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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: