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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

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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

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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

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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

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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 coordinates Courtesy: Spencer Gross

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Capitol Forest LIDAR project LIDAR data acquired in the spring of 1999 covering 5.2 km 2 within Capitol State Forest, near Olympia, WA Variety of silvicultural treatments have been applied in this area Area covered by LIDAR flight Washington State Seattle Olympia

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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/m 2 Laser pulse rate: 7000 pulses/second Maximum echoes per pulse: 4

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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 DTMLIDAR DTM

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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

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LIDAR for forest structure analysis High-density LIDAR data within Capitol Forest study area Same area in 1 ft orthophoto

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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)

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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

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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

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Bayesian LIDAR scan analysis for characterization of forest structure 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

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ytyt Bayesian LIDAR scan analysis for interpretation of forest scenes: Model formulation A single LIDAR measurement y t 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 Observed data: y t represent LIDAR measurements acquired over a forest t * * * * * * * T LIDAR scan space (3-D vectors) analogous to image space (2-D pixels)

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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(y t | x), is termed the sampling distribution

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Modeling Laser-Canopy Interaction The sampling distribution p(y t | 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 y t given a certain vertical distribution of canopy foliage, x The parameters of the vertical distribution of foliage density, x, determine of global spatial organization of canopy materials – represented as a mixture model y t * x Parameters of this mixture model provide a detailed, quantitative description of forest structure (Landsberg, 1986) t T

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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(y t | x)

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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(y t | 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 Bayesian LIDAR scan analysis: Inferential approach

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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 Posterior inference via Markov Chain simulation

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Bayesian LIDAR scan analysis for characterizing forest structure: Inferential approach Scan space T Parameter configuration corresponding to posterior mode Most probable foliage distribution, given LIDAR data * * * * * * * * * * * * *

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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

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Spatially explicit forest measurement through Bayesian 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

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x Spatially explicit forest measurement through Bayesian LIDAR scan analysis: Model formulation The sampling distribution p(y t | x) describes the probability that a given laser pulse, traveling along a specified 3-D vector t, will reflect from a particular location y t given a certain configuration of tree objects x. The object configuration x will determine the global spatial organization of canopy materials -- modeled as a spatial point process t T ytyt * Each object (tree) x i is an element of object space U, and can be identified by location, size, crown form, and foliage density (size, form, density) (x, y) x i U

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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 Spatially explicit forest measurement through Bayesian LIDAR scan analysis Spatially explicit forest measurement through Bayesian LIDAR scan analysis

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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, x n may denote the (x,y) location of a tree, while the mark, m n, 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

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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 Modeling the Spatial Distribution of Trees: The Prior Distribution

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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

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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) Posterior inference for spatially explicit Bayesian LIDAR scan analysis (cont.)

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MAP Estimate of object configuration * * ** * * * * * * * * * ** * * * * * * * * * * * * * * ** * * * * * * * * LIDAR data: y (x, y) (size, form, density) Spatially explicit forest measurement through Bayesian LIDAR scan analysis: Inferential approach

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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

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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 Conclusions

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