Rowe Ground Classification and Below Ground Response Assessment of
Forested Regions using Full-Waveform LiDAR
Jonathan Rowe
[email protected]
Advisor: Dr. Jan van Aardt
Committee: Paul Romanczyk, Dave Kelbe, Bob Kremens
Senior Project, Chester F. Carlson Center for Imaging Science
College of Science
Rochester Institute of Technology
Fall 2013
ABSTRACT
To gain a better understanding of how forested ecosystems function, research has
been performed to characterize and model specific features within the forest using
imaging techniques. Since the 1960s, light detection and ranging (LiDAR) has been used
to generate three dimensional models of scenes by emitting a laser pulse and recording
the time it takes for the pulse to interact with a scene and return back to the instrument.
These times are converted to discrete ranges, often able to record multiple returned
ranges per laser pulse. More recently, a new type of LiDAR instrument has been used in
research that has the ability to digitize the reflected energy at a much finer scale, giving it
the ability to record the entire waveform of reflected laser energy from the scene. Since
the technology is so new, its potential is still not fully understood in the scientific
community. In this paper, we focus on this new technology as a means to locate and
model the ground of a forested region based on a 100m by 100m study area within the
Harvard Forest in Massachusetts. The ground layer, called a digital elevation model
(DEM), is important in LiDAR forest research because many other models, such as
understory and canopy height models, require accurate DEM estimation. It became
apparent that this task is not as easy with waveform LiDAR as with discrete LiDAR
because in some cases, the waveform energy distribution extends below the ground level.
Although discrete LiDAR can sometimes contain below ground hits, intensity and range
thresholds tend to eliminate the issue from becoming a serious difficulty in estimating the
DEM. In addition to generating a DEM derived from waveform products provided by the
National Ecological Observatory Network (NEON), we focus on how to characterize
these below ground responses and understand where they are coming from. Our reference
data include a discrete derived DEM from NEON’s same sensor, and a discrete derived
DEM generated by NASA’s G-LiHT system. Results show that our proposed method
produced a DEM with root mean square deviation metrics of 293.7m and 7.41m when
compared with the NEON and G-LiHT DEM, respectively. Assessment of the below
ground responses reveal that the strongest relationship of below and above ground hits
happened within the first meter of elevation above ground, yielding an R2 value of
0.2557. Overall, however, our method did not produce an acceptable accurate model to
determine the cause of the below ground echoes.
1 Rowe 1. INTRODUCTION
With the dramatic changes in the Earth’s climate and the increased demand for timber
and other wood supplies, the need for characterization and modeling of our planet’s
forests and vegetation is at an all-time high. To safely and efficiently assess our human
impact in these areas, we must first be able to model the quality of vegetation of the
forest of interest. Many parameters can be used to describe the health and biomass of the
trees, such as spectral characteristics and physical attributes, but these parameters are not
easily modeled. Foresters gain knowledge of a forest biomass by taking field
measurements, which include ground-based measurements of trunks and leaves through
use of hand held instruments, ground-based remote sensing, and airborne remote sensing.
Two-dimensional images of the Earth’s surface collected by airborne and spaceborne
sensors are valuable sources of data for understanding these vegetation parameters
(Singh, 1989). The most common form of remote sensing used for this purpose is multispectral imaging, which is acquired by a sensor with multiple bands that detects energy
reflected from a scene in the visible, near infrared, and short wave infrared regions of the
electromagnetic spectrum. The problem with these systems is that even though high
spatial resolutions can be interpreted, the resulting images are two-dimensional and thus
cannot account for elevation characteristics of the vegetation. These elevation
characteristics can consist of canopy height measurements, differentiation between
canopy and understory, and specific elements such as the general location of leaves,
branches, etc. Many of these limitations of two-dimensional imaging techniques may be
compensated for by using three-dimensional measurement techniques, which allow for
separation of objects found at different heights above the Earth’s surface. This height
information is crucial to generating separate models for ground and canopy surfaces, as
well as other height-dependent classification products (Wulder, 1998). One of the most popular remote sensing techniques used to capture three-dimensional
measurement data is light detection and ranging (LiDAR). LiDAR is an active form of
remote sensing, meaning that it provides its own source of energy, rather than using
separate sources of illumination, such as the sun, for two-dimensional imaging methods.
