In: Wagner W., Szekely, B. (eds.): ISPRS TC VII Symposium - 100 Years ISPRS, Vienna, Austria, July 5-7, 2010, IAPRS, Vol. XXXVIII, Part 7B 
Surface roughness 
smooth I* 0 - 0,031 fro] 
| E3 0,031-0,062 
I ■0,062 - 0,106 
rough ■ 0,106 - 0,198 
Visual smoothing 
(10m foca! mean) 
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T i* 
'■’V' 
Figure 2. Surface roughness raster layer (1.0 m resolution), classified in 4 roughness categories from smooth (red) to rough (blue). 
Non-wooded areas are masked out (in light yellow). Detail: Smoothed visual impression through applying a focal mean operator. 
3.1 Surface roughness (SR) 
Surface roughness was defined as small scale height variations 
up to a few decimeters above ground. In mathematical terms the 
standard deviation of the detrended z-coordinates of all ALS 
terrain echoes is computed. The detrending of the ALS heights 
is important for slanted surfaces, where else the computed 
standard deviation would increase with increasing slope (i.e. 
height variation), even with the surface being plane. The unit of 
the subsequently derived SR parameter is in meters and can be 
compared between different flight epochs and ALS systems. 
Further algorithmic details can be found in Hollaus & Hofle 
(2010). 
Figure 2 shows a derived SR raster layer featuring a terrain 
related variation of ±0.2 m (-0.2 < dz < 0.2). All laser echoes 
within a 1.0 m neighborhood were considered in the plane 
fitting and standard deviation calculation process. The finally 
derived SR raster layer has a spatial resolution of 1.0 m, i.e. 
with the mean standard deviation value of all points falling in 
one predefined 1.0 m grid cell attached as attribute. Using four 
classes for visualization gives a good first indication on regional 
surface roughness variations in the study area. More than 50% 
of the total forested area is thus classified as having a very 
smooth surface (red, yellow) and around 25% show slightly 
higher deviations (green, blue). White pixels display ‘no data’ 
areas, i.e. areas where no information about the immediate 
surface is available. These can be data errors, but primarily it is 
due to the forest canopy being too dense thus preventing the 
laser beam from reaching the ground. 
The detail image displayed in Figure 2 is the result of applying 
a focal neighborhood function to the original raster. The mean 
value of all cells of the input raster within a specified 
neighborhood is calculated and assigned to the corresponding 
cell location of the output raster. For the described raster a 
circular neighborhood (10 m radius) was chosen, i.e. all grid 
cells having its centers encompassed by this circle are included 
in the calculation. Using focal operations is a form of 
generalization smoothing the visual impression of the input 
data. It is particularly valuable for identifying hot spot regions 
and spatial patterns in heterogeneous raster data. It is very 
important to decide first how to deal with existing ‘no data’ 
values in the input data. For the displayed SR raster the option 
of ignoring ‘no data’ values in the calculation was chosen. 
Another possibility would be to assign ‘no data’ to the output 
grid cell in case any of the considered neighboring cells has a 
‘no data’ value. With just around 15% of the pixels in forested 
areas featuring ‘no data’ values it was decided to accept 
uncertainties entailed with ignoring those pixels and rather look 
at resulting generalized regional spatial patterns. It becomes 
clear that in the northern woods of the study area very smooth 
surfaces prevail while in the more heterogeneous southern parts 
surface in general tends to be rougher. 
3.2 Terrain roughness (TR) 
Terrain roughness is described as the unevenness of the terrain 
surface (including rocks and low vegetation) at scales of several 
meters. In mathematical terms this implies calculation of the 
standard deviation of height of non-terrain ALS echoes above 
terrain (normalized height) within boxes of predefined size. In 
contrast to the SR computation, only echoes close but above 
terrain (>0.2 m) are considered for the TR derivation. Two 
different vegetation story layers are analyzed in this context, 
one considering very low brushwood or undergrowth between 
0.2 m and 1.0 m (e.g. bushes and shrubs; TR I; Figure 3) and 
the other considering understory vegetation between 0.2 m and 
3.0 m (TRII; Figure 4). The second layer is particularly 
valuable for identifying different types of trees (e.g. large 
coniferous trees with few - mostly cut - branches in the lower 
levels or broadleaf trees with just stem and crown compared to 
smaller trees with branches hanging down to the ground). 
Figures 3 and 4 show that these two TR parameters yield much 
more ‘no data’ values than the previously described SR 
parameter (>70% for TR I, >60% for TR II compared to ~15% 
for SR). Besides the same potential causes mentioned above 
being (1) data errors or (2) very dense tree crowns preventing 
the laser beam reaching the analyzed height level, no 
information in the ALS data can also signify empty space in 
reality. So, in fact even ‘no data’ values can provide valuable 
information in that context. Looking at the study site overview 
it is apparent that there is more TR data recorded in the 
southern parts of the study site. Anyhow, at this level of detail 
also in those areas just very little variation is detected in TR I. 
Values in TRII show a slightly different picture, with (1) 
featuring a somewhat higher information density (i.e. 37% vs. 
27% for TR I) and (2) featuring more variation (i.e. mean value 
of 0.22 vs. 0.05 in TR I). The latter is also related to the larger 
vertical focus of this specific parameter (0.2 < dz < 3.0).