空載全波形光達為一主動式遙測系統，除了可快速取得地表之三維坐標外，還可將雷射回傳能量值透過密集取樣紀錄成連續波形。透過對回波的模擬與分析，可進一步推算雷射光束所涵蓋的範圍內地表物的物理特性，提供使用者豐富的資訊應用於地形三維重建與地物辨識之依據。
在應用全波形光達資料於地物分類時，首先須先對波形進行擬合(fitting)，進而分析其特性。本研究將濾除背景雜訊後的波形資料，以立方平滑雲線的方式進行擬合，透過二次微分法偵測波形波峰並萃取波形參數，包括波寬(width)、振幅(amplitude)。在波形存有多重回波的情況，可從中萃取多重回波特徵包括第一與最後回波之時間差、波峰數、平均振幅。利用萃取出的波形參數，配合正規化高程(normalized height)、強度(intensity)做為地物分類的特徵。本研究使用隨機森林(random forest)作為分類器，並將分類成果與常用的高斯分解法做比較，藉此探討立方平滑雲線應用於全波形光達資料的成效。
本研究結果顯示，立方平滑雲線相較與高斯法擬合誤差較小，並保留了更多波形資訊。在地物分類的部分，在容易混淆的建物邊緣與樹林，多重回波特徵能提高其分類精度。另外相較於高斯，立方平滑雲線除了分類精度較優外，能以更快速的方式來計算特徵，適合於擁有大量資料的全波形光達。

Airborne Full-Waveform LiDAR (FW) is an active remote sensing system. It not only provides the three-dimensional coordinates about the ground objects but also record the whole return signal as the waveform. The physical properties of objects in a ray can be obtained by fitting and analyzing the waveform. It offers useful information to user for three dimensional reconstruction and land cover distinguishing.
In the processing of FW LiDAR data for land-cover classification, the waveform fitting and analysis are the first steps. In this study, the waveform data was fitted by cubic smoothing spline after eliminating the background noise. The amplitude and width was derived based on the peaks detected by second derivative method. In the case of the waveform with the multiple returns, the feature such as time difference of first and last return, peak numbers, and average amplitude was obtained. These waveform parameters combined with intensity and normalized height was utilized as the features for land-cover classification. The classifier used in this study was Random Forest. In order to discuss the effect of cubic smoothing spline, the classification result was compared to the Gaussian decomposition method which is a popular method in full-waveform application.
The experimental results indicate that cubic smoothing spline provide the smaller fitting error and keep more information in the waveform. The land cover classification results demonstrate that the multiple return features are helpful for the building edge and trees which are easily misclassified. In addition, cubic smoothing spline is suitable for full-waveform Lidar data with the better classification result and efficiency.

林郁珊，2012，應用空載全波形光達資料於波形分析與地物分類，碩士論文，國立交通大學土木工程學系。
盧佑樺，2013，二次微分法於空載全波形光達之特徵萃取與地物分類，碩士論文，國立中央大學土木工程學系。
Breiman, L. (2001). Random forests. Machine Learning, 45(1), 5-32.
Bretar, F., Chauve, A., Mallet, C., & Jutzi, B. (2008). Managing full-waveform lidar data: a challenging task for the forthcoming years. In: International Archive of Photogrammetry, Remote Sensing and Spatial Information Sciences, Beijing, China. XXXVII (Part B1), 415-420
Celis, M. R. (1985). A trust region strategy for nonlinear equality constrained optimization (nonlinear programming, sequential quadratic). (Ph.D. thesis), University Micriofilms International. Retrieved　July 19, 2014,from http://scholarship.rice.edu/handle/1911/15885
Chauve, A., Mallet, C., Bretar, F., Durrieu, S., Pierrot-Deseilligny, M., & Puech, W. (2007). Processing Full-waveform LiDAR Data: Modelling Raw Signals. In: ISPRS Workshop on Laser Scanning and SilviLaser, Espoo, Finland. XXXVI (Part 3/W52), 102-107.
Chauve, A., Vega, C., Durrieu, S., Bretar, F., Allouis, T., Deseilligny, M. P., & Puech, W. (2009). Advanced full-waveform lidar data echo detection: Assessing quality of derived terrain and tree height models in an alpine coniferous forest. International Journal of Remote Sensing, 30(19), 5211-5228.
Dempster, A.P., Laird, N.M., & Rubin, D.B. (1977). Maximum Likelihood from Incomplete Data via the EM Algorithm. Journal of the Royal Statistical Society. Series B (Methodological), 39, 1-38.
Fieber, K.D., Davenport, I.J., Ferryman, J.M., Gurney, R.J., Walker, J.P., Hacker, J.M. (2013). Analysis of full-waveform LiDAR data for classification of an orange orchard scene. Isprs Journal of Photogrammetry and Remote Sensing, 82(0), 63-82.
Guo, L., Chehata, N., Mallet, C., & Boukir, S. (2011). Relevance of airborne lidar and multispectral image data for urban scene classification using Random Forests. Isprs Journal of Photogrammetry and Remote Sensing, 66(1), 56-66.
Hovi, A., Korpela, I. (2014). Real and simulated waveform-recording LiDAR data in juvenile boreal forest vegetation. Remote Sensing of Environment, 140, 665-678.
Jutzi, B., Stilla, U. (2006). Range determination with waveform recording laser systems using a Wiener Filter. Isprs Journal of Photogrammetry and Remote Sensing,61(1), 95-107.
Leica. (2014). Leica ALS70. Retrieved July 18, 2014, from http://www.leica-geosystems.com/en/Leica-ALS70-Airborne-Laser-Scanner_94516.htm
Levenberg, K. (1944). A method for the solution of certain problems in least squares Quart. Applied Math., 2, 164-168.
Lin, Y. C., Mills, J. P., & Smith-Voysey, S. (2010). Rigorous pulse detection from full-waveform airborne laser scanning data. International Journal of Remote Sensing, 31(5), 1303-1324.
Mallet, C., Bretar, F. (2009). Full waveform topographic lidar: State-of-the-art. Isprs Journal of Photogrammetry and Remote Sensing,64(1), 1-16.
Mallet, C., Bretar, F., Roux, M., Soergel, U., & Heipke, C. (2011). Relevance assessment of full-waveform lidar data for urban area classification. Isprs Journal of Photogrammetry and Remote Sensing, 66(6), S71-S84.
Mallet, C., Lafarge, F., Bretar, F., Roux, M., Soergel, U., & Heipke, C. (2009). A stochastic approach for modelling airborne lidar waveforms. In: Laserscanning, Paris, France. XXXVIII, 201-206.
Marquardt, D.W. (1963). An algorithm for least-squares estimation of nonlinear parameters. Journal of the Society for Industrial and Applied Mathematics, 11(2), 431-441.
Mücke, W. (2008). Analysis of full-waveform airborne laser scanning data for the improvement of DTM generation. (Master's thesis), Vienna University of Technology. Retrieved July 19, 2014, from http://publik.tuwien.ac.at/files/PubDat_170289.pdf
Optech. (2014). ALTM Pegasus. Retrieved July 19, 2014, from
http://www.optech.com/index.php/product/pegasus-altm/
Riegl. (2014). LMS-Q560. Retrieved July 19, 2014, from
http://www.riegl.com/uploads/tx_pxpriegldownloads/10_DataSheet_Q560_20-09-2010_01.pdf
Riegl. (2014). LMS-Q680i. Retrieved July 19, 2014, from
http://www.riegl.com/nc/products/airborne-scanning/produktdetail/product/scanner/23/
Roncat, A., Bergauer, G., & Pfeifer, N. (2011). B-spline deconvolution for differential target cross-section determination in full-waveform laser scanning data. Isprs Journal of Photogrammetry and Remote Sensing, 66(4), 418-428.
Trimble. (2014). Trimble AX80. Retrieved July 19, 2014,from
http://www.trimble.com/imaging/AX80.aspx?dtID=overview&
Tsai, F., & Philpot, W. (1998). Derivative analysis of hyperspectral data. Remote Sensing of Environment, 66(1), 41-51.
Wagner, W., Ullrich, A., Ducic, V., Melzer, T., & Studnicka, N. (2006). Gaussian decomposition and calibration of a novel small-footprint full-waveform digitising airborne laser scanner. Isprs Journal of Photogrammetry and Remote Sensing, 60(2), 100-112.

Wagner, W., Ullrich, A., Melzer, T., Briese, C., & Kraus, K. (2004). FROM SINGLE-PULSE TO FULL-WAVEFORM AIRBORNE LASER SCANNERS: POTENTIAL AND PRACTICAL CHALLENGES. In: International Archives of Photogrammetry, Remote Sensing and Spatial Information Sciences. 35, 201-206 (Part B203)
Yao, W., Krzystek, P., Heurich, M. (2012). Tree species classification and estimation of stem volume and DBH based on single tree extraction by exploiting airborne full-waveform LiDAR data. Remote Sensing of Environment, 123, 368-380.