The energy provided by LiDAR instruments is in the form of a laser pulse. This pulse is
emitted towards a target, and with each interaction a portion of the initial pulse energy is
reflected back to the sensor, generating a waveform of energy characteristic to the
specific scene being scanned. Early LiDAR systems were only capable of digitizing 1-4
responses, which resulted in discrete samples. For every one of these responses, the time
between sending and receiving the laser pulse is recorded. Using the speed of light, range
between the sensor and point of reflection is calculated. Included with the time recording
for each pulse, the scan angle of the sensor, platform attitude of the airplane (pitch, roll,
yaw, and heading) for airborne scanning, and global positioning of the instrument itself
are stored. Combining all of these factors, the locations of every discrete return can be
precisely mapped on the Earth’s surface (Wehr and Lohr, 1999). By the 1990s, LiDAR
instruments had developed such that the entire waveform of back-scattered energy could
be recorded onto the sensor. These waveforms have the potential to provide much more
information about the scene content than discrete sampling, especially with vegetative
scenes. Most discrete responses in vegetation correspond to either canopy or ground,
2 Rowe while every once and a while gaining an extra response in between, but the full waveform
of a response accounts for all the interactions in the emitted laser pulse’s path (Mallet and Bretar, 2009). Waveform LiDAR processing is similar to discrete processing in that many models
and products are derived in reference to the ground. Therefore, classifying the ground
proves to be one of the most important tasks. The most common LiDAR derived product
containing ground classification is called a digital elevation model (DEM), which can be
represented as either a raster or a vector based triangular irregular network (Wagner, et al., 2004). DEMs are used in many fields of study for purposes such as surveying, flood
mapping, line-of-sight analysis, urban planning, cartography, land use modeling, and
many others. In vegetation analysis, the DEM provides the tool used in deriving canopy
height models and understory segmentation. With discrete LiDAR, ground classification
is usually performed by storing the final returns of all the laser scans and removing
outliers, or the returns where the laser pulse never made it to the ground (Lewis and Hancock, 2007). With full-waveform LiDAR this process proves to be more difficult.
This is due to observed phenomena where the waveform consists of responses below the
ground level. This occurs because of multiple scattering of the energy from the initial
laser pulse and the extra time it takes for the scattered energy to return to the sensor.
Therefore, the challenge arises of how to account for the belowground multiple-scattering
echoes (Pirotti, 2011). The purpose of this research is to study these belowground echoes to try and gain an
understanding of why they exist and how to remove them in order to perform a more
accurate ground assessment of the waveform. In addition, I will address the relationship
between the multiple-scattering responses and the content just above the ground surface,
such as brush, as well as the canopy.
2. LITERATURE REVIEW
Many studies have been performed on the assessment of full-waveform LiDAR and
its applications to measuring vegetation. One of the most important steps in the
processing pipeline comes first, namely signal deconvolution. When a raw waveform is
recovered at the sensor, it appears stretched and does not provide an accurate indication
of features in the scene. This is due to a combination of the receiver impulse response, the
sensor’s variable outgoing pulse signal, a fixed time gate for detection, and system noise.
