Weighted Spherical Sampling of
Point Clouds for Forested Scenes
Alex Fafard, Ali Rouzbeh Kargar, and Jan van Aardt
Abstract
Terrestrial laser scanning systems are characterized by a
sampling pattern which varies in point density across the
hemisphere. Additionally, close objects are over-sampled
relative to objects that are farther away. These two effects
compound to potentially bias the three-dimensional statis-
tics of measured scenes. Previous methods of sampling have
resulted in a loss of structural coherence. In this article,
a method of sampling is proposed to optimally sample
points while preserving the structure of a scene. Points are
sampled along a spherical coordinate system, with prob-
abilities modulated by elevation angle and squared dis-
tance from the origin. The proposed approach is validated
through visual comparison and stem-volume assessment
in a challenging mangrove forest in Micronesia. Compared
to several well-known sampling techniques, the proposed
approach reduces sampling bias and shows strong perfor-
mance in stem-reconstruction measurement. The proposed
sampling method matched or exceeded the stem-volume
measurement accuracy across a variety of tested decima-
tion levels. On average it achieved 3.0% higher accuracy
at estimating stem volume than the closest competitor.
This approach shows promise for improving the evalua-
tion of terrestrial laser-scanning data in complex scenes.
Introduction
Lidar (light detection and ranging) has become an established
tool in the general field of remote sensing, given its ability
to collect active three-dimensional spatial measurements of
a scene (Lim and Suter 2009; Dassot, Constant and Fournier
2011). By emitting pulses of light and de
with precise timing, and assuming a ho
dium, a measurement of distance is obta
the task that is being conducted, a lidar unit is typically built
with either a raster or a spherical scan path (Hopkinson
et al.
2004). In the case of airborne platforms, the raster paradigm
is usually implemented, since it affords the ability to follow a
whisk-broom sensor path as the platform moves forward. Due
to this motion, and given a sufficiently high temporal fre-
quency, sampling is relatively uniform with the velocity vec-
tor (Lin, Benziger and Habib 2016). In the case of a spherical
scan path, as in a semispherical ground-scanning (terrestrial)
lidar unit, there is a nonuniform density of samples accrued
over the surface of constant phase. This implies that at a fixed
radius from the origin of capture, the density of the inscribed
spherical surface will vary as a function of position. This can
be readily visualized by imagining that at some elevation
angle
ϕ
there are
L
θ
azimuthal steps which take the system
through some angular ring
E
∈
{0,2
π
} (Figure 1). Given that the
angular spacings
Δ
ϕ
and
Δ
θ
between samples along the set
of axes are held to be constants, the spatial density of points
will be significantly greater as one approaches the elevation
“poles” of the sphere of constant phase. In other words, the
distance between azimuthal rings decreases as the elevation
angle approaches
b
π
, where
b
is any integer. These azimuthal
rings are illustrated as the black circular samples in Figure 2.
In practice, this effect is found to manifest as an over-sam-
pling of points which are near either nadir or zenith to the
sensor. This can introduce a bias in the structural assessment
of lidar data and affect the accuracy of mapping and modeling
Alex Fafard, Ali Rouzbeh Kargar, and Jan van Aardt are with
the Department of Imaging Science, Rochester Institute of
Technology, Rochester, NY, 14623 (
).
Photogrammetric Engineering & Remote Sensing
Vol. 86, No. 10, October 2020, pp. 619–625.
0099-1112/20/619–625
© 2020 American Society for Photogrammetry
and Remote Sensing
doi: 10.14358/PERS.86.10.619
Figure 1. Above the geometry of a surface of constant phase
as in a spherical scanning system. Here the elevation and
azimuthal planes are illustrated with corresponding angular
variables with their Cartesian correspondents.
Figure 2. Effect of on-grid sampling on the samples acquired
along the surface of constant phase. The squares represent
the on-grid samples, and the circles are the samples
acquired along the sphere. The drift of values shows the
effect of interpolation on the data.
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
October 2020
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