# An Improved Skewness Balancing Filtering Algorithm Based on Thin Plate Spline Interpolation
## 1 Introduction
Segmentation-based filtering algorithms always rely on two main steps, namely, segmentation and filtering. In contrast to the abovementioned three kinds of methods, this kind of approach first applies some segmentation methods, such as region growing, for clustering the scatter points. Then, filtering is realized based on the segmentation results. Many researchers combine segmentation methods with traditional filtering algorithms and obtain good filtering performance. For example, [PERSON] and [PERSON] [28] modified the linear-prediction method proposed by [PERSON] and [PERSON] [31] using a region growing algorithm and improved the filtering accuracy at break lines. Since segmentation-based algorithms can use more semantic information, this kind of method generally performs much better than other kinds of methods. However, the performance of this kind of method relies heavily on the segmentation results. If the segmentation results are not accurate, a larger filtering error will be obtained. The above-mentioned filtering methods are mainly proposed for airborne laser scanning (ALS) data. In addition to ALS, two other LiDAR techniques, namely, terrestrial laser scanning (TLS) and mobile laser scanning (MLS), are also developed vary fast. Thus, many researchers have been focusing on developing filtering algorithms for TLS or MLS data. [PERSON] et al. [32] proposed an adaptive filtering for TLS point clouds using morphological filters and spectral information. In their method, the morphological filtering windows can be adapted to different types and sizes of plants. Thus, a more accurate representation of the soil surface can be obtained. In order to improve the accuracy, robustness and efficiency of the filtering method, [PERSON] and [PERSON] [33] proposed a fast ground filter for TLS data via scan line density analysis. By evaluating the local point density within a scan line, the ground candidates are first separated. The region growth algorithm is then used to get a better ground points clustering results. MLS owns a similar scan geometry to TLS. The main difference between MLS and TLS is that the scanner of MLS keeps continuously moving. [PERSON] et al. [34] first organized the MLS data into vertical profiles and then candidate ground points were selected using an alpha shape algorithm. [PERSON] et al. [35] proposed a new filtering method to filtering ground surface points from MLS point clouds based on range constraint, slope constraint and angular position constraint. From the aforementioned studies, it can be seen that although most filtering algorithms can obtain good filtering performance, almost all the approaches need to predefine parameter thresholds. For example, in the simple morphological filter (SMRF) algorithm proposed by [PERSON] et al. [22], after optimizing the parameters, the filtering total error decreased from 4.40% to 2.97%. In the progressive morphological filtering method proposed by [PERSON] et al. [23], five parameters need to be set. Generally, optimized parameters always lead to a better filtering result. Conversely, optimizing parameters is always time consuming. Moreover, determining an optimized parameter is generally for inexperienced researchers. For these reasons, some filtering algorithms with good performance in the literature are hard to use in practice. To avoid complicated parameter settings, a statistical filtering algorithm called skewness balancing was developed by [PERSON] et al. [36]. In this unsupervised method, no parameters, such as a threshold or weighting factor, are required to be set. The algorithm can remove nonground points automatically. Moreover, this approach can achieve promising performance in flat areas. However, since this approach assumes that nonground points, such as building roofs, are always located above terrain, it is obvious that this method will cause a larger filtering error in fluctuating areas.