In theory, the resolution of the waveform signal can be recovered by deconvolving the
system response from the measured signal (Wagner 2006). Many approaches have been
taken to perform this deconvolution. L.B. Lucy developed one of the most popular,
known as the Richardson-Lucy algorithm, in 1974. This is an iterative procedure based
on Bayes’ statistical theorem (Richardson, 1972; Lucy, 1974). Harsdorf and Reuter
(2000) stated that this approach resulted in the most dependable results when compared
to Fourier transform and non-negative least squares methods (Harsdorf and Reuter, 2000). Wu et al. tested the Richardson-Lucy algorithm against the Wiener (Wiener, 1949) and non-negative least squares and arrived at the same conclusion (Wu et al., 2009; Wu 2011; Wu et al., 2012). Wagner et al. also advocates for the RichardsonLucy algorithm for all of their waveform pre-processing (Wagner, Ullrich, Melzer, et al., 2004; Wagner et al., 2006; Wagner et a l., 2007; Wagner et al., 2008). 3 Rowe A majority of digital elevation model extraction methods from full waveform LiDAR
involve digitizing the waveforms to discrete samples (Sithole and Vosselman, 2004; Hollaus et al., 2006; Wagner et al., 2008). One common fact that all discrete DEM
generation algorithms share is that they only rely upon geometric criteria, such as
elevation relationships between neighboring points, to eliminate non-ground hits (Pfeifer 2004). With waveform data, characteristics of individual Gaussian-like echoes within
the waveform can be evaluated to assess whether or not it refers to a ground location.
Doneus and Briese (2006) proposed a two-step approach to evaluating these individual
echoes for ground assessment. They first eliminate all last echo points with a significantly
greater echo width than the echo width of the system waveform. Next, standard filtering
procedures are performed, outlined by Kraus and Pfeifer (1998) and Briese et al. (2002)
to remove non-ground points (Doneus et al., 2008). These filters divide the study area
into grid-like regions and extract the lowest elevation response for each region.
Afterwards, standard geometric criteria are used to remove points with large elevation
differences from neighboring points (Kraus and Pfeifer, 1998; Briese 2002). Many studies do not account for the underground responses in their extraction of the
DEM. There have been no studies completely dedicated to the understanding of the
below ground echo phenomena. Researchers consider these phenomena to be
unimportant in the extraction of waveform-derived products. The most common approach
taken to deal with the belowground echoes is to assume that it is due to system noise. A
noise threshold is selected based on a fraction of largest magnitude of all the peaks in the
waveform. Every response peak below this threshold is assumed noise and negated from
the analysis (Asner et al., 2007; Wagner et al., 2008; Kronseder et al., 2012). The
estimate of 1/10th was suggested by Chhatkuli et al. (2012), whose study shows that
ground penetration increased by 50% in autumn and 20% in winter (Chhatkuli et al., 2012). As mentioned, another approach taken is to remove all last echoes with a greater
echo width and standard deviation than the echo width of the entire system waveform
(Doneus and Briese 2006). Although these methods do a decent job at removing below
ground responses from the waveform, they do not account for why the echoes exist, or
how we can go about understanding them.
3. MATERIALS
3.1 Study Area
The study area is centered on the Boston University/University of Massachusetts
Boston Harvard forest hardwood site. The Harvard Forest Hardwood site is 100m by
100m with a center of (42.53100° N, 72.18210° W). The site, in association with
Harvard University and the Long Term Ecological Research Network, is considered a
wildland “core” site, which statistically represents unmanaged wildlife conditions across
NEON’s 30-year history. It consists of dense hardwood trees with thick canopy coverage.
Both ground truth and airborne measurements were taken of the area in the summer of
2012.
4 Rowe 3.2 Field Measurements
Field data for this research were collected from five reference points within the 100m
by 100m plot by a team comprised of researchers from the University of Massachusetts
Boston, University of Massachusetts Lowell, and Boston University. For each of the
sites, data for the surrounding trees were collected, including tree identification number,
range and bearing from a reference location, species, whether or not an occlusion of the
trunk is present, and classification of the crown prominence. Diameter at breast height
(DBH) and height were also measured for select trees. DBH and tree height are valuable
measurements for inputs to models that predict parameters such as biomass.
