aerial laser scanning

Commission VI Special Interest Group Technology Transfer Caravan

Aerial Laser Scanning

Claus Brenner with contributions from George Vosselman and George Sithole

Institute of Cartography and Geoinformatics University of Hannover, Appelstr. 9a, 30167 Hannover, Germany [email protected] www.ikg.uni-hannover.de

Claus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006


Contents Airborne laser scanning principles Errors and strip adjustment Filtering of ALS data Extraction and modelling



Airborne laser scanning principles



Basic components of an ALS system

DGPS Control & data recording INS

Laser Ranging unit Deflection unit

GroundClaus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006


Laser

Laser

Semiconductor lasers or Nd:YAG lasers pumped by semiconductor lasers Mostly Nd:YAG = neodymium-doped yttrium aluminium garnet, Nd:Y3Al5O12 Emits at = 1064 nm (near infrared) Bathymetric scanners often use = 532 nm (green) obtained by frequency doubling Others: e.g. 810 nm (ScaLARS), 900 nm (FLI-MAP), 1540 nm (TopoSys) Properties exploited: high collimation, high optical power

Pulsed (time of flight ranging) or continuous wave (CW, sidetone ranging)



Pulsed laser operationSignal amplitude

Laser

tp

t trise

Typical characteristics: Pulse width tp = 10 ns ( Pulse rise time trise = 1 ns ( 3 m @ speed of light) 30 cm @ speed of light)

3m

Peak power Ppeak = 2,000 W Energy per pulse E = Ppeak tp = 20 J Average power (@ pulse repetition rate F = 10 kHz) Pav = E F = 0.2 W


Ground


Continuous laser operationModulation signal

Laser

t

Signal amplitude

t

GroundModulation signal

Characteristics (ScaLARS):Signal amplitude

Two modulation frequencies fhigh = 10 MHz, flow = 1 MHz short = 30 m, long = 300 m Average power (continuous operation) Pav = 0.26 WClaus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006


Ambiguities (pulse)

Laser

Travelling time: h=R

ttravel =Ground

2R cttravel = 6.7 s

Example: h = R = 1000 m

tp = 10 ns can be neglectedAT

next pulse t ttravel tp t

Maximum pulse frequency (assuming no transmit / receive overlap):

AR

f max = 1 / ttravel =

c 2Rfmax = 150 kHz

Example: h = R = 1000 m



Ambiguities (CW)

Laser

Maximum unambiguous range determined by long : Ground

Rmax = Example:

long2Rmax = 150 m

AT

long = 300 m

tAR

Range gating: Known height, possible range differences < 150 m Range tracking: If no steps > 150 m are present

t



Scanning mechanisms & ground patternsOscillating mirror Rotating polygon Nutating mirror (Palmer scan) Fiber switch

Deflection unit

Laser

(same for receiving optics)

Z-shaped, sinusodial

Parallel lines

Elliptical

Parallel lines



Polygon mirror example25 cm @ 0.5 mrad beam divergence

Deflection unit

/2=20 h=500 m 0.08 70 cm 364 m

500 pulses / line

0.08

1 cos 2 i79 cm Repetition rate 50 kHz, average pulse rate 25 kHz

Swath width

2h tan = 0.7 h = 364m 2

50 lines / s 83 cm v = 150 km/h



Fiber switch details (TopoSys Falcon)Laser

Deflection unit

To ground and back

ReceiverClaus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006


Fiber scanner exampleFiber 128 ...

Deflection unit

/2=7 h=500 m 0.25h / 127 = 0.002 h 1m

Fiber 3 spot diameter 25 cm Fiber 2

Swath width

Fiber 1 630 lines/s 11 cm v = 252 km/h

2h tan = 0.25h = 123m 2



Palmer scan7 deg. nutating mirror 30 deg. nutating mirror (hypothetical)

Deflection unit

Scan pattern with forward motion of aircraft (7 deg. nutating mirror)



Beam divergence Laser beam widens with distance Beam divergence D, aperture diameter Theoretical limit by diffraction

2.44

D

Example: = 1064 nm, D = 10 cm

0.026 mrad

h

2

Typical values for ALS: = 0.3 2 mrad Ground spot diameter

DI

DI, diameter of illuminated area Ground(not to scale)

