空載雷射測距技術(光達)能夠快速且精確的對大範圍區域進行掃描，以獲
取高解析度的地貌資訊，光達測繪技術已被廣泛的應用到遙測相關領域以及其
他相關應用。而點雲分類是點雲資料處理流程中一個相當重要的步驟，其分類
成果可用於製作數值地表模型、數值高程模型以及三維都市建模等應用。在點
雲分類的議題中，已有多篇相關之研究被提出，但由於不同物體在特定狀況下
可能具有類似的特性，因此分類精度之提升仍有值得討論的空間。分類成果的
優劣取決於使用之特徵(features)是否能有效地辨別不同物體，因此本篇研究著
重於建立可以充分描述物件幾何性質的特徵，以提升點雲分類的精度。在已知
用於點雲分類的特徵中，幾何特徵(eigenfeatures)可描述光達點雲的分布是趨近
於線狀(1D)、面狀(2D)或者是近似球狀分布(3D)。該種類的特徵一般是由樣本
共變異數矩陣(sample covariance matrix)以及樣本平均值(sample mean)計算求得。
然而，幾何特徵的計算容易受到點雲取樣分布以及資料中存在之大錯的影響，
進而使其計算成果不準確。因此，本研究提出一基於加權共變異數矩陣
(weighted covariance matrix)以及加權平均(weighted mean)之方法，用以計算更
為可靠的幾何特徵。由實驗結果顯示，無論是定量或定性分析，本研究所提出
的方法所計算之幾何特徵較傳統方法更加穩定、可靠，且分類成果也有所改善。

Light Detection and Ranging (LiDAR) sensors with the ability of acquiring high
spatial resolution and accuracy 3D data over a large area is increasingly being used
in the fields of remote sensing and surveying with many applications. The
classification of airborne LiDAR data is a fundamental and critical process in the
related applications such as digital terrain/elevation model (DTM/DEM) generation
and three-dimensional urban modeling. Although researchers have proposed many
classification methods for LiDAR data, the problem has not been fully solved due to
the similar characteristics possessed by different objects such as ground and nonground
objects. One of the keys to a successful classification is the features as well
as the feature space used in the separation of different objects. Therefore, this study
aims to develop advanced features to well describe the geometric characteristics of
objects for improving the classification accuracy. Among existing features,
eigenfeatures calculated from sample covariance matrix with sample mean are
popular in geometric description of LiDAR data. They can describe the local
geometric characteristics of a point cloud and indicate whether the local geometry is
linear, planar or spherical. However, they suffer from certain drawbacks; notably,
they are not robust statistics, meaning that they are sensitive to the sampling and the
outliers of data. To obtain reliable eigenfeatures from LiDAR data with sparse, noisy,
and incomplete sampling, we introduce a novel method to calculate and obtain
eigenfeatures based on weighted covariance matrix and weighted mean. Each point
in a neighborhood of tensor structure is assigned a weigh to balance the spatial
contributions of points. In the experiments, qualitative and quantitative analyses on
airborne LiDAR data show a clear superiority of the proposed method over the
III
classification using standard eigenfeatures.

Antonarakis A. S., Richards K. S., and Brasington J. (2008), “Object-based land
cover classification using airborne LiDAR,” Remote Sensing of Environment,
112, pp. 2988~2998.
Aurenhammer, F., and Klein, R. (2000), “Voronoi Diagrams, Ch. 5” in Handbook of
Computational geometry, Ed. J.-R Sack and J. Urrutia, Amsterdam Netherland:
North-Holland, pp. 201~290.
Axelsson, P. (1999), “Processing of laser scanner data — algorithms and applications,”
ISPRS Journal of Photogrammetry and Remote Sensing, 54, pp. 138−147.
Axelsson, P. (2000), “DEM generation from laser scanner data using adaptive TIN
models,” International Archives of the Photogrammetry, Remote Sensing and
Spatial Information Sciences, vol. XXXIII, pp. 110~117.
