Hans-Gerd Maas 
  
Least-Squares Matching with Airborne Laserscanning Data 
in a TIN Structure 
Hans-Gerd Maas 
Institute of Photogrammetry and Remote Sensing 
Dresden Technical University 
Helmholtzstr. 10 
D-01062 Dresden, Germany 
e-mail hmaas@rcs1.urz.tu-dresden.de 
Keywords: 
Airborne laserscanning, least-squares matching, TIN, accuracy 
Abstract: 
A number of tasks in airborne laserscanning require the establishment of correspondences between point data from 
neighbouring strips, or referencing between point clouds and object models. These tasks may be solved by interpolating 
laserscanner data, which are usually irregularly distributed 2'/,-D points, to a regular grid and applying standard photo- 
grammetric matching techniques. Instead, the paper presents a formulation of least squares matching based on the 
original data points in a triangulated irregular network structure, thus avoiding degrading effects caused by the interpo- 
lation. The technique determines shifts in all three coordinate directions together with their covariance matrix. It can be 
shown that applying matching techniques to laserscanner data causes large systematic errors of the shift parameters in 
the case of partial occlusions. The presented formulation on the basis of a TIN structure allows for manifold extensions 
to solve this problem. 
The technique and a number of extensions have been implemented and applied to the measurement of strip errors in an 
airborne laser scanner dataset with moderate point density, consisting of 20 strips including crossing strips. The paper 
shows the results from this test, discusses the advantages of the presented technique and the limitations of matching 
techniques applied to laserscanner data. Special attention has to be paid to problems caused by height discontinuities in 
the data and by the fact that the design matrix in least squares matching is derived from observations with stochastic 
properties. The latter leads to precision figures that are usually much too optimistic. A detailed analysis of the design 
matrix and extensive testing lead to better funded precision figures for the standard deviation of the obtained shift 
parameters. These are in the order of one centimeter in height direction and one decimeter in horizontal direction, 
corresponding to about '/;sth of the average point spacing. 
1. Introduction 
Least-squares matching (LSM) is a technique that is being applied regularly by photogrammetrists for the establishment 
of correspondences between images taken from different viewing points, or between subsequent images of an image 
sequence. Formulated for two-dimensional greyscale images (F ‘rstner 1984, Grhn 1985), it determines the parameters of 
an affine transformation between corresponding patches of two or more images. Typical application fields of LSM are the 
determination of homologous points between consecutive images and image strips in a conventional aerotriangulation, 
or the matching between strips of linear array cameras. 
Just like conventional photogrammetric image data, airborne laserscanning data of larger areas is also acquired in a 
stripwise manner. Basically, the 2'/,-D point clouds generated by airborne laserscanning are directly geo-referenced due 
to the use of GPS/INS systems onboard the aircraft. Because of errors of these instruments or sub-optimalities of the 
GPS/INS integration, however, points of neighbouring laserscanner strips will usually show vertical discrepancies in the 
order of several centimeters and horizontal discrepancies in the order of a few decimeters (Huising and Gomes Pereira, 
1998). The significance of these discrepancies depends on the application and the point density: in datasets with a point 
density of approximately one point per ten square metres, as are being used for the generation of digital elevation 
models, one will often only notice the vertical discrepancies; in datasets with several points per square meter used for 
the generation of 3-D city models, both vertical and horizontal discrepancies are often clearly noticeable. 
  
548 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 
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