ISPRS Commission III, Vol.34, Part 3A ,Photogrammetric Computer Vision“, Graz, 2002 
  
E{(X,Y) -n - f u*y)n? -— r°)}= ( — f(u°))Ar, + f (u°)Ar, T 
You a 
ou [2 A od ad | 
with 
u* 2 X cosa? - Y sina? - d? 
as the approximate signed distance of a point to the edge. This 
equation can be formulated for all laser points near an edge. The 
gradients of the reflectance strength are derived from the 
analytical edge response function rj*f(u)(r;-ro). This approach 
has several advantages over the standard least squares image 
matching: 
e As the partial derivative df/du equals zero for points at a 
distance of larger than R from the edge location, these 
points will not directly effect the estimation of the edge 
location, but only contribute to the estimation of the 
reflectance values on either side of the edge. The edge 
location is primarily determined by the points with 
footprints that actually cross the edge. The gradients at 
those positions are properly modelled by the edge response 
function and thus do not cause a bias in the estimation of 
the edge location. 
Since the gradients are derived analytically, they are not 
affected by the (high amount of) noise in the reflectance 
data. Maas [2000] noted that the low signal-to-noise ratio in 
the coefficients of equations for matching height data 
caused an overestimation of the matching precision. The 
usage of an analytical edge model will allow a more realistic 
estimation. 
e The observation equations can be formulated for the 
original laser points and do not require computations on an 
additional data structure, like a TIN. 
In order to obtain accurate results, one should, however, select 
long edges for the matching. This is required because of the 
high noise level in reflectance data, but also since only few 
points may fall within a distance of R from the edge. The 
amount of these points depends on the ratio between the point 
distance and the footprint size and on the orientation of the edge 
with respect to the scan lines. In bad configurations only very 
few or even no points may contribute to the edge location 
estimation. This should, however, then result in a very high 
value of the estimated edge location precision. By checking the 
propagated reflectance variances those edges can be selected 
that have a good location accuracy. 
The edge location equations above were formulated such that an 
edge is located in a single laser data set. If the assumption can 
be made that the systematic errors in the laser data do not cause 
a rotation of an edge, the edge fitting can also be done 
simultaneously in two or more point sets, using the same edge 
orientation Q for all point sets in which the edge is visible. This 
may further improve the offset estimation between strips. 
Initial values are required for all four edge parameters ry, r;, 0, 
and d. They can easily be obtained by low level image 
processing of the gridded reflectance data. Figure 8 shows 
detected long edges that were obtained in the lower image of 
figure 5 by a straight line growing algorithm on a median 
filtered image. Statistical tests on the fit of the reflectance data 
to the edge model should be used to eliminate those edges that 
can not be modelled properly by this model. This can be the 
case if the edge is slightly curved or if other objects near the 
edge violate the assumption that the reflectance strength is 
homogeneous on both sides of the edge. 
  
Figure 8: Extracted lines on a median filtered reflectance 
image. 
As for matching height data, one should avoid reflectance edges 
near occlusions or height jumps. By examining the height data, 
this can be verified easily. 
4. CONCLUSIONS 
In this paper it was shown that the determination of offsets 
between laser altimetry datasets can not be solved reliably by 
standard least squares image matching algorithms. This holds 
for height data as well as for reflectance data. Height jump 
edges in laser altimetry data show the same behaviour as edges 
in binary imagery. Their location may show a bias which 
depends on the edge length and the orientation of the edge with 
respect to the scan line direction. 
For matching height data it was advocated to also use linear and 
planar features besides points for which offsets can be 
determined in three dimensions. Because of the limited width of 
linear features a model based fitting may often be required. 
Reflectance data may be suitable for the estimation of 
planimetric offsets, even though its noise level is often fairly 
high. In order to avoid biases in the estimation of edge 
locations, the response of a laser beam to a grey value edge 
needs to be modelled. The usage of such an edge response 
function also enables the computation of noise free gradients, 
which results into a better convergence behaviour and a more 
realistic estimate of the edge location precision. 
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Burman, H., 2000. Adjustment of Laserscanner Data for 
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Crombaghs, M.J.E., R. Brügelmann, E.J. de Min, 2000. On the 
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In: International Archives of Photogrammetry and Remote 
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Fórstner, W., 1986, Prinzip und  Leistungsfáhigkeit der 
Korrelation und Zuordnung digitaler Bilder. In: Proceedings of 
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