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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B7, 2012 
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia 
     
TENSOR-BASED QUALITY PREDICTION FOR BUILDING MODEL 
RECONSTRUCTION FROM LIDAR DATA AND TOPOGRAPHIC MAP 
B. C. Lin!*, R. J. You? 
Department of Geomatics, National Cheng Kung University, 1 University Road, Tainan City, Taiwan — 
! cclin0520(g gmail.com 
*rjyou@mail.ncku.edu.tw 
KEY WORDS: LiDAR, tensor analysis, robust least squares, data fusion, building model reconstruction 
ABSTRACT: 
A quality prediction method is proposed to evaluate the quality of the automatic reconstruction of building models. In this study, 
LiDAR data and topographic maps are integrated for building model reconstruction. Hence, data registration is a critical step for 
data fusion. To improve the efficiency of the data fusion, a robust least squares method is applied to register boundary points 
extracted from LiDAR data and building outlines obtained from topographic maps. After registration, a quality indicator based on 
the tensor analysis of residuals is derived in order to evaluate the correctness of the automatic building model reconstruction. Finally, 
an actual dataset demonstrates the quality of the predictions for automatic model reconstruction. The results show that our method 
can achieve reliable results and save both time and expense on model reconstruction. 
1. INTRODUCTION 
The airborne LiDAR technique has been extensively adopted 
for the purpose of quickly acquiring a large number of highly 
qualitative point clouds, and it has become widely implemented 
in 3D building models. LiDAR data provides an accurate 
representation of building surfaces, but since it has poor texture 
information, accurate building boundary extraction from 
LiDAR data may be difficult to obtain (Maas and Vosselman 
1999). Therefore, the building boundaries can be implemented 
by using additional data sources, such as 2D topographic maps. 
Since a data fusion of LiDAR data and 2D map information 
takes advantage of both surface and boundary information, a 
great many researchers have investigated it in order to 
reconstruct buildings (Maas and Vosselman 1999; Vosselman 
and Dijkman 2001; Filin 2002; Overby et al. 2004). In general, 
building roof patch features are first extracted from LiDAR data. 
Next, building models are reconstructed by combining the 
building boundaries obtained from ground plans and the 
intersection lines of adjacent planar faces derived from LiDAR 
data. 
However, the coordinate systems of LiDAR data and 2D maps 
are often different. To overcome the problem of coordinate 
systems of various data sources, data registration is a critical 
step for fusion of LiDAR data and the topographic map 
information (Schenk and Csatho 2002; Filin et al. 2005; Gruen 
and Akca 2005; Park et al. 2006). 
In this study, plane segments in LiDAR data are extracted in the 
feature space based on the tensor voting computational 
framework (Medioni et al. 2000). The tensor voting algorithm 
implements features such as faces, lines and points through a 
symmetric tensor field directly derived from data. All geometric 
structures (surfaces, lines and points) can therefore be inferred 
simultaneously. 
  
* Corresponding author. 
For data registration, the transformation parameters between 
LiDAR data and topographic maps are estimated using a robust 
least squares method (RLS). After registration, height 
information derived from LIDAR data is involved in 
topographic maps and then the spatial positions of building 
outlines can be reconstructed. To completely reconstruct a 3D 
building model, the roof ridges extracted from LiDAR data 
should be added (You and Lin 2011a). 
To achieve reliable results, a quality indicator derived from 
tensor analysis based on the residuals of the boundary point is 
introduced. The indicator can be use for checking the 
correctness of the building model in an automatic 
reconstruction process. Therefore, both time and expense on 
model reconstruction can be saved. 
In the following, the feature extraction based on the tensor 
voting method is first described. In section 3, the data 
registration and residual tensor analysis are address. Finally, the 
residual tensor on different building cases of actual airborne 
LiDAR dataset is analyzed. 
2. FEATURE EXTRACTION BASED ON TENSOR 
VOTING METHOD 
In this study, the tensor voting method (TVM) is adopted to 
extract roof faces from LiDAR data since this method can 
sufficiently consider the geometric relationships between 
surrounding points. In the TVM, a second order tensor field 
should be first constituted, and then planar features, namely 
roof faces, can be extracted from irregularly distributed LIDAR 
point clouds (You and Lin 2011a). 
The geometric feature of a point can be described by a second- 
order symmetric tensor which is expressed as follows: