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PROBABILISTIC TOPOGRAPHIC MAPS FROM RAW, FULL-WAVEFORM AIRBORNE

LIDAR DATA 

André Jalobeanu1, Gil R. Gonçalves2

FCTUC, INESC - University of Coimbra, PortugalCGE - University of Évora, Portugal

AGU FM’11 EP51EAutoProbaDTM project

PTDC/EIA-CCO/102669/2008, FCOMP-01-0124-FEDER-010039

Outline

Objectives

LiDAR principles

Bayesian waveform processing

Probabilistic DEM

Study area in Portugal

Recommendations

Perspectives USGS

Scientific objectivesAutoProbaDTM project

Automated Probabilistic Digital Terrain Model generation from raw LiDAR data

Generate gridded elevation models for topographic mapping and environmental studies

Robustly estimate the bare ground topography

Provide predictive elevation accuracy maps

Minimize the user interaction: automation

Process large datasets (1G waveforms)

Principles of LiDARlight detection and ranging

1. Time of flight measurement(waveform acquisition)

2. Scanning:aircraft motion + laser rotation3. Direct georeferencingIMU: DGPS+INS

Riegl

Bayesian inference

p(θ | observations) =p(observations | θ)× p(θ)

p(observations)

evidence

(useful for model comparison)

likelihood

image formation model

prior model

(a priori knowledge

about the observed object)

parameters of interest

(unknown solution)

OBJECTIVE:

posterior probability

density function (pdf)

Bayes’ rule:

Zk

elevationpdf

Waveforms and ground extraction

Complex Point Spread Function (PSF) - ringing

Ground peak contamination by low vegetation

Variability: amplitude, width, noise...

PSF modeling - 3 peaks (ringing)

Full deconvolution:artifacts (noisy/oversmooth)

Partial deconvolution (Diracs)Target = single Gaussian PSFRinging removal without artifacts, no regularization required

1. Partial waveform deconvolution

artifacts!

original

deconvolved (partial)

original

deconvolved (full)

–t (ns)

–t (ns)–t (ns)

ampl

itud

eam

plit

ude

PSF

2. Bayesian ground range inference

wav

efor

m

full estimation window

Ground peak = Gaussian (position, width, amplitude)

Background = Gaussian noise (mean, variance)

Full estimation window: classical (Bayesian) Gaussian fitting

Partial estimation window: contaminated peak modelingModel 0 (Gaussian peak) & Model 1 (no peak)

Extra parameters:- model 0 width- mean, variance for model 1

Bayesian inference:unwanted parameters areintegrated out automatically

mod

el 1

wei

ghts

model 0

weights

full

win

dow

wei

ghts

Define search intervals using Bayesian model selection1. Model 0 (Gaussian peak) / Model 0 (no peak) > Significance Level2. Peak amplitude > Threshold

Ground: compute only the first interval

Compute the ground position pdfSum over model 0 & peak width, or use joint pdf and Gauss approx.

Real waveforms: robust inference!

–t (ns)–t (ns)

ampl

itud

e

ampl

itud

e

search interval

ground pos. pdf

search interval

ground pos. pdf

σt = 0.1 ns (1.5 cm)σt = 0.3 ns (4.5 cm)

Bayesian ground range inference

–t (ns)

–t (ns)

Simulations: ground peak + 2nd peak + noise

Ful

l win

dow

bias

!O

ptim

al w

indo

wco

nsis

tent

/ gr

ound

trut

h

ampl

itud

eam

plit

ude

wid

enin

gfa

ctor

–t (ns)

–t (ns)

wid

enin

gfa

ctor

search interval

ground pos. pdf

search interval

ground pos. pdf

Towards a probabilistic DEM

Wave

waveformprocessing

Georef

directgeoreferencing

Grid

jointgridding & filteringra

nge,

σra

nge

X, Y

, Z, σ

Z

Raster: z, σz

POS file:trajectory, attitudewaveforms y(t) timestamps, θ

raw LiDAR data

DEM + error map

Calibrateboresight alignment Analyze

DEM-derived products

internalparameters

Study area and data acquisition

Elevation range: 150-350 mLand cover: fields, shrubs, isolated trees, forests, hills, lakes,small rivers, villages and isolated housesGeomorphology: fault scarps, knickpointsTotal area: 216 km2 (150 km2 specified point density)Flight altitude: 1500m AGL (normal), 3000m AGL (experimental)Point density: 3.8 pts/m2 (total >600M waveforms), 60% overlap, 100 GB raw data

NW of Arraiolos, Portugal

10 km

Flight trajectory (June 2, 2011) and densityFlight planning and data acquisition: IMAO (France) www.imao-fr.com

LiDAR: IGI LiteMapper 6800 (Riegl LMS-Q680i)

Double density

Simple density

5 km

GPS Field work (control points)

Over 5700 points: isolated, tracks, x-sectionsDGPS, GPRS, RTK... from 1 to 5cm vertical accuracyMostly elevation control points, a few features (buildings, sports fields)

Use raw waveform data

Sample the topography at a sufficient densityApply Shannon’s sampling theorem to avoid aliasing point spacing ≈ footprint size➔ consistent change detection, ground motion, deformation...

Make sure the calibration is done right

Fly as low as the budget permits, allow sufficient overlap

Have a good reference GPS station

Acquire some control points, just in case...

Recommendationsfor accurate, consistent and useful probabilistic DEMs

Filtering and classification- Vegetation filtering and bare earth gridding (simultaneous)- Classification, segmentation of the DEM

Computational efficiency- Process large volumes of raw data, roughly 100 GB- Complexity of the gridding and filtering algorithms

Full automation- Unsupervised gridding and classification: parameter estimation- Automatic calibration (boresight) from normal flight lines

Full uncertainty map computation- Inversion of sparse matrices for variance/covariance computation

Work in progress...

sites.google.com/site/autoprobadtm