传统激光雷达(light detection and ranging,LiDAR)数据处理均采用固定数的波形分解方法,容易遗漏部分重叠的返回波,降低波形拟合精度。为了实现可变数波形分解,本文提出了一种自动确定波形分解数的方法。假定波形数据服从混合高斯分布,并以此建立理想的波形模型;定义用于控制理想模型与实际波形拟合程度的能量函数,用吉布斯分布构建或然率;根据贝叶斯定理构建刻画波形分解的后验概率模型;设计可逆跳转马尔科夫链蒙特卡洛(reversible jump Markov chain Monte Carlo, RJMCMC)算法模拟该后验概率模型,以确定波形分解数并同时完成波形分解。为了验证提出算法的正确性,分别对不同区域的ICESat-GLAS波形数据进行了波形分解试验,定性和定量分析结果验证了本文方法的有效性、可靠性和准确性。
Full waveform LiDAR data record the signal of the backscattered laser pulse. The elevation and the energy information of ground targets can be effectively obtained by decomposition of the full waveform LiDAR data. Therefore, waveform decomposition is the key to full waveform LiDAR data processing. However, in waveform decomposition, determining the number of the components is a focus and difficult problem. To this end, this paper presents a method which can automatically determine the number. First of all, a given full waveform LiDAR data is modeled on the assumption that energy recorded at elevation points satisfy Gaussian mixture distribution. The constraint function is defined to steer the model fitting the waveform. Correspondingly, a probability distribution based on the function is constructed by Gibbs. The Bayesian paradigm is followed to build waveform decomposition model. Then a RJMCMC (reversible jump Markov chain Monte Carlo) scheme is used to simulate the decomposition model, which determines the number of the components and decomposes the waveform into a group of Gaussian distributions. In the RJMCMC algorithm, the move types are designed, including updating parameter vector, splitting or merging Gaussian components, birth or death Gaussian component. The results obtained from the ICESat-GLAS waveform data of different areas show that the proposed algorithm is efficient and promising.
[1] ZUO Zhiquan,ZHANG Zuxun,ZHANG Jianqing.A High-quality Filtering Method with Adaptive TIN Models for Urban LiDAR Points Based on Priori-knowledge[J]. Acta Geodaetica et Cartographica Sinica, 2012, 41(2): 246-251. (左志权, 张祖勋, 张剑清. 知识引导下的城区LiDAR点云高精度三角网渐进滤波方法[J]. 测绘学报, 2012, 41(2): 246-251.)
[2] SUI Lichun, ZHANG Yibin, LIU Yan, et al. Filtering of Airborne LiDAR Point Cloud Data Based on the Adaptive Mathematical Morphology[J]. Acta Geodaetica et Cartographica Sinica, 2010, 39(4): 390-396. (隋立春, 张熠斌, 柳艳, 等. 基于改进的数学形态学算法的LiDAR点云数据滤波[J]. 测绘学报, 2010, 39(4): 390-396.)
[3] PARRISH C E, NOWAK R D. Improved Approach to LiDAR Airport Obstruction Surveying Using Full-waveform Data[J]. Journal of Surveying Engineering, 2009, 135(2): 72-78.
[4] SUN G, RANSON K J. Modeling LiDAR Returns from Forest Canopies[J]. IEEE Transactions on Geoscience and Remote Sensing, 2000, 38(6): 2617-2626.
[5] MALLET C, BRETAR F. Full-waveform Topographic LiDAR: State-of-the-art[J]. ISPRS Journal of Photogrammetry and Remote Sensing, 2009, 64(1): 1-16.
[6] BLAIR J B, RABINE D L, HOFTON M A. The Laser Vegetation Imaging Sensor: A Medium-altitude, Digitisation-only, Airborne Laser Altimeter for Mapping Vegetation and Topography[J]. ISPRS Journal of Photogrammetry and Remote Sensing, 1999, 54(2-3): 115-122.
[7] SUN Guoqing, RANSON K J, ZHANG Zhongjun. Forest Vertical Parameters from LiDAR and Multi-angle Imaging Spectrometer Data[J]. Journal of Remote Sensing, 2006, 10(4): 523-530. (孙国清, RANSON K J, 张钟军. 利用激光雷达和多角度频谱成像仪数据估测森林垂直参数[J]. 遥感学报, 2006, 10(4): 523-530.)
