightly larger than that of the PTD method. Considering that the PTD method involves complex parameter settings, such as thresholds of iteration angle and distance, the proposed method has the advantage of a high degree of automation with satisfying filtering accuracy. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Sample**} & \multicolumn{3}{c}{**The Proposed Method**} \\ \cline{2-4}  & **Type I** & **Type II** & **Total** \\  & **(\%)** & **(\%)** & **(\%)** \\ \hline samp12 & 5.55 & 8.49 & 6.97 \\ samp21 & 0.47 & 9.65 & 2.50 \\ samp31 & 5.52 & 3.44 & 4.56 \\ samp41 & 7.43 & 11.14 & 9.29 \\ samp54 & 2.26 & 5.34 & 3.91 \\ samp61 & 6.57 & 8.71 & 6.64 \\ samp71 & 1.41 & 22.82 & 3.84 \\ Mean & 4.17 & 9.94 & 5.39 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Accuracy indexes for the seven samples. Figure 7: Comparison of total errors of the proposed method and previous filtering methods. In recent years, some other modified filtering methods have also been proposed to improve filtering performance. [PERSON] et al. [4] proposed an improved morphological filtering method based on geodesic transformations of mathematical morphology. In their method, it is unnecessary to select different window sizes or determine the maximum window size. Thus, the robustness and automation of the morphological filtering method can be enhanced. [PERSON] et al. [5] put forward an improved top-hat filtering with sloped brim to extract ground points. To suppress the omission error caused by protruding terrain features, [PERSON] et al. [5] inspected the elevation change intensity of the transitions between the obtained top-hats and outer brims. In doing so, the filtering performance of the method towards various terrain environments can be improved. Most traditional morphology-based algorithms have difficulties in protecting terrain details, especially when using larger filtering windows. To solve this problem, [PERSON] et al. [7] first proposed a hybrid filtering model that combines a traditional morphology-based filter and an interpolation-based filter. The morphological filters removed the nonground points with filtering window gradually downsizing. Meanwhile, Kriging interpolation is adopted based on the corresponding filtering windows. The experimental results show that the improved method has a significant advantage in protecting terrain details, thereby providing good filtering performance. [PERSON] and [PERSON] [29] improved the classic progressive TIN (triangular irregular network) densification (PTD) method based on segmentation. In their method, point clouds are first segmented by region growing. Then, each terrain segment is added to the TIN iteratively. In so doing, the improved method can achieve a smaller omission error and total error than the traditional PTD method. All the above-mentioned methods evaluate the filtering performance using the data sets provided by the ISPRS. This paper compares the type I error, type II error, and total error with those of the other four methods, as shown in Figures 9-11. From Figure 9, it can be found that the proposed method achieved smaller type I errors than most of other methods, especially for samp41.