= D + 2h tan( 2) 2h tan( 2) h

Example: = 1 mrad 1 m diameter @ h = 1 km flying height



Power balance

Ar

4 - Power received:

Ar Pr = M M PT 2 R 21 - Power transmitted:

M 2 Ar = PT 2 R 2

R

PT3 - Power reflected, assuming Lambertian surface:

PT = 2000 W Atmospheric transmission M = 0.8 Ar = 80 cm2 (Dr = 10 cm) R = 1 km Reflectivity = 0.5

M PT 2

2 - Power received: Ground

M PT

Pr = 4 10-10 PT = 800 nWClaus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006


ReflectivityReflectivity vs. materialMATERIAL Dimension lumber (pine, clean, dry) Snow White masonry Limestone, clay Deciduous trees Coniferous trees Carbonate sand (dry) Carbonate sand (wet) Beach sands, bare areas in desert Rough wood pallet (clean) Concrete, smooth Asphalt with pebbles Lava Black rubber tire wall REFLECTIVITY @ = 900 nm 94% 80-90% 85% up to 75% typ. 60% typ. 30% 57% 41% typ. 50% 25% 24% 17% 8% 2%Source: www.riegl.co.at

Range vs. reflectivity

M 2 Ar Pr = PT 2 2 R120

R

Range factor [%] *

100 80 60 40 20

0

20

40

60

80

100

Target reflectivity [%]

* Normalized to 100% @ 80% reflectivity



Interaction with target

AT

tAR

first pulse

last pulse

5m t tp Pulse width 10 ns 3 m @ speed of light h = 1.5 m pulses separableClaus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006


Interaction with targetAT

tAR,1

t1

Detection accuracy 10-15% t of rise time 2-5 cmAR,2

t2

7 ns Measured range will be an intermediate value (mixed echo)

t



Interaction with target... t

AR

t Large area, small reflectivity Small area, large reflectivity (same for sloped terrain)

Minimum detectable object size depends on reflectivity Measured range depends on distribution of reflectivity inside laser ground spot area



Interaction with target

Canopy penetration gets worse with increasing scan angles

Specular reflection Water, wet surfaces, slate no return signal



Pulse:AT

RangingAT

CW:

Ranging unit

AR

t t t

AR

t t

Range

Range

R=

c t 2c t 2 c 1 t rise 2 S/N

R=

1 short 2 2

Range resolution

Range resolution

R =

R =

short c 1 = 4 4 f highshort 1 4 S/N

Range accuracy

Range accuracy

R

R



Ranging: Pulse vs. CW In CW ranging, resolution and accuracy can be improved by using higher modulation frequencies Resolution: CW, short = 30 m (10 MHz), /2 = 1/16384 (14 bit) Cf. required time resolution for pulse ranging: t = 2 R / c = 6.1 ps (164 GHz) ! R = 0.9 mm !

Ranging unit

For the accuracy, S/N is important depends on transmitted power, e.g. Pulse Ppeak = 2000 W vs. CW Pav = 1 W R,CW / R, pulse = 85, achieved by 2000 x power [Wehr, Lohr 99] Pulse lasers with high power are available CW semiconductor lasers with Pav > 2 W, fhigh > 10 MHz scarce R, pulse typically 2-5 cm Does not apply to centimetre level measurement in the close range domain!Claus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006


Ranging: full waveform analysistree crown power line

Ranging unit

AR

bush

ground

First pulse t0AR

Last pulse t1

tData recorder

1 GS/s tData recorder



Ranging: full waveform analysis

Ranging unit

Source: Riegl, 2006



Ranging: full waveform analysis

Ranging unit

Unlimited number of returns per shot Multiple target detection down 0.5 metres Surface roughness, slope Vegetation Discontinuities User-defined post-processing methods, no need for real time, neighbourhood analysis Riegl LMS-Q560, Litemapper 5600, Optech ALTM 3100, TopEye Mark II



Examples of ALS



Scanner examplesSystem Laser Altitude Range measurements Scan frequency Scan angle Pulse rate Beam divergence Beam pattern Optech ALTM 3100EA 1064 nm 80 3500 m up to 4 max. 70 Hz max. 25 max. 100 kHz 0.3 mrad oscillating, sawtooth Riegl LMS-Q560 near IR 30 1500 m full waveform max. 160 Hz max. 30 max. 100 kHz, 50 kHz @ 22.5 0.5 mrad rotating polygon, parallel TopoSys Falcon II 1540 nm 60 1600 m first and last max. 630 Hz 7 (fixed) 83 kHz 0.5 mrad fiber switch, parallel