[8] PANG Yong, LI Zengyuan, CHEN Erxue, et al. LiDAR Remote Sensing Technology and Its Application in Forestry[J]. Scientia Silvae Sinicae, 2005, 41(3): 129-136. (庞勇, 李增元, 陈尔学, 等. 激光雷达技术及其在林业上的应用[J]. 林业科学, 2005, 41(3): 129-136.)
[9] MEANS J E, ACKER S A, HARDING D J, et al. Use of Large-footprint Scanning Airborne LiDAR to Estimate Forest Stand Characteristics in the Western Cascades of Oregon[J]. Remote Sensing of Environment, 1999, 67(3): 298-308.
[10] BRENNER A C, ZWALLY H J, BENTLEY C R, et al. ATBD V3.0 Derivation of Range and Range Distributions from Laser Pulse Waveform Analysis for Surface Elevations, Roughness, Slope, and Vegetation Heights [J/OL]. http://glas.wff.nasa.gov.2000.
[11] SPAANS K H, RONSE A L A B. Reconstruction of an ICESat Full Waveform by Terrestrial and Airborne Laser Scanning[J]. Earth and Planetary Observation Letters, 2007, 3(20): 1-9.
[12] LI Qi, MA Hongchao. The Study of Point-cloud Production Method Based on Waveform Laser Scanner Data[J]. Acta Geodaetica et Cartographica Sinica, 2008, 37(3): 349-354. (李奇, 马洪超. 基于激光雷达波形数据的点云生产[J]. 测绘学报, 2008, 37(3): 349-354.)
[13] WANG Jinhu, LI Chuanrong, ZHOU Mei. Airborne Full-waveform LiDAR Data Processing and Application[J]. Foreign Electronic Measurement Technology, 2012, 31(6): 71-75, 79. (王金虎, 李传荣, 周梅. 机载全波形激光雷达数据处理及其应用[J]. 国外电子测量技术, 2012, 31(6): 71-75, 79.)
[14] HUG C, ULLRICH A, GRIMM A. Litemapper-5600-A Waveform-digitizing LiDAR Terrain and Vegetation Mapping System[J]. International Archives of Photogrammetry, Remote Sensing and Spatial Information Sciences, 2004, 36(8/W2): 24-29.
[15] WAGNER W, ULLRICH A, DUCIC V, et al. Gaussian Decomposition and Calibration of a Novel Small-footprint Full-waveform Digitising Airborne Laser Scanner[J]. ISPRS Journal of Photogrammetry and Remote Sensing, 2006, 60(2): 100-112.
[16] HOFTON M A, MINSTER J B, BLAIR J B. Decomposition of Laser Altimeter Waveforms[J]. IEEE Transactions on Geoscience and Remote Sensing, 2000, 38(4): 1989-1996.
[17] MA Hongchao, LI Qi. Modified EM Algorithm and Its Application to the Decomposition of Laser Scanning Waveform Data[J]. Journal of Remote Sensing, 2009, 13(1): 35-41. (马洪超, 李奇. 改进的EM模型及其在激光雷达全波形数据分解中的应用[J]. 遥感学报, 2009, 13(1): 35-41.)
[18] GREEN P J. Reversible Jump Markov Chain Monte Carlo Computation and Bayesian Model Determination[J]. Biometrika, 1995, 82(4): 711-732.
[19] WEN Hanjiang, CHENG Pengfei. Introduction to Principle of ICESAT/GLAS Laser Altimetry and Its Applications[J]. Science of Surveying and Mapping, 2005, 30(5): 33-35. (文汉江, 程鹏飞. ICESAT/GLAS激光测高原理及其应用[J]. 测绘科学, 2005, 30(5): 33-35.)
[20] SUN G, RANSON K J, KIMES D S, et al. Forest Vertical Structure from GLAS: An Evaluation Using LVIS and SRTM Data[J]. Remote Sensing of Environment, 2008, 112(1): 107-117.
[21] NELSON R, RANSON K J, SUN G, et al. Estimating Siberian Timber Volume Using MODIS and ICESat/GLAS[J]. Remote Sensing of Environment, 2009, 113(3): 691-701.
[22] MALLET C, LAFARGE F, ROUX M, et al. A Marked Point Process for Modeling LiDAR Waveforms[J]. IEEE Transactions on Image Processing, 2010, 19(12): 3204-3221.
