International Archives of the Photogrammetry, Remote 
  
during a strip might cause some displacement; however, 
IMU data helps to bridge such critical gaps. 
* Last, but not least, the missing rigorous supervision of the 
whole measuring process has to be mentioned. 
Instead of the minimal solution cited above (single ground 
reference station and geoid) the subsequent alternative is 
proposed which eliminates the shortcomings of the above: 
* Use of more GPS ground reference stations surrounding 
the area of interest. This may (probably better) be achieved 
by a virtual reference station (Wanninger, 2003). 
Supposing known ground-survey coordinates of all these 
ground reference stations, this also eliminates the 
(unknown) linear portion of the geoid’s undulation. The 
undulations of higher degree remain; they might be 
neglected for the usually relative small extent of practical 
projects. 
e Some of the GPS ground reference stations may be 
replaced by ground reference points which can be 
“identified” somehow in the point clouds of the laser 
scanner strips (see 2.1). For planimetric fitting, roofs of 
buildings and/or prominent fault lines in the terrain are 
suitable, for mere height fitting, horizontal areas free of 
vegetation are recommended. In photogrammetric 
terminology, we call those reference points usually control 
points. 
* Monitoring a many of plane and height discrepancies in 
the common areas of overlapping laser scanner strips and, 
therefrom, improvement of GPS-positioning and IMU- 
attitude data. Mathematically, this can be formulated with 
correction polynomials (of probably quite low degree) for 
the registered orientation elements as function of time: one 
strip — one polynomial. This procedure preserves the high 
neighbouring precision of both system components and 
copes with any drifting phenomena. The adjustment of all 
these sets of coefficients of the polynomials has to be done 
simultaneously for all strips of a block (key word: block 
adjustment by strips) — using the positions of 
corresponding points (features) in the overlapping areas as 
observations. Their residuals are to be minimised in the 
adjustment. A statistically better approach is the strategy to 
use original observations (Kraus, 1997a): the polar 
coordinates recorded by the laser scanner; given position 
and attitude of the scanner, the Cartesian ground 
coordinates are (simple) functions of those recorded 
(V, z, p) values, i.e. nadir-angle V , fore-sight angle X 
and distance p. 
The above outline of a technique to improve the geometric 
quality of laser scanner data should give an idea how to 
overcome gaps between strip surfaces. Unfortunately, the 
proposed method requires access to the original data of the 
laser scanner: GPS, IMU, and Polar data as function of time. 
The laser scanner companies want to provide 3D-data for the 
end-user — so, they want to provide *DTMs" (i.e. grids) resp. 
point clouds in the national ground-survey co-ordinate System, 
only; key word "user-friendly". But this *end-product" is prone 
to having bias and is too late in the process-chain for 
elementary repair. Nevertheless, we have to stress the fact that 
our criticism is valid only for exploiting the full potential of 
laser scanner data: we want to get the few-cm-precision of the 
laser scanner also as accuracy of the end product. 
Some provisorily (temporary) solution was proposed in (Kager, 
Kraus, 2001): it was based on raw 3D-data given in the 
Sensing and Spatial Information Sciences, Vol XXXV, Part B1. Istanbul 2004 
national co-ordinate system strip by strip. Instead of correcting 
flight path (dGPS) and attitude data (IMU), we tried to 
compensate for the apparent XY Z-deformations by correction 
polynomials for individual strips of ground points. This 
procedure has the disadvantage that it copes merely with 
phenomena and does not assess the true problem. But it has the 
advantage that the necessary data is available to end-users. 
Here we aim at a strict, highly automateable procedure 
minimizing 3D-gaps. Before going into adjustment details we 
have to discuss the determination of strip-tying features. 
2. DETERMINATION OF STRIP-TYING FEATURES 
The principle of strip-tying by features is shown in figure | 
using a special case. As we are not able to associate 
homologous points in the point-clouds created by Lidar (LIght 
Detection And Ranging), we have to recourse to simple 
geometric features like planes which can be derived from 
regions of Lidar-points. Such a plane-feature is an 
approximation of the tangent-plane of the underlying surface. 
So, we associate first order differentials of the surface and call 
them “homologous features” — a generalization of the well- 
known “homologous points” of standard photogrammetry. It 
should be mentioned here that the term “feature” also includes 
lines (straight or curved). But this aspect should not be followed 
here in detail, since a line can be conceived as intersection of 
planes (surfaces) and handled by these means. 
  
  
  
  
  
  
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* Height control points / 7 Patch area 
Laser scanner points em Patch centre 
Figure 1: Principle of height block adjustment with laser 
scanner strips 
At some chosen ground position XY, a plane can be 
interpolated into every point-cloud of overlapping strips. Since 
the available orientation of the raw strips is relatively good, we 
can expect that the homologous features will also overlap. 
2.1 "homologous points" vs. "homologous planes" 
A point has three coordinates - so, knowing them in 3D-space 
this point has no degrees of freedom. A tie-point, i.e. a point 
common to overlapping regions lets no (relative) degrees of 
freedom to the such tied regions. 
A plane has two degrees of freedom - so, a point in one region 
can move in two independent directions with respect to the 
other region. A tie-plane, i.e. a plane common to overlapping 
regions lets also two degrees of freedom to the such tied 
regions. Le., the such tied surfaces may shift relatively in two 
directions; the shift in the third direction (the surface's normal) 
is fixed (relatively!). 
From these deliberations one can ask for equivalence conditions 
between homologous planes and homologous points. The 
556 
Inte. 
  
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