# An Improved Skewness Balancing Filtering Algorithm Based on Thin Plate Spline Interpolation
## 1 Introduction  
In recent decades, the airborne light detection and ranging (LiDAR) technique has developed very quickly and become an one important means for acquiring remote sensing data [1; 2]. The airborne LiDAR system is generally composed of a laser scanner, a global positioning system (GPS) and an inertial measurement unit (IMU) [3]. With these three components cooperating with each other, a large amount of LiDAR point clouds reflected from the ground and objects (cars, trees, buildings, etc.) can be obtained. Compared with traditional remote sensing methods, such as photogrammetric mapping, airborne LiDAR has the following advantages: (1) the external environment has little influence on the LiDAR technique; thus, an airborne LiDAR system can generally work in any environment and all-weather conditions; (2) LiDAR can describe the earth surface with a large number of points,which is beneficial for modeling; and (3) LiDAR pulses can penetrate the tree canopy, which makes this technique convenient for detecting topography in forest areas [4; 5; 6; 7]. Owing to these advantages, airborne LiDAR has been applied to many applications, such as three-dimensional building model construction [8; 9], power line inspection [10], change detection [11], and land cover classification [12]. To realize these applications, one key step is to obtain a digital terrain model (DTM). In other words, ground points should be separated from object points first. This process is called filtering. In the past two years, many researchers have been making efforts in this area, and diverse algorithms have been presented. These filtering algorithms can be classified into four categories: slope-based [13; 14; 15; 16; 17], morphology-based [18; 19; 20; 21; 22; 23], triangular irregular network (TIN)-based [24; 25; 26; 27] and segmentation-based [28; 29; 30] filtering algorithms. The slope-based filtering algorithm was first proposed by [PERSON] [14]. He assumed that terrain does not change greatly. That is, if the slope between two adjacent points is greater than a given threshold, there must be one point that belongs to an object. However, this assumption is false when encountering undulating terrain, such as cliffs or ridges. To solve this problem, [PERSON] [17] modified this method by adjusting thresholds based on local terrain. This improvement enables this method to achieve promising results in complicated environments. Morphology-based filtering algorithms always adopt progressive strategies. The filtering thresholds are adaptively calculated as the filtering window changes gradually [23]. The main problem for this kind of approach is how to set an appropriate filtering window. A larger filtering window flattens terrain details, while a smaller filtering window cannot filter larger objects, such as building roofs. [PERSON] et al. [7] improved the progressive morphology approach by combining it with multilevel Kriging interpolation. As a result, a smaller filtering error was achieved. TIN-based approaches utilize a progressive manner to realize filtering. First, some located lowest points are selected as seed points and a rough TIN surface is built based on these ground seeds. Then, the iteration angle and distance of each point are calculated according to the TIN. The points are added to the TIN if their iteration angle and distance are less than the predefined thresholds. This process is iterated until no more points meet the requirements [24]. The built TIN is changed from coarser to finer while the filtering accuracy is progressively improved. Conversely, the initial built TIN has a great influence on the final filtering result. If the initial ground seeds are not selected correctly, the final filtering results will have a larger filtering error. To resolve this problem, [PERSON] et al. [26] applied morphological opening operations to obtain more potential ground seeds. Their experimental results show that this improvement enhances the robustness of this traditional method.