camera-to-object distance during image acquisition (~581
mm) ensures that individual
DEM
s accurately represent the
gravel-bed surface. Individual particles are clearly defined,
which is necessary to undertake grain-scale roughness analy-
ses, such as monitoring changes in the particles’ slope and
orientation with water-work
.
Large data files for individual
DEM
s will make merging of
those
DEM
s computationally expensive, and often not feasible
(Barazzetti
et al
., 2013). Therefore we studied the effect resam-
pling has on the merged
DEM
. Here,
DEM
resampling interpolates
a
DEM
on a less dense grid system. In Bertin
et al
. (2014) we
showed the effect of raw point cloud interpolation onto regular
grids with different spacing using a ground truth. The bench-
mark grid size we tested was 0·25 mm for that study. We found
that raw point clouds should be interpolated onto grids with
spacing closely matching the original point data spacing in
order to reduce smoothing artifacts. In order to be able to com-
pare the present results with previously studied benchmarks,
we also restrict the minimal grid size to 0·25 mm for this study,
although the individual
DEM
s would allow us to go as low as
0.14 mm (i.e., a
DEM
grid spacing matching the pixel size at the
distance of the gravel bed). Figure 4 shows the results of resam-
pling for an individual
DEM
onto coarser grids. The middle
DEM
(
DEM
-2) is taken as an example. Four tests were performed: resa-
mpling the original
DEM
characterized by a 0·25 mm sampling
distance, onto grids with spacing 0.5 mm, 0.75 mm, 1 mm, and
1.5 mm, respectively. The internal reliability of the resampled
DEM
s is assessed to decide if
DEM
resampling before merging is
suitable (Figure 4). The point-wise mean unsigned error (
MUE
)
and standard deviation of error (
SDE
) were computed after dif-
ferentiation of the resampled
DEM
s with the original
DEM
:
MUE
=
−
=
∑
i
n
i
i
r o
n
1
(5)
SDE
r o r o
n
i
n
i
i
i
i
=
−
(
)
− −
(
)
=
∑
1
2
(6)
where
r
i
= resampled elevations;
o
i
= original elevations
.
Figure 4 shows that
DEM
resampling impacted small fea-
tures, particles’ edges and gaps especially. In this application,
resampling was considered to have a minor effect up to a 1
mm grid, after which
SDE
passed the 0.1 mm mark. Individual
DEM
s were therefore resampled onto a grid with 1 mm spacing
before merging. It ensured a computationally efficient merg-
ing and handling of the resulting
DEM
, with minimum impact
on the recorded topography
.
Figure 5 shows the composite
DEM
after seamless merg-
ing. It is clearly seen that standard averaging of the overlap
Figure 4. Internal reliability of DEM resampling, i.e., point-wise comparison between DEMs after resampling and original DEM, character-
ized by 0·25 mm sampling distance. Comparison was performed on the original grid, i.e., 0·25 mm. (Left) DEM of absolute difference
between the DEM resampled onto a grid with 1 mm spacing and the original DEM (Right) Internal reliability statistics.
Figure 5. Final DEM after merging. The sampling distance is 1 mm and the theoretical depth resolution is 0·32 mm.
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
January 2016
35