Bartels, M., and Wei, H. (2006), “Rule-based improvement of maximum likelihood
classified LIDAR data fused with co-registered bands,” Annual Conference of
the Remote Sensing and Photogrammetry Society, pp. 1~9.
Bartels, M., and Wei, H. (2010), “Threshold-free object and ground point separation
in LiDAR data,” Pattern Recognition Letters, 31, pp. 1089~1099.
Bishop, C. (2006). Pattern Recognition and Machine Learning, New York, Inc.
Secaucus, NJ, USA: Springer-Verlag.
Bork, E. W., and Su, J. G. (2007), “Integrating LIDAR data and multispectral imagery
for enhanced classification of rangeland vegetation: a meta analysis,” Remote
Sensing of Environment, 111 (1), pp. 11~24.
Brodu, N., and Lague, D. (2012), “3D terrestrial lidar data classification of complex
natural scenes using a multi-scale dimensionality criterion: Applications in geomorphology,” ISPRS Journal of Photogrammetry and Remote Sensing, 68,
pp. 121~134.
Carlberg, M., Gao, P., Chen, G., and Zakhor, A. (2009), “Classifying urban landscape
in aerial LiDAR using 3D shape analysis,” 16th IEEE International Conference
on Image Processing, pp. 1701~1704.
Castillo, E., and Zhao, H. (2009). “Point cloud segmentation via constrained
nonlinear least squares surface normal estimates,” Technical report, UCLA.
Chang, C.-C., Lin, C.-J. (2001), LIBSVM: a library for support vector machines.
Software available at: <http://www.csie.ntu.edu.tw/~cjlin/libsvm>.
Charaniya, A., Manduchi, R. and Lodha, S. (2004), “Supervised parametric
classification of aerial lidar data,” In: Real-Time 3D Sensors and their Use
Workshop, in conjunction with IEEE CVPR, pp. 30~37.
Chen, H. (2002), “Principal Component Analysis with Missing Data and Outliers,”
Technical Report, Electrical and Computer Engineering Department Rutgers
University, Piscataway, NJ.
Choi, Y., Jang, Y., Lee, H. and Cho, G. (2008), “Three-Dimensional LiDAR Data
Classifying to Extract Road Point in Urban Area,” IEEE Geoscience and
Remote Sensing Letters, 5 (4), pp. 725~729.
Cobby, D. M., Mason, D. C., and Davenport, I. J. (2001), “Image processing of
airborne scanning laser altimetry for improved river flood modelling,” ISPRS
Journal of Photogrammetry and Remote Sensing, 56 (2), pp. 121~138.
Cobby, D.M., Mason, D. C., Horritt, M. S., and Bates, P. D. (2003), “Twodimensional
hydraulic flood modelling using a finite element mesh decomposed
according to vegetation and topographic features derived from airborne scanning
laser altimetry,” Hydrological Processes, 17, pp. 1979~2000.
Demantke, J., Mallet, C., David, N., and Vallet, B. (2011), “Dimensionality based
scale selection in 3D LiDAR point cloud,” International Archives of the
Photogrammetry, Remote Sensing and Spatial Information Sciences, vol.
XXXVIII, pp. 97~102.
Ducic, V., Hollaus, M., Ullrich, A., Wagner, W. and Melzer, T. (2006), “3D
Vegetation mapping and classification using fullwaveform laser scanning,” In:
EARSeL and ISPRS Workshop on 3D Remote Sensing in Forestry, Vienna,
Austria, pp. 211~217.
Elmqvist, M., Jungert, E., Lantz, F., Persson, Å., and Söderman, U. (2001), “Terrain
modelling and analysis using laser scanner data,” International Archives of the
Photogrammetry, Remote Sensing and Spatial Information Sciences, vol.
XXXIV, pp. 219~227.
