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