Others: FLI-MAP (Fugro-Inpark), LiteMapper (IGI mbH), GeoMapper 3D (Laseroptronix), ALS series (Leica), TopEye MK II (TopEye AB)Claus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006


Optech ALTM 3100

All images taken from www.optech.ca



Riegl LMS-Q560 / LMS-Q280i

(Scanner & data recorder only)

Images taken from www.riegl.co.at



IGI LiteMapper

(uses scanners from Riegl)Images taken from www.litemapper.com Claus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006


TopoSys

Falcon II, III (fiber)

Harrier (uses scanners from Riegl)Images taken from www.toposys.de Claus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006


FLI-MAP

FLI-MAP 400

All images taken from www.flimap.com



Errors and strip adjustment



Errors and strip adjustment Error sources Geometrical error budget Strip adjustment



Coordinate systems

tIRF

ECF

tARFDGPS INSLaser Ranging unit

IRF

Deflection unit

Inertial reference frame Moving with aircraft

Aircraft/ scanner reference frame Moving with aircraft

Earth centered reference frame ECEF, WGS84Claus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006


Error sources

Laser measurement (range, angle: electronics aging & drift) DGPS (receiver, satellite constellation, ground reference constellation) INS (receiver: frequency, drift) Offset / alignment between GPS, INS, laser scanner Dynamic bend of IMU / scanner mounting plate Time synchronization and interpolation (GPS: 1-10/s, INS 200/s, turbulent flight) Transformation to local coordinate system

Basic geometric configuration



Error budget (geometry)Z X0, Y0, Z0 h

Y

R

Z

Y X X



due to error in

Error budget (geometry) 0 0 0 20.9 7.5 16.1 0 20.9 0 0 14 1.3 2.5 0 5.6 12.1 0 0 0 4 8 5 5 4 cm 0 0 0 8 0 8 0 0 0 8 0 0 R X0 Y0 Z0 Total 22.4 23.6 27.6 26.4 26.4 26.5 9.4 11.7 17.0Total @h=1000

53.0 56.2 66.6 63.5 63.5 63.6 9.4 19.1 37.3

X

15 30 0

Y

15 30 0

Z

15 30

Assumptions: h = 400 m (except last col. h = 1000 m), = = =0, = = 0.03, = 0.04, = 0.02, R = 5 cm, X0 = Y0 = Z0 = 8 cm

0-5 5-10 10-15 15+

Source: [Baltsavias, 1999a]



Error budget: conclusions 0 X 15 30 0 Y 15 30 0 Z 15 30 0 5.6 12.1 0 0 0 4 8 20.9 0 0 14 0 20.9 0 7.5 16.1 0 1.3 2.5 5 5 4 0 0 8 0 8 0 0 0 8 0 0 R X0 Y0 Z0 Total 22.4 23.6 27.6 26.4 26.4 26.5 9.4 11.7 17.0Total @h=1000

53.0 56.2 66.6 63.5 63.5 63.6 9.4 19.1 37.3

Y slightly larger than X for small (due to error) changes for larger (due to error)Source: [Baltsavias, 1999a]Claus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006



53.0 56.2 66.6 63.5 63.5 63.6 9.4 19.1 37.3

R has only marginal influence on Z and almost no influence on X, Y.Source: [Baltsavias, 1999a]Claus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006



53.0 56.2 66.6 63.5 63.5 63.6 9.4 19.1 37.3

Z smaller than X, Y and less dependent on h Reason: R, Z0 dominate and are nearly independent of h Z mainly depends on Z0 (GPS!) (and R) for small

Source: [Baltsavias, 1999a]



Error budget: conclusions 0 X 15 30 0 Y 15 30 0 Z 15 30 0 5.6 12.1 0 0 0 4 8 20.9 0 0 14 0 20.9 0 7.5 16.1 0 1.3 2.5 5 5 4 0 0 8 0 8 0 0 0 8 0 0 R X0 Y0 Z0 Total 22.4 23.6 27.6 26.4 26.4Y X, 26.5 9.4 11.7 17.0Total @h=1000

53.0 56.2 66.6 Z 63.5 63.5 63.6 9.4 19.1 37.3

Z given is too optimistic especially for sloped terrain, X, Y dominateSource: [Baltsavias, 1999a]Claus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006


Counter measures

Constructional measures Highly stable mechanics, low drift in electronics, highly accurate time sync., internal reference measurement Calibration Factory calibration of laser scanner, GPS/INS alignment Flight specific measures Good satellite constellation, close reference station, little turbulence

Still systematic errors will remain, especially visible at strip overlaps strip adjustment



Strip adjustment

Create a seamless data set by correcting for the systematic errors.

(Slide provided by George Vosselman) Claus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006


Strip adjustment Analogy to independent model adjustment with selfcalibration parameters Modelling of shifts, drifts and other systematic errors Measurement of tie points Measurement of control points Adjust strips such that corresponding tie points are transformed to same terrain point misclosures at control points are minimal



Strip adjustmentIndependent strips with tie points Strips transformed to reference system

(ifp / J. Kilian)(Slide provided by George Vosselman) Claus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006


Strip adjustment

1D strip adjustment 3D strip adjustment Measurement of corresponding points in height data ditches and ridges in height data edges in reflectance data



1D adjustment only correct the height mathematical model for control point in strip s

H = a s + bs Xas bs cs Xsc , Ysc

(

c Xs

)+ c (Ys

c Ys

)

offset in height tilt in flight direction tilt across flight direction centre of strip s



1D adjustment mathematical model for tie point between strip s and strip t

H = a s + bs Xt t

( ) + c (Y ) a b (X X ) c (Y Y )c Xs c t s c Ys c t t



Problems unmodelled errors lead to large distortions case: range offset or scale error in the scanning angle possible solutions: more reference points cross stripsbefore adjustment

after adjustment

tilt offset



3D adjustment

Modelling systematic errors in terrain coordinates: Approximation by 1st and 2nd order polynomials. Modelling the effect of sensor errors on terrain coordinates. 3D adjustment requires estimation of 3D offsets between overlapping strips strips and reference data.



3D adjustment

Two approaches: Take height differences in suitable areas as observations (cf. area based matching) First extract corresponding features, then use those as observations (cf. feature based matching)



Segmentation of overlaps


(Slide provided by George Vosselman)


Offset estimationPlanimetric offsets may be estimated from sloped surfaces reflection data

Claus Brenner (Slide provided by George Vosselman) International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006


Offset estimationHeight differences only are not sufficient

flat roof

gable roof



Measurement of tie pointsArea based image matching Simple mathematical modelling Geometric transformation

X s = X t + X Ys = Yt + Y Radiometric transformation

Z s ( X s , Ys ) = Z t ( X t , Yt ) + Z(Slide provided by George Vosselman) Claus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006


Using ditchesFitting of point clouds to ditch profile model No data interpolation Noisy free gradients Better accuracy estimates



Eelde datasetPoint density 1 pts / 3 m2 Strip width 225 m

Claus Brenner (Slide provided by George Vosselman) International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006


Ditch measurements



Pixel size 2m


Point clouds

Original data

After fitting

Original data

After fitting(Slide provided by George Vosselman) Claus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006


Using gable roofsPoint density 6 pts/m2 Strip width 90 m Measurements 6 ridge lines




Using gable roofs


Pixel size 1 m



Using gable roofs

Next strip overlap Measurements 10 ridge lines



Using gable roofs



Point cloudsOriginal data After fitting



Offset estimation in reflectance dataReflection data is noisy peak reflection strength, no integration low reflectance strength in case of multiple heights within footprint footprint much smaller than point distance needs to be modelled

Long edges are preferred



Conclusions offset estimation Offsets estimated in height and reflectance data will be biased when using standard image matching tools. Offset estimations in height data should use continuous surfaces only. Fitting models to height data avoids interpolation errors. Modelling edge response in reflectance data allows unbiased offset estimation, but requires long edges.



3D strip adjustment results Model: 3 shifts, 3 rotations, and 3 rotation drifts Sensor Point density Flying height Number of strips Number of tie points before adjustment after adjustment Relative improvement FLI-MAP 5-6 pts/m2 110 m 2 75 15.2 cm 9.7 cm 36% Optech 0.3 pts/m2 500 m 4 46 35.6 cm 20.3 cm 43%



3D strip adjustment results FLI-MAP before adjustment after adjustment relative improvement Optech ALTM before adjustment after adjustment relative improvement x 16.4 11.2 32% x 48.6 26.0 47% y 20.0 11.6 42% y 40.5 24.5 40% z 5.0 4.7 6% z 11.6 8.5 27%



Conclusions strip adjustment Many errors may occur. Strip adjustment in combination with error models can eliminate most systematic errors. Strip adjustment can be used for data correction or as a quality control tool. Remaining systematic errors may reveal errors that are difficult to model. New errors are still discovered.



Filtering of ALS data



Filtering Introduction Digital elevation model (DEM), digital terrain model (DTM): Ground Digital surface model (DSM): top surface In open terrain, the separation surface between air and bare earth DEM is different from measured laser points due to very different reasons: Measurement errors of ALS system (position, orientation, range) Interaction with target (mixed points in vegetation) Interpretation (buildings are not part of the DEM by definition) Filtering: classification of points into terrain and off-terrain Basis for DTM generation, detection of topographic objects

dy dx


Raster

TIN


Filtering



Filtering



Filtering



Filtering

(Source: George Vosselman)Claus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006


Filtering approaches

Basic approaches Mathematic morphology Progressive refinement Linear prediction Segmentation

Points / local neighbourhood vs. segments



Filtering of ALS data Introduction Morphologic operators and slope based filtering (Vosselman, 2000) Linear prediction and hierarchic robust interpolation (Kraus & Pfeifer 1998, Pfeifer et al. 2001) Progressive TIN densification (Axelsson, 2000) Segmentation based filtering (Sithole, Vosselman 2005) ISPRS filter test



Morphologic operators and Slope based filtering



Erosion, dilation, opening, closing Erosion and dilation for binary images I Image, s two-dimensional structure element Erosion:

1 if (i, j ) s : I (r + i, c + j ) = 1 ( I s )(r , c) := 0 else Dilation:

1 if (i, j ) s : I (r + i, c + j ) = 1 ( I + s )(r , c) := 0 else Opening:

I o s := ( I s ) + s Closing:

I s := ( I + s ) sClaus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006


Example: Opening (I)

=

I

s

I-s

+

=

I-s

s

I o s := ( I s ) + s



Example: Opening (II)

=

I

s

I-s

+

=

I-s

s

I o s := ( I s ) + s



Example: Opening (III)

=

I

s

I-s

+

=

I-s

s

I o s := ( I s ) + s



Equivalent definitions using min and max Erosion:

( I s )(r , c) := min I (r + i, c + j )( i , j )s

1 if (i, j ) s : I (r + i, c + j ) = 1 ( I s )(r , c) := 0 else

Dilation:

( I + s )(r , c) := max I (r + i, c + j )( i , j )s

Define kernel function k

0 (i, j ) s k (i, j ) := 1 else Then, erosion and dilation are given by:

k(i) i

( I k )(r , c) := min[I (r + i, c + j ) k (i, j )](i , j )

( I + k )(r , c) := max[I (r + i, c + j ) + k (i, j )](i , j )Claus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006


Erosion using k(i,j)I k( I k )(r , c) := min[I (r + i, c + j ) k (i, j )](i , j )

r

k(i) i

I-kClaus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006


Morphological operators for grey scale images (here, DSM)

DSMErosion

k(i) i Dilation

DTMOpening



Original DSM(opening)

11x11 m2

15x15 m2

21x21 m2

31x31 m2 Claus Brenner

International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006


Original DSM

(opening)

11x11 m2

15x15 m2

21x21 m2

31x31 m2 Claus Brenner



Original DSM

DTM obtained by opening



Modification: dual rank filters Minimum / maximum may be problematic if outliers are present Use of rank filters is more robust Rank function: returns the mth element of sorted values

Rm ({I1 , I 2 ,..., I n }) := ( Sort ({I1 , I 2 ,..., I n }))[m] Then, erosion and dilation become

( I m k )(r , c) := Rm ({I (r + i, c + j ) k (i, j ) (i, j )}) ( I + m k )(r , c) := Rn +1 m ({I (r + i, c + j ) + k (i, j ) (i, j )}) Note: n = # zeros in k ,

