(Table 1). These two indicators rejected a large number of
points, 56 percent and 34 percent, respectively. Despite a land
cover composed of bare land and low vegetation, the high
number of points rejected by the number of peaks indicator
probably resulted from the size of the footprint, inducing
additional returns from uneven ground or boulders (Brenner
et al.
, 2003). Therefore, for an area with heterogeneous land
cover or substantial tree coverage, where multiple echoes
are likely, the number of peaks indicator will possibly reject
an intractable number of points from the dataset. To ensure
a good spatial distribution in such conditions, this indicator
choice may well be excessive and require refinement (for
example, a more intelligent indicator could filter out weak-
amplitude peaks).
The application of the reflectivity and the signal/noise
indicators provided similar decreases in the
RMSE95
, of
0.33 m and 0.26 m, respectively (Table 1). Yet, the reflectivity
indicator was responsible for a 20 percent rejection rate,
while only 3 percent of the original points were rejected
based on the signal/noise indicator. Their similar impact on
the
RMSE95
was explained by higher
RMSE95
(12.87 m) for the
rejected points from the signal/noise indicator, with respect to
8.15 m for the points rejected by the first. In this respect, the
signal/noise indicator was better able to identify erroneous
elevations points from
GLA14
data.
Tables 1 and 2 show that the combination of all indicators
resulted in 31 percent (100 percent to 69 percent) of the
points being retained from the original dataset and provided
a 19 percent (1.32 m) decrease in
RMSE95
relative to the
RMSE95
reference value of 7.13 m. Final evaluation of the
CDED
shows a
RMSE95
of 5.81 m with an average of 0.27 m,
while maximum and minimum differences are respectively
12 m and −16 m, showing a slight upward shift from the
CDED
with respect to
GLA14
data. The rejection of so many
points might have been a problem if the spatial distribution
of the remaining points was substantially sparser than the
original dataset, anywhere in the
AOI
. Fortunately, this was
not observed; the filtered points still had a good spatial
distribution even though they exhibited a lower density than
the original tracks.
Compared to the methodology presented in this paper,
the method from Huang
et al
. (2013) led to fewer rejected
points (24 percent versus our 69 percent) and to a greater
reduction in
RMSE95
. This higher benefit can be explained by
the 100 m value used as a threshold for removing the outliers
(instead of 50 m as in this paper). The
RMSE95
prior to filtering
was 27.9 m (7.13 m in this paper) and a final, post-filtered
RMSE95
value of 9.6 m (5.81 m in this paper), resulting in
an improvement of 18.3 m. The fact that fewer points were
rejected can be explained by the fact that the Huang
et al
.
(2013) method focuses exclusively on removing data points
outside the 2
σ
range for the distribution of three parameters
(pulse-broadening, reflectivity, and detector gain) whereas our
method aimed to filter out all contaminated data targeted by
the selected indicators. Gonzales
et al
. (2010), with a filtering
method based on pulse width, obtained
RMSE95
results similar
to ours (6.23 m versus 5.81 m) and for the percentage of the
remaining points (28 percent versus 31 percent) after the
basic filtering process. Both studies used
SRTM
as a reference
and included a mountainous area in their study site, possibly
explaining why the final accuracies are lower than the one
achieved in this paper. These comparisons with other filtering
studies show that results from this paper are in line with
those previously published. Yet, the method presented in this
paper is applicable to all laser campaigns whereas the method
from Huang
et al.
(2013) has to be adjusted for each laser
campaign. While it is also the case for the method presented
by Gonzales
et al.
(2010), it lacks the completeness of our
method since it is not filtering out potentially erroneous
points due to attitude miscalculation, saturation, and,
arguably, scattering. However, pulse width could possibly
be considered as an additional parameter for the filtering
method presented in this paper, contributing further to the
elimination of points due to irregular surface components.
Its contribution should be studied further, with respect to the
selected indicators in the present study.
Exclusive Filtering Analysis
Results from the exclusive filtering are presented in Table 3.
They provided the means to evaluate the pertinence of each
selected indicator. It can be seen that the signal/noise and
saturation indicators failed to exclusively filter elevation
points. The signal to noise failure is related to the fact that the
gain is adjusted from the amplitude of the previous returned
echoes (Zwally
et al.
, 2008) and the signal/noise is calculated
using the maximum amplitude of the echoed pulse: the same
points are detected as potentially erroneous by both indica-
tors. Therefore, they are redundant. However, since the gain
indicator provided filtering results with a substantial decrease
in the root mean square error (Table 1) and showed a much
broader capacity for point rejection (a substantially greater
number of exclusively filtered points in Table 3), it appears
more pertinent than the signal/noise indicator.
T
able
3. P
roportion
of
points
exclusively
filtered
out
(
rejected
)
by
each
indicator
: T
he
“N
umber
of
points
exclusively
rejected
”
is
the
number
of
points
retained
after
a
second
filtering
of
the
rejected
points
in
T
able
2
using
a
combined
-
indicator
(
all
indicators
but
the
one
under
evaluation
)
filter
;
the
reference
for
the
proportion
column
is
the
“
number
of
rejected
points
”
column
of
table
2
Indicator
Number of points
exclusively rejected
Proportion (%)
Slope
329
90%
Attitude
335
23%
Gain
17136
42%
Saturation
0
0%
Reflectivity
1166
8%
Signal/Noise
0
0%
Nb of peaks
8427
23%
Concerning the saturation indicator, our analysis showed
that the gain and the reflectivity indicators rejected most of
the points that were initially rejected by this indicator. The
reason was that the more aggressive constraining criteria of
the reflectivity indicator supplanted the rejection criteria for
saturated echoes. A high value of the gain indicator, with its
attendant incitation of saturation in the face of rapid changes
in surface reflectivity, tended to complement, to a degree,
the dominant rejection actions of the reflectivity indicator.
Finally, the saturation points that were not rejected by the
reflectivity and gain indicators were rejected by the indicator
based on the number of peaks, without a clear relationship
between these processes. Because of that, safely withdrawing
the saturation indicator from the methodology presented in
this paper requires further tests over other study sites.
In summary, except for the signal/noise indicator, which
was redundant with respect to the gain indicator (and the
saturation indicator whose ability to filter points exclusively
or lack thereof was deemed to require further study) all
indicators were complementary and useful in the filtering
methodology presented in this paper. Indeed, the statistics
of Table 3 indicated that each of the remaining indicators
was able to identify potentially erroneous
GLA14
elevation
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
September 2015
705
