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compared to the merged DEM (Figure 5). Small gravel particles
are hardly distinguishable in the non-merged DEM. It is suited
for general bed-roughness analysis, but analysis on the rela-
tionship between detailed grain roughness and bed roughness
is not possible with the non-merged DEM. Visually, no differ-
ences are distinguishable between merged DEM s resampled at
0·25 mm and 1 mm, respectively, which agrees well with our
analysis as presented in Figure 4.
The non-merged DEM was compared with the composite DEM
obtained using merging. No particular trend was observed in the
DEM of Difference (DoD), outside from a reduced sharpness of the
non-merged DEM at the edges and gaps between gravel particles.
For this reason, we solely report the results of the quantitative
evaluation. The difference between the two DEMs was character-
ized by a MUE of 1·30 mm and a SDE of 1·68 mm globally over
the test section. This represents the internal reliability of the
non-merged DEM. One can see that DEM quality is considerably
degraded compared with the composite DEM obtained from the
merging of three individual DEMs of better quality.
The last step in our evaluation of the merging method
examined the effect of scale variation, to simulate the merging
of coarser data with higher uncertainties (e.g., data collected
from aerial platforms). For the tests, the DEMs’ sampling
distance was degraded by a factor of 2 and 4, resulting in
new DEM grid sizes of 2 mm and 4 mm, respectively. De-
graded DEMs were registered and merged the same way as the
original DEM s, which were characterized by a 1 mm sampling
distance. The fundamental difference being that the preci-
sion of the horizontal alignment was changed from 1 mm to
2 mm and 4 mm for the two cases studied, respectively, since
the horizontal registration precision equals the DEM grid size
(see the “3D Co-Registration and Merging” Section). Figure
10 shows the residual maps after co-registration of DEM -1 and
DEM-2, for the two new DEM grid sizes. One can see the large
systematic errors resulting from the change in horizontal
registration precision, especially for the 4 mm case. This is
because the position of the stitching line was offset by 1 mm
and 3 mm compared with the optimum position detected us-
ing the 1 mm resolution DEM s, for the 2 mm and 4 mm cases,
respectively. Resulting from the inaccurate horizontal align-
ment, seamless merging failed and the residual maps were
characterized by a MUE = 1.04 mm (SDE = 1.47 mm) and MUE
= 1.88 mm (SDE = 2.47 mm), for the 2 mm and 4 mm cases,
respectively, compared with MUE = 0.67 mm (SDE = 1.02 mm)
obtained using the original resolution of 1 mm (Figure 7).
It is clear that the decision on which DEM grid size to
choose (hence on the horizontal alignment precision) is
critical for effective merging. Coarse DEM merging can be
improved by resampling the DEMs onto finer grids, hence
improving the horizontal alignment precision, before co-
registration. After merging, the unnecessary high-resolution
DEM can be transformed back to its original sampling dis-
tance. When there is no a-priori knowledge of the optimum
registration resolution, this can be determined by error and
trial, until effective seamless merging is achieved. Here, the
degraded DEM s characterized by grid spacing of 2 mm and
4 mm, respectively, were resampled onto the original 1 mm
grid, before merging. This enabled detection of the optimum
stitching line, and thus satisfied the condition of seamless
merging (Figure 10).
Figure 9. (Top) DEM of the full test section obtained at once (no merging), represented on a grid with 1 mm spacing; the theoretical depth
resolution is 1·15 mm. (Bottom) Close-ups on bed structure without DEM merging (left); with DEM merging and resampled to 1 mm sam-
pling distance (middle); with DEM merging and 0·25 mm sampling distance (right).
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