FOREST INVENTORY PREDICTIONS FOREST INVENTORY PREDICTIONS FROM INDIVIDUAL TREE CROWNS -FROM INDIVIDUAL TREE CROWNS -

Regression Modeling Within a Regression Modeling Within a Sampling FrameworkSampling Framework

Jim Flewelling

in association with

ImageTree Corp.

FIA SYMPOSIUMOctober, 2006

OUTLINEOUTLINE

Make a Crown MapMake a Crown Map Sample the Crown MapSample the Crown Map Model the TreesModel the Trees Model-Assisted InferenceModel-Assisted Inference

ContextContext

Complete LiDAR & Digital Complete LiDAR & Digital photographyphotography

100% crown mapped.100% crown mapped. Number of stands >> # of field plots.Number of stands >> # of field plots. Unbiased for population totals.Unbiased for population totals.

Crown Segmentation, Crown Segmentation, Delineation & AttributionDelineation & Attribution

Identify individual crowns.Identify individual crowns. Locate center points.Locate center points. Delineate crown boundaries.Delineate crown boundaries.

(non-overlapping)(non-overlapping) Attribute species.Attribute species. Attribute height.Attribute height.

Individual Tree Crown (ITC) Individual Tree Crown (ITC) DelineationDelineation

Valleyfollowing

Deep shade

threshold

Rule-basedsystem

1995

Courtesy of Canadian Forest Service

Delineated Individual Tree CrownsDelineated Individual Tree Crowns

At ~30 cm/pixel,

81% of the ITCs are the

same as interpreted

crownsCourtesy of Canadian Forest Service

Delineated and Classified ITCsDelineated and Classified ITCs

Courtesy of Canadian Forest Service

Add in Stand BoundariesAdd in Stand Boundaries

Individual stand on

LiDAR image after tree polygon

creation. A polygon now

surrounds every visible tree crown.

©ImageTree Corp 2006

Completed Crown MapCompleted Crown Map

Census of individually delineated crowns.Census of individually delineated crowns. Location, Size, ShapeLocation, Size, Shape Center (centroid, or high-point)Center (centroid, or high-point) LiDAR HeightLiDAR Height Species Assignment or ProbabilitySpecies Assignment or Probability and more ?and more ?

StandsStands BoundariesBoundaries Auxiliary DataAuxiliary Data

OUTLINEOUTLINE

Make a Crown MapMake a Crown Map Sample the Crown MapSample the Crown Map Model the TreesModel the Trees Model-Assisted InferenceModel-Assisted Inference

Two-Stage SamplingTwo-Stage Sampling

1st Stage: Stands1st Stage: Stands 2nd Stage: Plots on Crown Map2nd Stage: Plots on Crown Map

PlotsPlots

Random Plot Center CoordinatesRandom Plot Center Coordinates GPS to those locationsGPS to those locations Establish fixed-area stem-mapped Establish fixed-area stem-mapped

plot.plot. Co-locate plots to find true position.Co-locate plots to find true position. Accept or reject altered coordinates.Accept or reject altered coordinates. Make fixed-area circular crown plot.Make fixed-area circular crown plot.

Fixed-Area Crown PlotFixed-Area Crown Plot

©ImageTree Corp 2006

Green dots

Edge Bias CorrectionEdge Bias Correction

Tree-Concentric Method

Matched Trees and CrownsMatched Trees and Crowns

Errors in SegmentationErrors in Segmentation One delineated crown = 2 neighboring trees.One delineated crown = 2 neighboring trees. One real tree wrongly divided into 2 crowns.One real tree wrongly divided into 2 crowns.

Trees entirely missed.Trees entirely missed. Ground vegetation seen as a tree.Ground vegetation seen as a tree. Understory trees don’t contribute.Understory trees don’t contribute. Technical improvements, but Technical improvements, but no no

absolute solution.absolute solution.

Matched Trees and CrownsMatched Trees and Crowns

TREE MATCHING SCHEMESTREE MATCHING SCHEMES

SubjectiveSubjective potential for significant biaspotential for significant bias

Crown Captures ALL in tessellated Crown Captures ALL in tessellated area.area. Expand crown area.Expand crown area.

Trees compete to be captured.Trees compete to be captured. Consider DBH, height, species …Consider DBH, height, species … Ground plot size > crown plot size.Ground plot size > crown plot size.

CROWN BASED SAMPLE FRAMECROWN BASED SAMPLE FRAME

REQUIREMENTREQUIREMENT Trees linked to segmented crowns.Trees linked to segmented crowns. Linkage must be Linkage must be independent of samplingindependent of sampling.. BUTBUT Linkages need not be physically correct.Linkages need not be physically correct. Suppressed trees need not be linked if sampled another way.Suppressed trees need not be linked if sampled another way.

Plot ConfigurationPlot Configuration

0.12 ac.