Flood, M. (2001), “LIDAR activities and research priorities in the commercial sector,”
International Archives of Photogrammetry and Remote Sensing, vol. 34 (3), pp.
3~7.
Gressin, A., Mallet, C., Demantké, J., and David, N. (2013), “Towards 3D lidar point
cloud registration improvement using optimal neighborhood knowledge,”
ISPRS Journal of Photogrammetry and Remote Sensing, 79, pp. 240~251.
Gross, H., and Thoennessen, U. (2006), “Extraction of Lines from Laser Point
Clouds,” International Archives of the Photogrammetry, Remote Sensing and
Spatial Information Sciences, vol. XXXVI, pp. 86~91.
Gross, H., Jutzi, B. and Thoennessen, U. (2007), “Segmentation of tree regions using
data of a full-waveform laser,” In: ISPRS Conference Photogrammetric Image
Analysis (PIA), Vol. 36, IAPRS, Munich, Germany.
Haala, N. and Brenner, C. (1999), “Extraction of buildings and trees in urban
environments,” ISPRS Journal of Photogrammetry & Remote Sensing, 54 (2-3),
pp. 130~137.
Lodha, S., Kreps, E., Helmbold, D., and Fitzpatrick, D. (2006), “Aerial LiDAR Data
Classification Using Support Vector Machines (SVM),” In: IEEE Proceedings
of the International Symposium on 3D Data Processing Visualization, and
Transmission, Chapel Hill, NC, pp. 567~574.
Lohmann, P., Koch, A., and Schaeffer, M. (2000), “Approaches to the filtering of
laser scanner data,” International Archives on Photogrammetry and Remote
Sensing, vol. 33, pp. 540~547.
Luo, C., Safa, I., and Wang, Y. (2009), “Approximating gradients for meshes and
point clouds via diffusion metric,” SGP '09 Proceedings of the Symposium on
Geometry Processing, Aire-la-Ville, Switzerland, pp. 1497~1508.
Mallet, C., Bretar, F., Roux, M., Soergel, U., and Heipke, C. (2011), “Relevance
assessment of full-waveform lidar data for urban area classification,” ISPRS
Journal of Photogrammetry and Remote Sensing, 66 (6), pp. S71~S84.
Matikainen, L., Kaartinen, H. and Hyyppä, J. (2007), “Classification tree based
building detection from laser scanner and aerial image datas,” International
Archives of Photogrammetry, Remote Sensing and Spatial Information Sciences,
vol. 36 (Part 3/W52), pp. 280~287.
Meng, X., Wang, L., Silvan, J., and Currit, N. (2009), “A multi-directional ground
filtering algorithm for airborne LIDAR,” ISPRS Journal of Photogrammetry and
Remote Sensing, 64 (1), pp. 117~124.
Merigot, Q., Ovsjanikov, M., and Guibas, L. (2011), “Voronoi-Based Curvature and
Feature Estimation from Point Clouds,” IEEE Transactions on Visualization and Computer Graphics, 17 (6), pp. 743~756.
Mountrakis, G., Im, J., and Ogole, C. (2011), “Support vector machines in remote
sensing: A review,” ISPRS Journal of Photogrammetry and Remote Sensing, 66
(3), pp. 247~259.
Roggero, M. (2001), “Airborne laser scanning: Clustering in raw data,” International
Archives of the Photogrammetry, Remote Sensing and Spatial Information
Sciences, vol. XXXIV, pp. 209~210.
Rusu, R., and Cousins, S. (2011), “3D is here: Point Cloud Library (PCL),” IEEE
International Conference on Robotics and Automation (ICRA), Shanghai, China,
May 2011, pp. 1~4.
Rottensteiner, F., Trinder, J., Clode, S. and Kubik, K. (2005), “Using the dempstershafer
method for the fusion of lidar data and multi-spectral images for building
detection,” Information Fusion, 6 (4), pp. 283~300.
