andersen

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°





• Revolutionizing airborne remote sensing

LIDAR (Light Detection And Ranging)



• 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 post-

processed and delivered as XYZ

Courtesy: Spencer Gross

coordinates

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







• 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

• Laser pulses can penetrate forest canopy through gaps

• Some laser pulses reach forest floor, other returns reflect from

canopy and sub-canopy vegetation

• 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 Same area in 1 ft orthophoto

study area

LIDAR for forest structure analysis



• “Forest structure is above ground organization of plant materials” –

(Spurr and Barnes, 1980)





• 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?



• Regular grid/lattice

- 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

- 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 T

space - the set of all 3-D vectors

t

associated with the potential paths of all

emitted laser pulses from the sensor to yt

the ground surface * *

* *

* *

• LIDAR scan space (3-D vectors) *

analogous to image space (2-D pixels)

Modeling Laser-Canopy Interaction





• Variability in spatial distribution of plant materials (leaves,

branches, stems, etc.) gives rise to gap probability function (Kuusk,

1991)





• The observed LIDAR measurements, y, will be related to the

distribution of foliage, x, through a probability distribution





• 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)

x



• The sampling distribution p(yt | x)

describes the probability that a given laser yt

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

Modeling laser transmission within the forest canopy



• Laser energy is backscattered as it passes through a vegetation

canopy



• 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





• 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





** *

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 Estimate of vertical foliage profile

plot data 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 (size, form, density)

object space U, and can be identified by

location, size, crown form, and foliage

density tT xi  U





• The object configuration x will

determine the global spatial organization of

canopy materials -- modeled as a spatial yt *

point process



• 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 (x, y)

given a certain configuration of tree objects x

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)







* *

* * * * *

* * ** * * *

* *

* * *

LIDAR data: y *

* * * * * ** *

* * *

*

* * * *

* *

*

(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