In: Wagner W., Székely, B. (eds.): ISPRS TC VII Symposium - 100 Years ISPRS, Vienna, Austria, July 5-7, 2010, IAPRS, Vol. XXXVIII, Part 7B 
The focus of the current paper is on the terrain roughness 
parameterization of the meso structure (Fig. 2). For the 
parameterization of the terrain roughness two approaches are 
investigated. In the first approach a geometric description by 
calculating the standard deviation of detrended terrain points is 
used. In the second approach the potential of the derived echo 
widths are analyzed for terrain roughness characterization. 
3.1 Standard deviation of detrended terrain points 
In this first approach the terrain roughness is parameterized by 
the standard deviation of the detrended z-coordinates of all 
FWF-ALS echoes within a raster cell or a certain distance of 
e.g. 1.0 m, which are located below a defined normalized height 
(dz) threshold (Fig. 3a). For the current study four different 
height thresholds (0.25 m, 0.5 m, 1.0 m, 2.0 m) are applied. The 
detrending of the FWF-ALS heights is important for slanted 
surfaces, where else the computed standard deviation would 
increase with increasing slope (i.e. height variation), even 
though the surface is plane. Algorithmically, simply the 
standard deviation of orthogonal regression plane fitting 
residuals is chosen. Taking the residuals to a best fit plane can 
be compared to a prior detrending of the heights. The 
orthogonal regression plane fitting (Fig. 3b) is favored over 
vertical fitting because for very steep surfaces the vertical 
residuals can become very large, even though the plane fits very 
well to the points. In this sense orthogonal fitting means that the 
orthogonal distances from plane to points is minimized. In 
practical, for every laser echo the orthogonal plane fitting is 
performed in a local neighborhood (i.e. considering all terrain 
echo neighbors in a certain distance for plane computation; e.g. 
<1.0 m) and stored as additional attribute to the original laser 
echo. 
Figure 3. Standard deviation of detrended terrain points: a) 
Predefined cube or cylinder for selecting echoes used for plane 
fitting, b) Principle of orthogonal regression plane fitting 
(modified from www.mathworks.com). 
The unit of the so derived terrain roughness parameter is in 
meters and can be compared between different flight epochs 
and ALS systems. Finally, the derived standard deviations are 
averaged per raster cell. 
3.2 Echo width of terrain points 
The meso structure is defined to be smaller than the footprint 
diameter (Fig. 2). Such structures can be obtained either 
directly, if a high point density with overlapping footprints is 
given or the range resolution of the scanner system allows 
distinguishing multiple echoes in the magnitude of few 
decimeters, which is currently not achieved by state-of-the-art 
scanners. The maximum sampling interval is currently 1.0 ns, 
which corresponds to approx. 15.0 cm (30.0 cm for both ways) 
(Wagner et al., 2006). For objects few times larger than the 
sampling interval, the widening of the echo (i.e. larger echo 
width) indicates a certain vertical extent of the illuminated 
object, which can be assigned to roughness in a broader sense. 
For the used FWF-ALS data the received full-waveforms were 
digitized with an interval of 1 ns (Fig. 4). A Gaussian 
decomposition method was applied to estimate in addition to 
the location the scattering properties of the targets i.e. the 
amplitude and the echo width (Wagner et al., 2006). Therefore, 
the derived echo width of each single echo is representative for 
the roughness within the illuminated footprint (Fig. 4). For 
deriving the terrain roughness layer laser points within a 
maximal vertical distance (dz) to the DTM (dz = 0.25 m, 0.5 m, 
1.0 m, 2.0 m) are selected. For a laser beam with multiple 
echoes the illuminated footprint decreases depending on the 
collision area of the previous reflected echoes. Only single 
echoes are selected for the terrain roughness parameterization, 
in order to guarantee that only extended targets with similar 
footprint sizes are investigated. For this study the influence of 
varying flying heights and consequently to varying ranges, and 
the local incidence angle are neglected. Finally the terrain 
roughness layers are generated by aggregating the selected echo 
widths per raster cell (e.g. mean value). The unit of the terrain 
roughness layers is in nanoseconds and could be converted to 
meters. 
Figure 4. Full-waveform ALS system. A Gaussian 
decomposition is applied to derive echo widths, which are used 
for the parameterization of terrain roughness, (adapted from 
Doneus et al., 2008)