3.3 NEON LiDAR Data
NEON’s Airborne Observation Platform (AOP) provided an airborne full-waveform
LiDAR survey of the study area. An Optech Gemini instrument was used to capture the
LiDAR waveforms at a wavelength of 1064nm. An approximately 200m × 200m subset
of the NEON prototype waveform data was extracted about the site center; 110,367
waveforms were processed for the scene. Each waveform consists of 500 bands with 1ns
(0.15m) vertical spacing. The time gate of the 500 bands for each waveform was variable,
i.e., where the bands began recording at the first response of the waveform. Since a
variable time gate was used, a reference file was supplied for each waveform that
consisted of important location information such as northing, easting, and height of first
return, outgoing pulse reference bin location, and first returns bin reference location in
the return waveform. All northing and easting information were stored in Universal
Transverse Mercator (UTM) coordinates, the common coordinate system used with
LiDAR data. All data were converted to MATLAB-accepted formats for processing.
NEON also generated a discrete LiDAR point cloud of the study area. These data
were collected using the Optech Gemini instrument without the waveform digitizer in
use. ENVI LiDAR software was used to extract the DEM from the point cloud. This
product will be used as our primary reference data as it was sollected using the same
sensor as the waveform data.
3.4 G-LiHT LiDAR Data
Our second set of reference data for validating our implementations was generated by
the National Aeronautics and Space Administration’s Goddard LiDAR, Hyperspectral,
and Thermal Imager (G-LiHT). Although G-LiHT does provide additional imaging
information such as imaging spectroscopy and thermal imaging, we will only use the
digital elevation model derived from its discrete LiDAR component. The G-LiHT lidar
data were collected with a Riegl LD321-A40 system with a pulse frequency of 10kHz
and can process up to five returns per laser shot at 905nm (Cook et al., 2013). The DEM
is a rasterized surface interpolated to one meter. 4. WAVEFORM PRE-PROCESSING
Before specific analysis can be performed on the individual waveforms, some preprocessing needs to occur. Raw waveforms are not smooth functions in that they contain
both noise and intensity thresholding. The LiDAR sensor applies a detection threshold for
the reflected waveform that was used to filter out solar background light and detector
5 Rowe noise (M. Hofton 2000). As a result, only portions of the waveform whose
corresponding intensity was above the detection threshold are stored in the raw
waveform. This results in functions such as the one shown in blue in Figure 1. 5.1 Waveform Deconvolution
The deconvolution approach is important because it can remove the system effect
from the signal. The raw waveform was deconvolved with the outgoing pulse shape and
estimated system impulse response to estimate fine detail at the 30cm scale, which is the
Nyquist frequency for one nanosecond sampling. A one-dimensional implementation of
the Richardson-Lucy algorithm was used as the main deconvolution method (Richardson,
1972; Fish et al., 1995; Cawse-­‐Nicholson, 2013). The Weiner deconvolution algorithm
was also tested by Wu et al. (2011), but the specific application to one-dimensional data
did not produce as accurate input responses at the Richardson-Lucy approach (Wu et al., 2011). Figure 1 displays the result of this deconvolution. Figure 1: Normalized representation of a raw (blue) and deconvolved (green) waveform. The
horizontal line represents the detection threshold that the system implemented to remove noise and solar
background light from the raw signal. All returned intensity values that fall below this threshold are set to
zero. The deconvolved waveform was generated using the Richardson-Lucy deconvolution approach to
estimate an impulse response and retrieve the original input signal from the laser response.
As we can see from the deconvolved waveform, it was much easier to estimate time
locations where the laser interacted with the scene and reflected some of its energy. At
this point in the processing chain, we have enough information to begin to estimate
specific features in the scene. For example, the separations between the peaks at time bins
37 and 143 could be the difference between the canopy height and ground, with some
small responses in between for below-canopy tree features, and some responses below
ground for multiple-scattered responses. However, these estimations are still ambiguous
due to multiple geometric and radiometric issues, such as leaf and tree structure and
reflectance and transmittance, and more processing must be performed to gain a better
understanding of the scene content.
