International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part Bl. Istanbul 2004
surfaces since they correspond to laser footprints instead of
distinct points that could be identified in imagery (Baltsavias,
1999). Conventionally, surface-to-surface registration and
comparison have been achieved by interpolating both datasets
into a uniform grid. The comparison is then reduced to
estimating the necessary shifts by analyzing the elevations at
corresponding grid posts (Ebner and Ohlhof, 1994; Kilian et al.,
1996). Several issues can arise with this approach. First, the
interpolation to a grid will introduce errors especially when
dealing with captured surfaces over urban areas. Moreover,
minimizing the differences between surfaces along the z-
direction is only valid when dealing with horizontal planar
surfaces (Habib and Schenk, 1999). Postolov et al. (1999)
presented another approach, which works on the original
scattered data without prior interpolation. However, the
implementation procedure involves an interpolation of one
surface at the location of conjugate points on the other surface.
Additionally, the registration is based on minimizing the
differences between the two surfaces along the z-direction.
Schenk (1999) introduced an alternative approach, where
distances between points of one surface along surface normals
to locally interpolated patches of the other surface are
minimized. Habib et al. (2001) implemented this methodology
within a comprehensive automatic registration procedure. Such
an approach is based on processing the photogrammetric data to
produce object space planar patches. This might not be always
possible since photogrammetric surfaces provide accurate
information along object space discontinuities while supplying
almost no information along homogeneous surfaces with
uniform texture.
This paper deals with alternative approaches for utilizing linear
features derived from LIDAR data as control information for
aligning the photogrammetric model relative to the LIDAR
reference frame. The following section addresses the general
methodology and mathematical models of the suggested
approaches including the techniques adopted for extracting the
registration primitives from photogrammetric and LIDAR data.
The last two sections cover experimental results (using aerial
datasets) as well as conclusions and recommendations for future
work.
2. METHODOLOGY
In this paper, two approaches will be applied to incorporate
LIDAR lines in aligning the photogrammetric model to the
LIDAR reference frame. The first approach incorporates
LIDAR lines as control information directly in a
photogrammetric triangulation. The second approach starts by
generating a photogrammetric model through a
photogrammetric triangulation using an arbitrary datum (no
control information). LIDAR features are then used as control
for the absolute orientation of the photogrammetric model.
2.1 Approach 1: Direct involvement of LIDAR lines in
photogrammetric triangulation
Conjugate linear features in the photogrammetric and LIDAR
datasets should first be extracted and then incorporated in a
photogrammetric triangulation in which LIDAR lines will act as
the source of control to align the photogrammetric model. The
following subsections describe the procedures adopted to
extract straight line features in both datasets and how they are
included in the overall alignment procedure.
Photogrammetric straight-line features
The methodology for producing 3-D straight line features from
photogrammetric datasets depends on the representation scheme
of such features in the object and image space. Prior research in
this area concluded that representing object space straight lines
using two points along the line is the most convenient
representation from a photogrammetric point of view since it
yields well-defined line segments (Habib et al., 2002). On the
other hand, image space lines will be represented by a sequence
of 2-D coordinates of intermediate points along the feature.
This representation is attractive since it can handle image space
linear features in the presence of distortions as they will cause
deviations from straightness.
In general, the manipulation of tie straight lines appearing in a
group of overlapping images starts by identifying two points in
one (Figure la) or two images (Figure 1b) along the line under
consideration. These points will be used to define the
corresponding object space line segment. One should note that
these points need not be identifiable or even visible in other
images. Intermediate points along the line are measured in all
the overlapping images. Similar to the end points, the
intermediate points need not be conjugate, Figure 1.
1 1
ex * Tus
es EK
2 S a" ^X x. a’
e Aue
^ CS o
Image 1 Image 4 Image 1 Image 4
(a) (b)
e End points defining the line in object space
x Intermediate points
Figure 1: End points defining the object line are either
measured in one image (a) or two images (b).
For the end points, the relationship between the measured
image coordinates {(X,, Yı), (X, ¥,); and the corresponding
ground coordinates (X, Y Z) (X, Y Z,)} is established
through the collinearity equations. Only four equations will be
written for each line. The incorporation of intermediate points
into the adjustment procedure is achieved through a
mathematical constraint. The underlying principle in this
constraint is that the vector from the perspective centre to any
intermediate image point along the line is contained within the
plane defined by the perspective centre of that image and the
two points defining the straight line in the object space, Figure
2. This can be mathematically described through Equation |.
(x) ©
. J . .
In the above equation, V is the vector connecting the
perspective centre to the first end point along the object space
line, J is the vector connecting the perspective centre to the
second end point along the object space line, and ÿ is the
vector connecting the perspective centre to an intermediate
point along the corresponding image line. It should be noted
that the three vectors should be represented relative to a
common coordinate system (e.g, the ground coordinate
system). The constraint in Equation 1 incorporates the image
coordinates of the intermediate point, the Exterior Orientation
Parameters (EOP), the Interior Orientation Parameters (IOP)
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