The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
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corresponding points are considered as pseudo-conjugate points, 
and the best estimated calibration parameters are obtained when 
the distance between two points are minimized. 
Figure 4 shows that the ICP procedure is used to sequentially 
identify pseudo-conjugate points in the datasets, which are then 
used to estimate the calibration parameters for the airborne 
system. The iterative procedure will continue until there are no 
significant changes in the estimated parameters. 
f 
' 0 Î 
= *0J + R (0<t>K _i^ + R CO<l>K _iR\CD&<jAK R ß _i 
0 
V 
.-Pi[ 
patch are used as alternative primitives, and the adapted 
constraints for the calibration is the determinant of the four 
points: three points of the triangular patch and the point of 
irregular point data. Equation 3 shows the mathematical form of 
the determinant of four points; where X R , X R , and X R are 
vertices of triangular patch, and xj denotes the corresponding 
point from the airborne LiDAR data. The best estimated 
calibration parameters are obtained when the determinants are 
minimized. 
Figure 4 shows that the ICPatch method is used to sequentially 
identify conjugate point/patch pairs in the both datasets, and the 
recursive adjustment procedure will continue until there are no 
significant changes in the estimated calibration parameters. 
2.2 Point/Patch Primitives and ICPatch method 
For instances where no point-to-point correspondence between 
the terrestrial and airborne datasets can be assumed, one should 
consider alternative primitives for the calibration procedure. 
Instead of distinct points, one can use areal features, which can 
be identified in both data: calibration data and reference data. 
Such primitives, however, would require pre-processing of the 
LiDAR point cloud to extract areal features (e.g., segmentation, 
and plane fitting). In this research, we aim at selecting 
primitives, which can be derived with minimal pre-processing 
of the original LiDAR footprints. Moreover, the selected 
primitives should be reliably derived in any type of 
environment (e.g., urban and rural areas). To satisfy these 
objectives, we chose to represent airborne LiDAR data using 
the original footprints, while terrestrial LiDAR data is 
represented by triangular patches, which can be derived from a 
Triangulated Irregular Network (TIN) generation procedure. 
Figure 3 illustrates the case where the airborne LiDAR data 
denoted by X T is represented by a set of points while the 
terrestrial LiDAR denoted by X R is represented by a set of 
triangular patches. Due to the high density of the terrestrial 
LiDAR data as well as the relatively smooth characteristics of 
terrain and man-made structures, using TIN patches to describe 
the physical surface is quite acceptable. Corresponding point- 
to-patch is extracted by the iterative closest patch (ICPatch) 
procedure from TIN and irregular point data (Habib, 2006). 
After that, in the calibration procedure, the selected 
corresponding point and 
points in reference data« 
points in calibration target data« 
Conjugate 
point/patch 
Figure 3. The closest patch and point selected by the iterative 
closest patch procedure 
Xj = f(obsf,P) 
(3) 
Aribome LiDAR 
(raw measurements) 
Terrestrial LiDAR 
(point-cloud coordinates) 
ICP 
ICPatch 
i — 
X 
LSA 
LSA 
(LiDAR Eq.+pseudo-conjugati points) 
(LiDAR Eq.+conjugate point/patch) 
Calibration parameters 
Final result 
Figure 4. The calibration procedure using ICP and ICPatch 
methods 
2.3 Planar Patches and Modified Weight Matrix 
In this paper, the plane segmentation for the areal patches is 
introduced as an alternative approach that utilizes conjugate 
planar patches for the calibration procedure. The patches are 
extracted through an automated segmentation procedure. Then 
the conjugate patches are identified through checking their 
overlap, the compatibility of their surface normals, and their 
spatial distance. The matched planar patches are used in a 
point-based calibration procedure, which is similar to the 
approach using the point primitive and ICP procedure. In 
general, conjugate planar patches used with an additional 
constraint such as the normal distance, but this proposed 
approach uses pseudo-conjugate points and modified weight 
matrices instead of additional constraints. 
Figure 5 shows two planar patches which are extracted from 
terrestrial LiDAR data (reference data) and airborne LiDAR 
data (target data) respectively. The point X R and X T are not 
exactly conjugate points, but both points belong to the same 
object plane. To compensate for the fact that non-conjugate 
points are used based on the point primitive, the error ellipse is