A Novel Approach to Characterizing LiDAR Waveforms

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A Novel Approach to Characterizing LiDAR Waveforms
Geoffrey M. Henebry Eric Ariel L.
Salas Geographic Information Science Center of
Excellence South Dakota State University and
Naikoa Aguilar-Amuchastegui Department of
Environmental Studies University of North
Carolina-Wilmington Forest Carbon Lead
Scientist, World Wildlife Fund, as of 8/2010
Research supported through the NASA Biodiversity
program NNX09AK23G. Thank you!
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Synergistic Analyses of Data from Active and
Passive Sensors to Assess Relationships between
Spatial Heterogeneity of Tropical Forest
Structure and Biodiversity Dynamics Study site
Tropical forests on the Atlantic slope of Costa
Rica, specifically, the stands under sustainable
management by FUNDECOR, a Costa Rican
NGO. Project proposed 6/2008 Project funding
received 7/2009 First field campaign 6/2010
Focus today on a new approach that we very
recently developed for characterizing LiDAR
waveform data.
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• The Challenge of Analyzing LiDAR Waveforms - 1
• LiDAR (Light Detection And Ranging) is an active
  remote sensing technology that
• Uses laser light to illuminate the target area,
• Senses backscattering of the illuminating
  radiation, and
• Measures the time a laser pulse takes to travel
  back from regions of strong backscattering.
• A LiDAR waveform sensor records the power of the
  backscattering signal at fine temporal resolution
  which can be converted to distance.

Thus, the term laser altimetry LiDAR measures
altitudes.
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The Challenge of Analyzing LiDAR Waveforms -
2 But we are more interested in knowing
elevations Terrain elevation above or below
the waterline Vegetation height the crown of a
specific tree or the nominal height of a canopy
Vertical profile through a multilayered
canopy resolving foliage densities to
characterize habitat structure
The mapping from altitudes to elevations is
complicated by many confounding factors.
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• The Challenge of Analyzing LiDAR Waveforms - 3
• Waveform data have been actively collected for
  more than 15 years.
• Analyses of detected waveforms have been
  approached in three ways
• Multiple Gaussian curves fit to approximate the
  waveform
• Metrics relating the backscattering power to the
  cumulative distribution of backscattered
  illumination, such as HOME (height of median
  energy) and
• Descriptive statistics on the waveform.

I contend there is a richness in LiDAR waveforms
that has yet to be exploited by conventional
analyses.
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EXAMPLE 1 Duncanson LI, Neimann KO, Wulder MA.
2010. Estimating forest canopy height and terrain
relief from GLAS waveform metrics. Remote Sensing
of Environment 114138-154.
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EXAMPLE 2 Falkowski J. Evans JS, Martinuzzi S,
Gessler PE, Hudak AT. 2009. Characterizing
forest succession with lidar data an evaluation
for the inland Northwest, USA. Remote Sensing of
Environment 113946-056.
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EXAMPLE 3 Nelson R, Ranson KJ, Sun G, Kimes
DS, Kharuk V, Montesano P. 2009. Estimating
Siberian timber volume using MODIS and
ICESat/GLAS. Remote Sensing of Environment 113
691-701.
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EXAMPLE 4 Chen Q. 2010. Retrieving vegetation
height of forests and woodlands over mountainous
areas in the Pacific Coast region using satellite
laser altimetry. Remote Sensing of Environment.
1141610-1627.
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Assume that the waveform is displayed in
Cartesian coordinates with the abscissa
displaying time lapse t and ordinate displaying
backscattered power p.
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Moment Distance Method - 1 Let the subscript LP
denote the left pivot or earlier temporal
reference point and subscript RP denote the right
pivot or later temporal reference point.
MD can be computed from LP to any point on the
curve. More points give better shape definition.
MD can be computed from RP.
t
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Moment Distance Method - 2 The MD framework is
described in the following pair of equations
1
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The moment distance from the left pivot (MDLP) is
the sum of the hypotenuses constructed from the
left pivot to the power at successively later
times (index i from tLP to tRP) one base of each
triangle is the difference from the left pivot (i
tLP) along the abscissa and the other base is
simply the power at i. Similarly, the moment
distance from the right pivot (MDRP) is the sum
of the hypotenuses constructed from the right
pivot to the power at successively earlier times
(index i from tRP to tLP) one base of each
triangle is the difference from the right pivot
(tRP i) along the abscissa and the other base
is simply the power at i.
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Moment Distance Method - 3 From this pair of
moment distances, we form the Moment Distance
Index (MDI) and the MDI Normalized (MDIN)
MDI MDLP MDRP 3 MDIN MDI / (MDLP
MDRP) 4

• In the 1998 La Selva waveform, there are 133
  points on the curve between the LP and RP and the
  MDI 749.93
• In the 2005 La Selva waveform, there are 153
  points on the curve between the LP and RP and the
  MDI 1538.18

We propose that MDI can be used to capture
dynamics in canopy structure.
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Three waveform types found in LVIS data from La
Selva
MDI vs. waveform landmarks
?Max Peak Early
?Max Peak Late
?Equal Peaks
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Time series of waveform landmarks and MDIs
calculated using a time series of simulated LiDAR
returns from a 30m x 30m forest stand grown in
silico with Zelig, a spatially-explicit forest
gap model developed by Dr. Dean Urban, Duke.
Data courtesy of Dr. Guoqing Sun, NASA/GSFC.
Note that shortly after year 120, the first
peak disappears and does not reappear until
about year 240. There is an interpretation of
these results that links MDI to the succession of
peaks.
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• Concluding Thoughts
• The Moment Distance framework and the Moment
  Distance metrics offer a new and simple approach
  to characterizing LiDAR waveforms.
• We are exploring several questions
• How to select the pivots?
• How to select the range(s) of interest?
• How to process the waveform before MD analysis?
• When is MDIN or other MD metrics preferred to
  MDI?
• What are the effects of noise?
• What are the effects of sloping terrain?
• What are the temporal phenomenologies of MD
  metrics?

Early days, but I will venture this approach will
become very useful for mapping waveforms to
habitat structure and linking with organismal
occurrence/abundance data.