Rutzinger, M., Höfle, B., Hollaus, M., and Pfeifer, N. (2008), “Object-Based Point
Cloud Analysis of Full-Waveform Airborne Laser Scanning Data for Urban
Vegetation Classification,” Sensors, 8 (8), pp. 4505~4528.
Samadzadegan, F., Bigdeli, B., and Ramzi., P. (2010), “Classification of LiDAR data
based on multi-class SVM,” International Archives of the Photogrammetry,
Remote Sensing and Spatial Information Sciences, vol. XXXVIII, pp. 1~6.
Sampath, A., and Shan, J. (2010), “Segmentation and Reconstruction of Polyhedral
Building Roofs From Aerial Lidar Point Clouds,” IEEE Transactions on
Geoscience and Remote Sensing, 48 (3), pp. 1554~1567.
Secord, J. and Zakhor, A., (2007), “Tree detection in urban regions using aerial lidar
and image data,” IEEE Geoscience and Remote Sensing Letters 4 (2), pp.
196~200.
Seversky, L., Bergera, M., and Yin, L. (2011), “Harmonic point cloud orientation,”
Computers & Graphics, 35 (3), pp. 492~499.
Sithole, G. (2001), “Filtering of laser altimetry data using a slope adaptive filter,”
International Archives of the Photogrammetry, Remote Sensing and Spatial
Information Sciences, vol. XXXIV, pp. 203~210.
Sithole, G., and Vosselman, G. (2004), “Experimental comparison of filter algorithms
for bare-Earth extraction from airborne laser scanning point clouds,” ISPRS
Journal of Photogrammetry and Remote Sensing, 59 (1-2), pp. 85~101.
Sohn, G., and Dowman, I. (2002), “Terrain surface reconstruction by the use of
tetrahedron model with the MDL Criterion,” International Archives of the
Photogrammetry, Remote Sensing and Spatial Information Sciences, vol.
XXXIV, pp. 225~344.
Song, J. H., Han, S. H., Yu, K. Y., and Kim, Y. I. (2002), “Assessing the possibility
of land-cover classification using lidar intensity data,” Photogrammetric
Computer Vision Symposium 2002, ISPRS Commission III, vol. B, pp. 259~263.
Stanimirova, I., Daszykowski, M., and Walczak, B. (2007), “Dealing with missing
values and outliers in principal component analysis,” Talanta, 72 (1), pp.
172~178.
Stassopoulou A. and Caelli T. (2000), “Building Detection Using Bayesian
Networks,” International Journal of Pattern Recognition and Artificial
Intelligence, vol. 83, pp. 715~733.
Stow, D., Lopez, A., Lippitt, C., Hinton, S., and Weeks, J. (2007), "Object-based
classification of residential land use within Accra, Ghana based on QuickBird
satellite data,” International Journal of Remote Sensing, 28 (22), pp. 5167~5173.
Sun, W., Heidt, V., Gong, P., and Xu, G. (2003), “Information fusion for rural land-use classification with high-resolution satellite imagery,” IEEE Transactions on
Geoscience and Remote Sensing, 41 (4), pp. 883~890.
Vardi, Y., and Zhang, C.-H, (2000), “The Multivariate L1-Median and Associated
Data Depth,” Proceedings of the National Academy of Sciences of the United
States of America, 97, pp. 1423~1426.
Vohland, M., Stoffels, J., Hau, C., and Schuler, G. (2007), “Remote sensing
techniques for forest parameter assessment: multispectral classification and
linear spectral mixture analysis,” Silva Fennica, 41 (3), pp. 441−456.
Vosselman, G. (2000), “Slope based filtering of laser altimetry data,” International
Archives of Photogrammetry and Remote Sensing, vol. 33 (B3/2), pp. 935~942.
Wagner, W., Hollaus, M., Briese, C. and Ducic, V. (2008), “3D vegetation mapping
using small-footprint full-waveform airborne laser scanners”, International
Journal of Remote Sensing, 29 (5), pp. 1433~1452.