5.2 Waveform Decomposition
To get a better understanding of what these specific peaks correspond to, we must
isolate them from each other within the waveform itself. Doing so will provide vital
6 Rowe information about the specific waveform responses, such as peak amplitude, standard
deviation, and location (M. Hofton 2000). These statistics are extracted through a
process called waveform decomposition. Waveform decomposition assumes that the
energy distribution at every peak location can be modeled by Gaussian functions. The
iterative process selects a Gaussian distribution of arbitrary statistics and loops through
different inputs until the best match is defined through the root mean square error
(Wagner et al., 2007). As a result, a new array of stored points was generated, each
point containing peak amplitude, standard deviation, and time bin location properties.
This process essentially discretizes all of the waveforms, producing data similar to
discrete LiDAR. The difference was that the discretized waveforms can contain more
points per laser pulse and each point contains statistics about the laser energy interaction
at the scene. 5. DIGITAL ELEVATION MODEL GENERATION
5.1 Methods
The discretized waveforms can be plotted as a geographically referenced point cloud
using the time bin value for each peak and the geographic reference data provided for
each waveform by NEON. This referenced point cloud was used for DEM generation.
Figure 3 displays this point cloud.
Figure 3: 40m by 40m subset of the geographically referenced point cloud of the discretized
waveforms, focused at the center of the study area at (42.53100° N, 72.18210° W). Point sizes are displayed
according to their corresponding normalized intensity.
Figure 3 provides an excellent visual tool showing a region of the discretized point cloud.
As the plot shows, most of the emitted laser energy was reflected off the tree canopy,
leaving few ground points. Furthermore, by displaying the point sizes proportional to
their respective intensities, it can be seen that below ground multiple scattering echoes
have very small amplitudes (Persson et al., 2005). Using this plot, we can make
assumptions for two processing steps that can be used to remove data irrelevant to our
DEM extraction. This irrelevant data include the below ground and canopy responses.
7 Rowe First, an intensity threshold can be applied to remove the below ground responses. For the
purpose of this implementation, a value corresponding to 1/10th the maximum intensity in
the waveform was used as the threshold. Second, an elevation threshold can be applied to
remove the majority of above ground points. This threshold was selected by taking the
global threshold of the histogram of elevation values (Otsu, 1975). The result of these
two thresholding operations was a point cloud containing only points from the ground
and those just above the ground. A gridded sampling was used to divide the study area into smaller regions in order to
get a representative estimate of ground points. For each grid cell, the minimum point
coordinate of the lowest point was stored. This was most representative of ground
because the below ground responses have already been removed through thresholding
(Doneus et al., 2008). The size of the grid spacing was important to the ground
extraction because the grid size must be small enough to acquire a significant amount of
resulting ground points, but large enough to account for non-ground points (de Berg et al., 2008). For example, if a grid size of 2m by 2m was used and no ground points lie
within that grid, a point above ground may be assigned to ground for that location. After
evaluating many grid sizes, a final grid spacing of 10m by 10m was selected. This grid
size did produce cells that did not contain ground points, as we can see from Figures 4a
and 4b, but it contained the fewest non-ground hits of all grid sizes ranging from 1m to
20m. Using a grid size of 10m reduced the number of points in our cloud to 441, shown
in Figure 4a. There was still a chance, however, that the minimum point of a grid was not
ground. This potential issue was addressed using a triangulation method. The built-in
MATLAB function “DelaunayTri” was used to perform the Delaunay triangulation. The
algorithm takes three neighboring points and forms a circumcircle around them. If no
other points lie within that circle, the points are connected to form a triangular facet. If a
point does lie within the circumcircle, the specific three points are not triangulated (Lee, 1991; Kelbe, 2013). The result was a surface of triangular facets that connect the points
in the subsampled ground point cloud, shown in Figure 4b. Figure 4a. Subsampled point cloud containing one point in every 10m by 10m spacing. Since the
below ground responses were removed and the minimum point in each grid cell was selected, it was
assumed that these points approximate the ground.
8 Rowe Figure 4b. Delaunay triangulated grid of the ground points selected in Figure 4a. It was assumed that
the outlying points above the average ground surface do not correspond to ground.
