The use of airborne laser scanner data (LIDAR)
for forest measurement applications
Hans-Erik Andersen
Precision Forestry Cooperative
University of Washington
College of Forest Resources
Forest structure analysis using remotely sensed data
Three-dimensional forest structure information is required to
support a variety of resource management activities
- Timber inventory and management
- Habitat monitoring
- Watershed management
- Fire behavior modeling
- Forest operations
Limitations of two-dimensional image data for forest
structure analysis
• Traditionally, acquired through manual or semi-automated
interpretation of aerial photographs or digital imagery
• Vertical (3-D) forest structure information acquired directly
from field measurements or indirectly inferred from 2-D image
information
• New generation of active remote sensing technologies (LIDAR,
IFSAR) provide direct, 3-D measurement of vegetation and
terrain surface
Why now?
Convergence of two enabling technologies for acquisition of precise
position and orientation of active airborne sensor
1) Airborne global positioning systems (GPS)
- Differentially corrected
- Positional accuracy: 5-10 cm
2) Inertial navigation systems (INS)
- Utilize gyroscopes and accelerometers
- Orientation (pitch/roll) accuracy : ~ 0.005°
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Revolutionizing airborne remote sensing
LIDAR (Light Detection And Ranging)
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Active airborne sensor emits several
thousand infrared laser pulses per
second
Operates on principle that if location
and orientation of laser scanner is
known, we can calculate a range
measurement for each recorded echo
from a laser pulse
Components of system include INS
(inertial navigation system),
airborne differential GPS, and laser
scanner
Range measurements are postprocessed and delivered as XYZ
coordinates
Courtesy: Spencer Gross
Capitol Forest LIDAR project
• LIDAR data acquired in the spring of 1999 covering 5.2 km2
within Capitol State Forest, near Olympia, WA
• Variety of silvicultural treatments have been applied in this area
Washington State
Area covered by LIDAR flight
Seattle
Olympia
Flight parameters and system settings for
Capitol Forest LIDAR project
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Laser scanning system: SAAB
TopEye
Platform: Helicopter
Flying height: 650 ft
Flying speed: 25 m/sec
Scanning swath width: 70 m
Laser pulse density: 3.5
pulses/m2
Laser pulse rate: 7000
pulses/second
Maximum echoes per pulse: 4
LIDAR for topographic mapping
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Laser pulses can penetrate forest canopy through gaps
Some laser pulses reach forest floor, other returns reflect from
canopy and sub-canopy vegetation
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Allows for detailed modeling of terrain surface
USGS DTM
LIDAR DTM
LIDAR for forest structure analysis
LIDAR data represent direct measurements of three-dimensional forest structure
- “Small-footprint” vs. “large-footprint” systems
- “Continuous waveform” vs. “discrete return” systems
- Many small footprint, discrete return LIDAR systems can acquire multiple
measurements from a single laser pulse
Courtesy: Spencer Gross
LIDAR for forest structure analysis
High-density LIDAR data within Capitol Forest
study area
Same area in 1 ft orthophoto
LIDAR for forest structure analysis
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“Forest structure is above ground organization of plant materials” –
(Spurr and Barnes, 1980)
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Forest structural patterns are three-dimensional
- Growth at scale of individual tree crowns
- Competition for limited resources (light, water, nutrients)
LIDAR for forest measurement
applications
How do we parameterize this three-dimensional spatial distribution of
above ground biomass components?
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Regular grid/lattice
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Distribution of foliage generalized within grid cell area (i.e. 30 x 30 m
cells)
Provides extensive data relating to forest structure across landscape
Object/individual tree level
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Distribution of foliage associated with individual tree crowns
Provides intensive, detailed spatially explicit forest measurement data
Stochastic modeling and LIDAR forest sensing
• The distribution of LIDAR measurements throughout the canopy
contains information relating to forest structure in both vertical and
horizontal dimensions
• Large-footprint, continuous waveform LIDAR has been used
successfully to characterize forest structure patterns (Lefsky et al, 2002).
• Small-footprint, discrete return LIDAR measurements can be modeled
as observations from a stochastic process
• Stochastic model represents physical LIDAR sensing process
Bayesian LIDAR scan analysis for characterization
of forest structure
• Inferences can be carried out in probabilistic terms, allowing for
more complex, realistic modeling of forest spatial processes
• Sensing geometry is explicitly modeled (i.e. effects of scan angle,
etc.)
• A Bayesian statistical framework allows for sources of uncertainty
and prior knowledge to be quantified and incorporated into model
• Due to the complexity of the probability models, inferences are
typically based upon Monte Carlo simulation
Bayesian LIDAR scan analysis for interpretation of
forest scenes: Model formulation
• Observed data: yt represent LIDAR
measurements acquired over a forest
• A single LIDAR measurement yt is a
distinct point along a 3-D vector t
• t  T, where T represents the scan
space - the set of all 3-D vectors
associated with the potential paths of all
emitted laser pulses from the sensor to
the ground surface
• LIDAR scan space (3-D vectors)
analogous to image space (2-D pixels)
T
t
yt
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Modeling Laser-Canopy Interaction
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Variability in spatial distribution of plant materials (leaves, branches,
stems, etc.) gives rise to gap probability function (Kuusk, 1991)
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The observed LIDAR measurements, y, will be related to the
distribution of foliage, x, through a probability distribution
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This distribution, p(yt | x), is termed the sampling distribution
Modeling Laser-Canopy Interaction
• The parameters of the vertical
distribution of foliage density, x, determine
of global spatial organization of canopy
materials – represented as a mixture model

tT
• Parameters of this mixture model
provide a detailed, quantitative description
of forest structure (Landsberg, 1986)
• The sampling distribution p(yt | x)
describes the probability that a given laser
pulse, traveling along a 3-D vector t, at an
angle θ, will reflect from a particular location
yt given a certain vertical distribution of
canopy foliage, x
x
yt
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Modeling laser transmission within the forest canopy
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Laser energy is backscattered as it passes through a vegetation
canopy
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Probability of a beam of light passing through a canopy (i.e. not
reflected) is given by gap probability function, based upon Beer’s
law (Sun and Ranson, 2000):
p = e-(kS)/cosθ
where
p is the probability that the beam is not reflected,
k is a measure of foliage area projected onto a plane normal to the light beam,
 is the foliage area density, and
S is the distance that the beam travels through the canopy
θ is the off-nadir angle of the beam
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Models of this type can be used to determine the form of the
sampling distribution for LIDAR measurements p(yt | x)
Bayesian LIDAR scan analysis: Inferential approach
• In a Bayesian context, the posterior distribution of foliage
distribution parameters represents the probability of a particular
foliage density distribution, with parameter vector x, given the
observed LIDAR data, y:
p (y | x)  t  T p(yt | x) p(x)
• The mode of the posterior distribution will therefore represent
the most probable foliage distribution, given the LIDAR:
Posterior mode = argmax[p (y | x)]
• Finding the posterior mode is essentially a combinatorial
optimization problem
Posterior inference via Markov Chain simulation
• The target distribution can arise as the equilibrium distribution of a
special type of Markov chain – Green (1995)
• Moves within Markov chain consist of:
• addition of a model component
• deletion of an component
• change of object parameters
• splitting of a component
• merging of two components
• After a large number of steps, the subsequent samples can be
considered to be draws from the target (posterior) distribution
• Global optimization techniques used to determine the posterior
mode
Bayesian LIDAR scan analysis for characterizing forest
structure: Inferential approach
Scan
space T
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Parameter
Most
probable
configuration
foliage
distribution,
corresponding
to
given
LIDAR
data
posterior mode
Bayesian LIDAR scan analysis for characterizing vertical forest
structure: Example from Capitol Forest, WA
Stand structure projected from 1/5 acre field
plot data
Estimate of vertical foliage profile
from LIDAR scan analysis
Spatially explicit forest measurement through
Bayesian LIDAR scan analysis
• This modeling framework can also be used to infer individual tree
locations and dimensions
• Based upon theory developed in pattern recognition and computer
vision (Bayesian object recognition)
• Allows spatial interaction processes to be incorporated into model
• Output represents a spatially explicit representation of forest
canopy components
Spatially explicit forest measurement through Bayesian LIDAR
scan analysis: Model formulation
• Each object (tree) xi is an element of
object space U, and can be identified by
location, size, crown form, and foliage
density
(size, form, density)
xi  U
tT
• The object configuration x will
determine the global spatial organization of
canopy materials -- modeled as a spatial
point process
yt *
• The sampling distribution p(yt | x)
describes the probability that a given laser
pulse, traveling along a specified 3-D vector
t, will reflect from a particular location yt
given a certain configuration of tree objects
x.
