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This paper proposes a Gaussian mixture model of a ground filtering method based on hierarchical curvature constraints. Firstly, the thin plate spline function is iteratively applied to interpolate the reference surface. Secondly, gradually changing grid size and curvature threshold are used to construct hierarchical constraints. Finally, an adaptive height difference classifier based on the Gaussian mixture model is proposed. Using the latent variables obtained by the expectation-maximization algorithm, the posterior probability of each point is computed. As a result, ground and objects can be marked separately according to the calculated possibility. 15 data samples provided by the International Society for Photogrammetry and Remote Sensing are used to verify the proposed method, which is also compared with eight classical filtering algorithms. Experimental results demonstrate that the average total errors and average Cohen’s kappa coefficient of the proposed method are 6.91% and 80.9%, respectively. In general, it has better performance in areas with terrain discontinuities and bridges. Introduction Airborne light detection and ranging (lidar) systems measure the distance between the target and the instrument reference center through calculating the round-trip time of the laser pulse. When given the ground reference system, dense, geo-referenced, and accurate point clouds are generated (Meng et al. 2010). Compared with photogrammetric methods, lidar systems have the advantage of not being affected by the weather, being able to penetrate vegetation and obtain a large amount of spatial information efficiently (Meng et al. 2009). Currently, airborne lidar has been applied to many fields, including digital terrain model (DTM) construction (Chen et al. 2017; Ozcan and Unsalan 2017), three-dimensional building model generation (Yang et al. 2013; Huang et al. 2013; Zhou and Zhou 2014), road extraction (Hui et al. 2016), forest stand parameters estimation (Hyyppä et al. 2012), forest and urban vegetation biomass estimation (Shao et al. 2017; Zhang et al. 2019; Zhang and Shao 2021), etc. In most applications, to distinguish ground and nonground objects from lidar measurements, filtering must be performed. Airborne lidar technology has revolutionized the way to acquire DTM/digital surface model (DSM) due to its high efficiency, high precision, and penetrability (Mongus et al. 2014; Zhang et al. 2016). In recent years, many scholars have proved the effectiveness of lidar derived elevation modeling (Hingee et al. 2019; Vassilaki and Stamos 2020). Since the airborne lidar system provides an optimal solution for large-area, high-resolution terrain surface surveying and mapping, many studies have focused on using lidar data to extract terrain information. To construct DTM, one critical step is to filter out nonground point clouds, including those on bridges, buildings, vegetation, etc. Although the airborne lidar system can acquire a massive amount of data in a short time, the processing of lidar data requires a high time cost. According to previous research, about 60–80% of the postprocessing time is spent on manual filtering and classification (Flood 2001). Hence, it is invaluable to improve the efficiency of lidar filtering algorithms and reduce the complexity of parameter adjustment. Many researchers have proposed dozens of filtering algorithms in the past two decades. However, accurate filtering still remains a challenge. A comparative experiment was conducted by Sithole and Vosselman (2004) to test the performance of eight classic filtering methods in both city and rural sites. They pointed out that the eight algorithms filter precisely in flat rural scenes. However, the results of all filters are not satisfactory in urban regions with variant terrains. On the whole, surface-based filters produce better results in terms of filtering strategy. It is because they use more contextual information of lidar data than other filters. Since then, the 15 sample data sets have become a benchmark for testing the accuracy and performance of ground filtering algorithms. Most of the existing filtering algorithms need to adjust parameters according to the complex terrain environment, which is not user friendly. Our algorithm is based on the surface Photogrammetric Engineering & Remote Sensing Vol. 87, No. 9, September 2021, pp. 615–630. 0099-1112/21/615–630 © 2021 American Society for Photogrammetry and Remote Sensing doi: 10.14358/PERS.87. 