As shown in Figure 4b, some of the minimum points taken from the grid cells lie above
the average surface height. The most likely cause of this was that the 10m by 10m region
did not have a point corresponding to ground. Now that these outliers have been
determined, a simple angular threshold can be generated to remove them. Using simple
trigonometry, the angle (θ) between each point along the triangulation lines was
calculated using equations 1 and 2.
𝜃 = cos !!
!!
!!
(1)
Δd = Δx ! + Δy !
(2)
where Δd is the distance in northing and easting between two points and Δx, Δy, Δz are
the difference in easting, northing, and elevation, respectively. An angular threshold was
determined by referring to the reference data. Since the G-LiHT DEM is already
rasterized to one-meter resolution, these points were used to determine a maximum slope.
The maximum slope was calculated using equations 1 and 2. In this case, the Δx and Δy
are each one meter. Results of these computations imply that a maximum angle of 10°
should be used for the angle threshold in removing outlier points. Figure 5 displays the
resulting triangular network after the outlying points are removed.
9 Rowe Figure 5. Delaunay triangulated network of ground points after outlying points with an angle greater than
10 degrees of their neighboring hits were removed.
After the outlying points were removed, the points were translated onto a raster grid and
interpolated. MATLAB’s built-in “TriScatteredInterp” function was used to interpolate
the rasterized points to a density of 0.5m.
5.2 Results
The digital elevation model generated using the above method did not yield similar
results to our G-LiHT reference data, but was reasonably close to our NEON discrete
reference data. Since our ground was sampled at wide 10m by 10m intervals, there was
much more variability between ground points, resulting in a less smooth surface. Figure
6a displays the digital elevation model generated from the waveform LiDAR. Figures 6b
and 6c display the DEMs generated from G-LiHT and NEON data sets, respectively. The
differences between the waveform DEM and the two reference DEMs are shown in
Figures 6d and 6e, respectively.
Figure 6a: Digital elevation model generated through the waveform-based method described in section
5.2. The variability was attributed to the irregular 10m by 10m sample spacing.
10 Rowe Figure 6b: The digital elevation model
generated by G-LiHT’s Riegl LD321-A40
discrete LiDAR component. G-LiHT’s DEM
was given to us “as is.”
Figure 6c: The digital elevation model
generated by NEON’s Optech Gemini discrete
LiDAR component. This DEM, given a discrete
point cloud provided by NEON, was derived
using ENVI LiDAR’s ground extraction
algorithms.
Figure 6d. Difference of the waveform
derived DEM and the reference G-LiHT DEM,
where the waveform DEM was subtracted from
the G-LiHT.
Figure 6e. Difference of the waveform
derived DEM and the reference NEON discrete
DEM, where the waveform DEM was subtracted
from the discrete DEM.
Calibration inconsistencies between NEON’s and G-LiHT’s processing pipeline account
for offsets in elevation between the two models; however, this does not account for
differences in the ranges of elevation between the three models. Most likely, these range
shifts are due to time shifts produced during the deconvolution step. Elevation ranges and
standard deviations are calculated for each DEM, and the root mean square deviation
(RMSD) and mean elevation difference between the reference DEMs and waveform
derived DEM are highlighted in Table 1.
11 Rowe Table 1: Quantitative comparison of the waveform-derived DEM, NEON’s discrete DEM derived
using ENVI LiDAR and the discrete-derived DEM using G-LiHT’s data.
Elevation Range (m)
Standard Deviation (m)
RMSD (m)
Mean Elevation Difference(m)
Waveform-derived
15.48
3.19
---
G-LiHT Discrete
10.68
2.703
293.70
24.41
NEON Discrete
18.01
3.20
7.31
5.02
Statistically speaking, the waveform generated DEM was very different than the GLiHT DEM. This was due to two main causes. First, it was unknown where in the
reflected energy response G-LiHT’s system quantifies the discrete responses. For
example, when the waveforms were discretized, the location at the amplitude’s peak was
used for the location of the discrete point. Some LiDAR processing takes the full-width
half-max point of the leading edge to discretize a response. This can result in varying
differences between the two point locations because reflected energy distributions have
very different shapes due to different interactions with scene content. Secondly, in the
10m by 10m grid cells generated for identifying ground points, the point actually
representative of ground contained a relative amplitude less than 1/10th of the largest
amplitude in the waveform. In this case, the algorithm will select a point that was actually
above the ground. One way that we can justify ground point locations was by
understanding how below ground responses are formed.
