Hans-Gerd Maas 
  
Several authors have addressed discrepancies between adjacent strips of laserscanner data. Kilian (1994) describes a 
technique for laserscanner block adjustment based on measurements of horizontal and vertical shifts by least squares 
matching applied to strip data interpolated to a regular grid. Van Noort (1999) documents vertical strip differences based 
on the analysis of a very large amount of laserscanner data; de Min et al. (1999) developed techniques for laserscanning 
strip adjustment based on the measurement of height differences of control fields and along strip boundaries. The latter 
two techniques are restricted to the height dimension and use flat regions in the datasets to determine height differences. 
Planimetric and height discrepancies between strips may be measured by LSM applied to laserscanner data interpolated 
to a regular grid (Behan, 2000). Original laserscanner data points are, however, usually not regularly distributed, and an 
interpolation may introduce severe degrading effects. Therefore, LSM is better applied to the original irregularly distrib- 
uted laserscanner data points organised in a TIN-structure. 
In the following, the basic algorithm of LSM applied to 2'/,-D point data in a TIN structure will be described (chapter 2), 
and first results based on a dataset with moderate point density will be shown (chapter 3). Chapter 4 demonstrates 
problems caused by frequently occurring singularities and presents extensions of the technique to solve these problems. 
In chapter 5 application fields of the technique are identified and discussed. 
2. Basic algorithm 
The basic algorithm for LSM applied to laserscanner data in a TIN structure is derived from the standard implementation 
of LSM for raster image data and described in chapter 2.1. Requirements for the patches to allow determinability of all 
parameters are defined in chapter 22. Systematic errors of LSM in the case of discontinuities and refinements of the 
technique to avoid biased results are presented in chapter 4. Matching strategies indicating suitable points for matching 
are discussed in chapter 2.4. 
2.1 Formulation of LSM on a TIN structure 
The basic goal of least squares matching applied to laserscanner strip data is to unveil strip errors indicated by local 
discrepancies between point clouds taken from neighbouring or crossing strips. For that purpose, local patches are cut 
out of the overlap region. The shape of these patches may be arbitrary, but will often be circular or rectangular. The 2'/,- 
D data in these patches are shifted in all three 
coordinate directions in a way that the sum of T 2 
the squares of height differences reaches a rene a 
minimum. As the pointsets of the two patches L 
are not identical or arranged on a regular grid, : i ; 
matching is performed between discrete points idl toate : p virer 
in one patch and points derived from the , "a 
corresponding TIN mesh in the other patch. 
  
Observation equations are written for every ; 
original data point of both patches. The input Sk ecm tte 
for the observation vector is obtained by : : 
subtraction of a height computed by linear Y 
interpolation at the same location in the 
corresponding mesh of the TIN structure of the 
other patch. The gradients for the construction 
of the design matrix are given by the surface 
normal of that mesh. 
Ex 
Figure 1: TINs of patches in two laserscanner data strips. 
Formulated as a least squares adjustment procedure, the method converges after a few iterations. Obviously, the 
assignment of a point to a TIN-mesh may change during these iterations. The set of parameters to be determined in this 
procedure is limited to three shift parameters due to the nature of airborne laserscanner data, but may be extended. 
2.2 Requirements 
The local TINs to be matched must show surface normals in at least three non-coplanar directions to allow for the 
determination of all three shift parameters by LSM. In many cases, buildings or parts of buildings depict suitable objects 
for matching. Optionally, constraints may be introduced in situations with insufficient patch contrast, limiting the 
solution to the determination of a subset of the shift parameters. In fact, laserscanner data will often show large regions, 
where only a height shift parameter can be determined reliably. The technique may also be formulated as a multi-strip 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 549