Analysis Plot

Completed SampleCompleted Sample

Stands WeightsStands Weights CrownsCrowns

Size, Color, height, species guess, etc.Size, Color, height, species guess, etc. Weights (from edge effects)Weights (from edge effects) Associated Trees (Sp., DBH, Height)Associated Trees (Sp., DBH, Height)

Unassociated TreesUnassociated Trees

OUTLINEOUTLINE

Make a Crown MapMake a Crown Map Sample the Crown MapSample the Crown Map

Model the TreesModel the Trees Model-Assisted InferenceModel-Assisted Inference

Model Trees from CrownsModel Trees from Crowns

Trees = f(Stand, Crown, Window)Trees = f(Stand, Crown, Window) Pr{Crown has no trees} = f(….)Pr{Crown has no trees} = f(….) Pr{Crown has one tree} = f(…)Pr{Crown has one tree} = f(…) Pr{1st Tree = Pine} = f(….)Pr{1st Tree = Pine} = f(….) DBH(1st tree|Species) = f(…) + eDBH(1st tree|Species) = f(…) + e Ht(1st tree|Species) = f(Lidar ht, ..) + eHt(1st tree|Species) = f(Lidar ht, ..) + e Predictors for unassociated treesPredictors for unassociated trees

Model PredictionsModel Predictions

Expected results - crown or stand Expected results - crown or stand level.level.

DBH Distribution too narrowDBH Distribution too narrow (R-square < 1.00)(R-square < 1.00)

Variance added through simulation Variance added through simulation or “tripling”.or “tripling”.

OUTLINEOUTLINE

Make a Crown MapMake a Crown Map Sample the Crown MapSample the Crown Map Model the TreesModel the Trees

Model-Assisted InferenceModel-Assisted Inference

Sample DesignSample Design

Development Set of Sample StandsDevelopment Set of Sample Stands Used for fitting Equations.Used for fitting Equations.

Calibration Set of Sample StandsCalibration Set of Sample Stands Random Selection, With ReplacementRandom Selection, With Replacement Current: Probability proportional to Area.Current: Probability proportional to Area.

Use of Calibration SetUse of Calibration Set

Ratio Model Ratio Model Crown level or Plot level.Crown level or Plot level. BA = k BA = k (predicted BA) + e (predicted BA) + e

Asymptotically unbiased for key Asymptotically unbiased for key attributes:attributes:

BA, TPA, BA times Lorey height, by species.BA, TPA, BA times Lorey height, by species.

Variance for population mean (design-Variance for population mean (design-based).based).

MSE of Stand-level estimates.MSE of Stand-level estimates.

Combine Development & Combine Development & Calibration SamplesCalibration Samples

Fix Estimated Population Totals.Fix Estimated Population Totals. Refit the Models, with constrained Refit the Models, with constrained

totals.totals. Improved MSE’s, but difficult to Improved MSE’s, but difficult to

estimate. estimate. Alternatives with Single Data Set.Alternatives with Single Data Set.

Model-assisted approach (Sarndol)Model-assisted approach (Sarndol) Generalized Regression Generalized Regression

Generalized RegressionGeneralized Regression

Pred. Total = Pred. Total = (pred y) + Ratio Est Error (pred y) + Ratio Est Error Little (2004): “Design consistency - Little (2004): “Design consistency -

estimator converges to the population estimator converges to the population quantity … as the sample size increases, quantity … as the sample size increases, in a manner that maintains the features in a manner that maintains the features of the sample design.”of the sample design.”

Still need to allocate errors back to the Still need to allocate errors back to the model.model.

Summary - StatisticsSummary - Statistics

Trees and Segmented Crowns are not 1:1Trees and Segmented Crowns are not 1:1 Data can be collected that allows for Data can be collected that allows for

design-based inference of totals.design-based inference of totals. Totals are unbiased.Totals are unbiased. MSE’s at stand level from plot-level MSE’s at stand level from plot-level

results.results. Edge-bias avoidance.Edge-bias avoidance. Estimator properties greatly changed.Estimator properties greatly changed.

Summary - ApplicationSummary - Application

Attractive technology.Attractive technology. Best for which forest types (?)Best for which forest types (?)

Irregular spatial tree distributions.Irregular spatial tree distributions. Some multi-species situations.Some multi-species situations. Areas of difficult access. Areas of difficult access. Large Areas, Fast Results (future)Large Areas, Fast Results (future)

AcknowledgmentsAcknowledgments

Some slides were provided by Francois Some slides were provided by Francois Gougeon and are courtesy of Natural Gougeon and are courtesy of Natural Resources Canada, Canadian Forest Resources Canada, Canadian Forest Service.Service.

Other slides were provided by ImageTree Other slides were provided by ImageTree Corporation.Corporation.

ResourcesResources

2005 Silviscan 2005 Silviscan http://http://cears.fw.vt.edu/silviscancears.fw.vt.edu/silviscan//

2004 ISPRS Laser-Scanner for Forest and - 2004 ISPRS Laser-Scanner for Forest and - http://www.isprs.org/commission8/workshohttp://www.isprs.org/commission8/workshop_laser_forest/p_laser_forest/

ImageTree Corp. ImageTree Corp. www.imagetreecorp.comwww.imagetreecorp.com Pacific Forestry Center Pacific Forestry Center

http://www.pfc.forestry.ca/index_e.htmlhttp://www.pfc.forestry.ca/index_e.html Precision Forestry Coop (U.W.) Precision Forestry Coop (U.W.) http://www.cfr.washington.edu/research.shttp://www.cfr.washington.edu/research.s

mc/mc/

ReferencesReferences

Little, R. 2004. To model or not to Little, R. 2004. To model or not to model? competing modes of model? competing modes of Inference for finite population Inference for finite population sampling. J Am. Stat. Assoc. 99: 546-sampling. J Am. Stat. Assoc. 99: 546-556.556.

Sarndal, C, Swensson and Sarndal, C, Swensson and Wretman.1992. Model assisted Wretman.1992. Model assisted survey sampling. Springer.survey sampling. Springer.