6. BELOW GROUND ECHO ASSESSMENT
6.1 Methods
Now that a digital elevation model has been generated, we can use its surface to
assess the laser energy below ground. Our assumption was that these energy returns are a
result of content in the scene above ground. A voxel approach was taken to compare the
below ground energy distribution to the above ground energy distribution. The
implementation generates a voxels in three-dimensional space directly below and above
the DEM. The voxel is 10m by 10m in surface area, which is wide enough to locate
enough below ground points to accurately represent their characteristics. Within each
voxel, the means, the standard deviations, and the sums of the point amplitudes of the
existing discretized points’ intensities were calculated. We seek to prove that these
statistics below the DEM will correlate with those above the DEM, therefore accounting
for the multiple-scattering phenomena. The below ground voxels will be compared to
different elevation levels above the ground. Above ground voxels will range in height
from one meter to 30 meters, in one meter increments. In other words, 30 voxel
comparisons will be made for each 10m by 10m spacing in the study area. Number of
points, the mean amplitudes, and standard deviations of the points within the voxels will
be plotted alongside the corresponding statistics of the below ground voxel. Relationships
between the below and above ground voxels will be assessed through linear R2
regression.
12 Rowe 6.2 Results
Assessment of below ground responses yielded interesting results. It was assumed
that this phenomena was caused by multiple scattering by the laser vegetation structure
above ground. Comparisons of below ground data were performed on data above the
ground from one meter to 30 meter increments. Figure 7 provides an example of the
process using two above ground voxels. The first, labeled understory, accounts for all
points up to 5m above ground level. The canopy region refers to a voxel that accounts
for all points 5m above ground level.
Figure 7a. Relationship of the number of below ground responses to the number of understory
responses (blue) and canopy responses (green). Linear fitting lines are overlaid over the data that are used
to calculate the R2 regression.
Figure 7b. Relationship of the mean amplitude of below ground responses to the mean amplitude of
understory responses (blue) and canopy responses (green). Linear fitting lines are overlaid over the data
that are used to calculate the R2 regression.
13 Rowe Figure 7c. Relationship of the standard deviation of below ground responses to the standard deviation
of understory responses (blue) and canopy responses (green). Linear fitting lines are overlaid over the data
that are used to calculate the R2 regression.
We can qualitatively assume from Figure 7 that the below ground points have very little
correlation to the above ground points. If they did, the corresponding statistics would
form a linear relationship. Instead the points are scattered, implying very little
relationship. This relationship is measured quantitatively by calculating the R2 regression
component. As mentioned, the R2 value was then measured for a variety of above ground
voxel sizes. The results of these statistics are shown in Figure 8.
Figure 8: Comparison of R2 values for the number of points, mean amplitude, and standard deviation
of the amplitudes for varying voxel elevations above ground level.
14 Rowe Figure 8 provides valuable information about the occurrences of below ground echoes.
Calculating the R2 values with voxels of varying height above ground provided
information as to where the multiple scattering is occurring. R2 values calculated above
the voxel location make it easier to determine how valid the correlations between the
above ground points and below ground points are. For elevation levels where the R2
value is much greater below the threshold than above it, it is safe to assume that it is the
due to the interactions below the thresholds that result in the below ground echoes. This
is the case with the statistic relating number of points above and below the low elevation
thresholds. For the regression between the number of points in the first meter above the
ground and the below ground points, there was an R2 value of 0.26, which is the largest
R2 value of all relationships tested. All of the points lying above this one meter
threshold, when compared to the below ground points, resulted in an R2 of 0.01.