20-00080 Ka Zhang, Yehua Sheng are with the Key Laboratory of Virtual Geographic Environment (Nanjing Normal University) of Ministry of Education, School of Geography, Nanjing Normal University, the Jiangsu Center for collaborative Innovation in Geographical Information Resource Development and Application, the State Key Laboratory Cultivation Base of Geographical Environment Evolution (Jiangsu Province), No.1, Wenyuan Road, Nanjing, China; and the Key Laboratory of Urban Land Resources Monitoring and Simulation of Ministry of Natural Resources, No. 69, News Road, Shenzhen, China (zhangka81@126.com; shengyehua@njnu.edu.cn). Longjie Ye, Dong Su, Pengbo Wang, Shan Zhang and Na Zhao are with the Key Laboratory of Virtual Geographic Environment (Nanjing Normal University) of Ministry of Education, School of Geography, Nanjing Normal University, No.1, Wenyuan Road, Nanjing, China. Wen Xiao is with the School of Engineering, Newcastle University, NE1 7RU, Newcastle upon Tyne, United Kingdom (co-first author). Hui Chen is with the School of Geography and Ocean Science, Nanjing University, No. 163, Xianlin Avenue, Nanjing, China. Contributed by Zhenfeng Shao, August 28, 2020 (sent for review January 14, 2021; reviewed by Nan Yang, Bin Hu). PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING September 2021 615 filtering strategy and provides a set of more general parameters for filtering. The adjustment in the parameter is handed over to the expectation-maximization (EM) algorithm for automatic optimization. Therefore, our algorithm makes the task easier for inexperienced users. In this paper, an adaptive height difference classifier based on the Gaussian mixture model is proposed to maximize filter efficiency in areas with terrain discontinuities or steep slope. Compared with previous work (Hui et al. 2019), our approach has mainly two innovative points: (1) It uses the thin plate spline (TPS) function instead of low-order polynomial coefficients for iterative surface interpolation. Therefore, the proposed method can better fit the terrain. It is worth noting that only ground control points are used in the fitting process. (2) While solving the Gaussian mixture model, hierarchical curvature results are applied to initialize the probabilistic model parameters. In order to classify more accurately, the relative elevation is substituted into the Gaussian mixture model. By computing the posterior probability of each point, we can determine which lidar point belongs to the ground. Since the subsequent optimization process is based on probabilistic reasoning, the algorithm does not require a prior knowledge for parameter adjustment. Moreover, it can well overcome the influence of terrain gradient through the interpolation surface constructed by TPS. Related Work There are mainly four types of methods to filter airborne lidar point clouds: slope comparison, mathematical morphology, surface interpolation, and segmentation strategies. Alternatively, it is a wise strategy to choose a combination of several of them to filter the point cloud. For example, Chen et al. (2016) first used the regional growth method to obtain more ground seeds and then applied a surface interpolation method to filter out objects from the original lidar measurement. Hui et al. (2016) adopted Kriging interpolation to construct a surface corresponding to the change morphology window. In their method, the slope gradient based on the constructed surface is combined with the morphological opening operation for filtering. The results show that their approach can well preserve the detailed features of the terrain. Vosselman (2000) first adopted the slope of the line between two points in the lidar point clouds and set a threshold for filtering. This method is based on the hypothesis that the gradient of the ground will be much smaller than that of nonterrain (bridges, trees, etc.). However, this hypothesis limits the application of this method to gentle slope terrains. To overcome this limitation, many filters with an adaptive slope threshold have been proposed. Such filtering methods include the adaptive parameter approaches (Sithole 2001; Tseng et al. 2004; Susaki 2012), knowledge classifiers (Wang and Shan 2009), and directional filters (Wang and Tseng 2010). Generally, the slope-based method can perform well in areas where the gradient of the slope changes gently. However, it will fail in terrain where the slope varies sharply (cliffs) (Mongus and Žalik 2012). Furthermore, because contextual information of lidar point clouds other than slope is not considered, these methods will become unreliable in complex terrains. By rasterizing lidar data and taking the elevation as the gray value of a raster image, the morphological method can be transferred and applied to the filtering. In this type of filtering algorithm, morphological opening operations are widely used. Under the premise of the constant slope, Zhang et al. (2003) adopted a combined filtering strategy of gradually increasing morphological structural elements and height difference threshold. In each iteration, the first step is to use the open operation of the current structure element to obtain the filtered grid gray value. Then, by calculating the difference with the original grid elevation value and comparing it with the height difference threshold, ground points are selected if less than the threshold. Chen et al. (2007) considered that the slope of the real terrain is not constant, and t