ISPRS Commission III, Vol.34, Part 3A „Photogrammetric Computer Vision‘, Graz, 2002 
  
ON THE ESTIMATION OF PLANIMETRIC OFFSETS IN LASER ALTIMETRY DATA 
George Vosselman 
Department of Geodesy, Delft University of Technology, Thijsseweg 11, NL-2629 JA Delft, The Netherlands 
g.vosselman@geo.tudelft.nl 
Commission III, WG III/3 
KEY WORDS: Laser altimetry, strip adjustment, error estimation, least squares matching. 
ABSTRACT: 
Offsets between overlapping strips of laser altimetry data serve as the input for strip adjustment procedures that estimate and 
eliminate systematic errors in laser altimetry datasets. For a three-dimensional strip adjustment offsets are to be measured in three 
dimensions. Height offSets can be determined straightforward by comparing the heights of horizontal planes. Planimetric offsets are 
more difficult to determine. This paper shows that the usage of standard least squares matching algorithms on height data as well as 
on reflectance data may lead to significant biases in the estimation of planimetric offsets. For height data, a model based estimation 
of linear features is proposed since the number of locations in strip overlaps that are suitable for the estimation of offsets in three 
dimensions may not be sufficient to estimate all error parameters of a strip adjustment. To improve both the offset estimation and the 
offset variance estimation using reflectance data an edge response function is introduced. This function takes into account the 
difference in size of a laser beam's footprint and the distance between successive laser points. 
1. INTRODUCTION 
Laser altimetry surveys make use of measurements by GPS 
receivers, inertial navigation systems, and laser range finders. 
Due to errors in these components, the synchronisation, and 
calibration of the relative positions and attitudes of the 
instruments, systematic errors are often observed in the acquired 
digital elevation models (DEM) [Huising and Gomes Pereira 
1998]. Strip adjustment procedures have been devised to detect 
and eliminate these systematic errors by making use of 
measurements in overlaps between strips and reference objects 
[Kilian et al. 1996]. 
Over the last few years calibration procedures improved, 
resulting in smaller systematic errors in the DEM's. The 
necessity of a strip adjustment now depends on the accuracy 
demands. In the case of low accuracy demands (67 > 0.5 m) an 
adjustment may not be required, although the computation of 
the systematic errors, without actually correcting the data, could 
still be used to check whether the accuracy demands are met. 
For higher accuracy DEM production in the Netherlands (07 < 
0.15 m, systematic height error « 0.05 m), an adjustment of strip 
heights and tilts is incorporated in the standard procedure 
[Crombaghs et al. 2000]. Water boards demand average heights 
over large areas with even much higher accuracy (oz « 0.01 - 
0.02 m). For those requirements all systematic errors need to be 
modelled and eliminated to a high precision level. 
A proper modelling of the systematic errors in the DEM should 
address the sources of these errors: the biases in the 
instruments, synchronisation errors, and calibration errors in the 
determination of the relative sensor orientations. These errors 
should be modelled explicitly [Schenk 2001]. This requires a 
three-dimensional strip adjustment, and not just an adjustment 
of the point heights. Vosselman and Maas [2001] showed that 
systematic planimetric errors can be several times larger than 
systematic height errors. The impact of such errors on the 
determined terrain heights, of course, depends on the terrain 
slopes. Crombaghs et al. [2000] also showed the need for a 
complete error modelling. A strip adjustment with an 
incomplete error model was shown to lead to a deterioration of 
the DEM quality. 
The identification of corresponding positions in overlapping 
strips is an important step of the strip adjustment procedure. For 
a three-dimensional strip adjustment, offsets in X-, Y-, and Z- 
direction between overlapping strips need to be determined. 
This paper deals with several aspects of the determination of the 
planimetric offsets between strips. 
Various procedures for the measurement of corresponding 
points have been published in the photogrammetric literature. 
e Kilian et al. [1996] identified areas of interest by hand and 
determined the corresponding locations by a least squares 
matching of gridded height data. By analysis of the height 
data and the strip geometry, areas that were occluded in one 
strip are excluded from the matching. 
Burman [2000] made use of both height data and the 
reflectance strength of the laser pulses for the measurement 
of the strip offsets. Suitable areas for the simultaneous 
matching of height and reflectance images were determined 
by thresholding the response of the Sobel gradient operator. 
The matching equations were set up such that they directly 
resulted into the estimation of the heights at the DEM grid 
points. 
Maas [2000] formulated the matching problem on the 
height data in a TIN data structure, thus avoiding a loss of 
information due to gridding of the height data. Points near 
height jump edges were excluded from the matching by 
eliminating triangles with a steep slope. In this way areas 
with occlusions do not impact the matching result. In [Maas 
2001] corresponding positions between strips are estimated 
by using the height data for the determination of the Z- 
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