Although the number of points R2 decreases as the voxel height increases over the next
10 voxel sizes, it still remains much larger than its respective above-threshold R2 value.
This means that the strongest estimation we can make is that the below ground echoes are
related far more to the number of points just above the ground level than any other
elevation, as well as any other statistic describing the points. Standard deviations of
points residing in the voxels below 5m had the second strongest relationship to the below
ground points. This reflects the results of the study by Doneus and Briese (2006), where
below ground hits were filtered out based on the widths of the individual waveform
echoes. The mean of the amplitude R2 values remained fairly consistent throughout the
voxel heights lower than 19m, implying that the below ground points can not be
accurately modeled by the mean and standard deviation of the points up to 19m above
ground. For the above ground voxels with heights above 19m, there is a greater
relationship between the residing points and their below ground counterparts. The
number of points above the 26m to 28m voxels actually resulted in greater R2 values than
the ones within the voxel. This mean that at these thresholds the number of points above
influence the number of below ground points more than the number of points above
ground and below the threshold. Standard deviations and means of point amplitudes in
voxels covering the canopy regions increase as well. At voxel thresholds of 20m to 24m
there is a larger relationship of mean amplitude above the threshold to the means below
ground than anywhere else in the elevation region, but with a maximum R2 value of 0.05,
it is still not a strong enough of a relationship to accurately model the below ground
returns to multiple scattering in this elevation region. Based on the results shown in
Figure 8, the number of points and the mean of point amplitudes within the voxel at
lower voxel elevation thresholds provide the best estimation as to the location of the
multiple scattering phenomena.
7. CONCLUSIONS
The proposed method does not serve as a complete algorithm for ground extraction
using waveform LiDAR data, because it does not contain the quantitative precision that
the NEON and G-LiHT discrete DEMs do. The lack of precision was best reflected in the
15 Rowe quantitative comparison shown in Table 1. Inability in this approach to separate below
ground returns and above ground returns from actual ground hits resulted in the algorithm
selecting points above the ground to be ground points, which extended the range of
elevation in the model. In addition, there were many instances where the signal simply
did not reach the ground, resulting in the selection of above ground points independent of
a below ground counterpart. Other factors that may have influenced these results are
differences in the processing chains between the data provided by NEON and G-LiHT.
Since G-LiHT’s processing pipeline is unknown it is not possible to compare the time
shifts resulting from potentially different deconvolution methods. Since our ground truth
data were a discrete DEM generated by a separate organization, it was difficult to be
certain of our accuracy in comparison. This was due to the unknown variables in the
ground truth DEM’s processing chain.
Our assessment of underground responses shows that these occurrences are likely due
to multiple scattering of photons emitted by the laser in the scene, which delays their
return to the sensor and results in a larger range. Calculating R2 regression metrics for
below ground points compared to their above ground counterparts provided valuable
information in understanding where these scatterings occur. Figure 8 shows that the
strongest relationships are between number of points and standard deviation of
amplitudes of the points below ground and within 4-5m above the ground’s surface,
having maximum R2 values of 0.26 and 0.18 respectively. Since the relationship between
the below ground points and those points above these voxels are drastically smaller, we
can assume that the points within the 1-5m voxels themselves are the driving forces
behind these below ground echoes. There is little relationship between the points below
ground and the points between 5m and 19m above ground. This is expected because this
elevation range contains less content than both the ground level brush and the thick
canopy. In the canopy region of 19m to 28m, stronger relationships occurred for number
of points and standard deviation of those points, as well as mean amplitude values of the
points within that voxel. However, with the largest R2 value is this region being 0.11
(number of points within the voxel at 22m), it makes for a very inaccurate model. In
conclusion, our data show that the below ground responses have the strongest
relationship with the number of points and their standard deviations less than 4m above
ground, but with an R2 so low it is still not strong enough to generate an accurate model
of the below ground echoes.
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