(x, y)
x
Spatially explicit forest measurement through
Bayesian LIDAR scan analysis
• Inferences based upon the posterior probability density of object
configurations, conditional on the observed LIDAR data
• Prior distribution p(x) is a probability density over possible
object configurations
- Prior will penalize unrealistic forest patterns
- For example, large trees rarely grow close to one another
- We typically have some prior knowledge regarding the distribution of
tree dimensions in a given forest
Modeling the Spatial Distribution of Trees: The Prior Distribution
• Spatial point processes are a flexible class of models for
characterizing spatial patterns in the forest – Ripley (1981),
Penttinen et al. (1992)
• Marked point processes allow attributes to be attached to a point
- For example, xn may denote the (x,y) location of a tree, while the
mark, mn, may represent the crown diameter of this tree
• Markov point processes for modeling patterns with local
interactions
- Realistic assumption in forest dynamics
Modeling the Spatial Distribution of Trees: The Prior Distribution
• The Strauss process is a Markov point process used to model
pairwise interaction:
p(x) =  n(x)  s(x)
where
- n(x) = the number of points in the configuration x
- s(x) = the number of points within a specified distance from each other
- 0<  < 1
- When  < 1, there is inhibition between points
• Markov marked point process: interaction depends upon the marks
- Allows different interactions between trees of various sizes or species types
Posterior inference for spatially explicit Bayesian
LIDAR scan analysis
• In object recognition, global maximum of the posterior
distribution often of primary interest
• Maximum a posteriori (MAP) estimate of x
= argmax[p(x | y)]
= argmax[f (y | x) p(x)]
• MAP estimate represents the most probable global configuration
of tree objects, given the observed LIDAR data
Posterior inference for spatially explicit Bayesian
LIDAR scan analysis (cont.)
• Global optimization techniques (simulated annealing) can be
used to find the MAP estimate
• In theory, samples obtained, via Markov chain simulation, from
the tempered distribution
[p(x | y)]1/ T
will converge to the MAP estimate as T → 0
• Posterior distribution is a Markov object process
• Inferences can be based on samples drawn from the posterior
density:
p(x | y)  f (y | x) p(x)
Spatially explicit forest measurement through Bayesian LIDAR
scan analysis: Inferential approach
(size, form, density)
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* data: y
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LIDAR
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(x, y)
MAP Estimate of object configuration
Bayesian LIDAR scan analysis for spatially explicit forest measurement :
Example from Capitol State Forest, WA
MAP estimate of crown dimensions within 0.5 acre area of two-age stand
Conclusions
• Active LIDAR sensing technology provides means of
quantitatively characterizing three-dimensional forest structure
• Use of advanced computer vision and Bayesian inferential
techniques allows for automated extraction of detailed forest
information
• Methodology can be extended to incorporate other sources
of data (multispectral digital imagery, radar, etc.)
• Currently comparing to field-based and photogrammetric
forest measurements