1 , +1 +

m



Modification: points, irregular data Erosion (previously):

e(r , c) = ( I k )(r , c) = min (I (r + i, c + j ) k (i, j ) )(i , j )

pi

pj

Now:

e( pi ) := min (h( p j ) k (xij , yij ) )p j A

k (xij , yij ) Definition of the DEM:

DEM := p j h( p j ) e( p j )

{

}



Slope based filtering (Vosselman, 2000)e( pi ) := min (h( p j ) k (xij , yij ) )p j A

k (xij , yij )h

k

hmax (d ) Interpretation of k

k (x, y ) := hmax

( x

2

+ y 2 = hmax (d )

)

h1d1 Points at distance d1 can be lower by h1 d



Slope based kernel functionhmax (d )

d

DEM := p j h( p j ) e( p j )

{

}

Kernel function effectively suppresses slopes larger than its own slopeClaus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006

Derivation of suitable kernel functions hmax Idea 1: assume a maximum slope, e.g. 30%


hmax (d ) := 0.3d Since measurements are noisy, add confidence interval. Allow 5% of terrain points (with standard deviation ) may be rejected

hmax (d ) := 0.3d + 1.65 2

hmax (d )

d Arbitrary specification try to obtain from data


Derivation of suitable kernel functions hmax Idea 2: derive maximum height differences from data Training set with ground points only For each distance interval d, compute max(h) Also compute variance (of the maximum) for each d using cumulative probability distribution


Fmax (h) = F (h) N

Idea 3: minimize classification errors Effect of type I and type II errors is the same search for h where

2

P( pi DEM h, d , p j DEM) = 0.5 Requires training set with ground points and unfiltered data of the same area

1

2(Source: George Vosselman)

3


Derivation of suitable kernel functions hmax5m h


d 0m 10 m

P( pi DEM h, d , p j DEM)Black 0.0, white 1.0

-5 m(Source: George Vosselman)Claus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006

Derivation of suitable kernel functions hmax4Allowed height difference (m)


3Maximum Probabilistic

2

1

0 0 2 4 6 8 10Distance between points (m)(Source: George Vosselman)Claus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006


Example results


(Source: George Vosselman) Laser point density 5.6 points/m2. 2 m grid (top), 0.5 m grid (bottom). Maximum filter. Height difference of ditches: 0.5 m.


Example results(Source: George Vosselman) Perspective view. Laser point density 5.6 points/m2 (top), reduced to 1 point/16m2 (bottom)Claus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006


Linear prediction and Hierarchic robust interpolation



Interpolation using a summation of kernel functionsz2.5 2

1.5

1

(x1,z1)

?(xn,zn)1 2 3 4 5

0.5

x

-0.5

Given: Heights z at positions x:

z = ( z1x = ( x1

z2 L zn )

T

x2 L xn )

T

Find an interpolating function:Claus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006


Interpolation using a summation of kernel functions Idea: describe overall function as a sum of basis functions

f ( x ) = ki ( x)i =1

n

Simpler: as a sum of identical basis functions k depending only on the distance x-xi multiplied by a factor mi

f ( x) = mi k ( x xi )i =1

n

Example k(d)

k(d)

1 0.8 0.6 0.4 0.2

d1 2

-2

-1



Interpolation using a summation of kernel functions Interpolation!

f has to pass through the given pointsn

z j = f ( x j ) = mi k ( x j xi )i =1

Written in matrix form

k ( x1 x2 ) k ( x1 xn ) z1 k (0) k (0) k ( x2 xn ) z2 k ( x2 x1 ) = M O M z k(x x ) k(x x ) L k (0) n n 1 2 n Or, shorter

m1 m2 M m n

z = Km



Interpolation using a summation of kernel functions Solution (note: linear; exact solution)

m = K 1z Function f

Or, shorter

m1 n m f ( x) = mi k ( x xi ) = (k ( x x1 ) k ( x x2 ) L k ( x xn ) ) 2 M i =1 m n f ( x) = k T K 1z

Note: x variable k depending on x K z fixed1



Example using triangular kernel function2.5

2.5

2

2

1.5

1.5

1

1

0.5

0.5

1 -0.5

2

3

4

5

1 -0.5

2

3

4

5

x = (1, 2, 2.5, 3, 4 ) z = (1, 2, 1.75, 2, 0 )

m = K 1z = (1, 2.25, 0.5, 2.25, 0 )

2.5

f (x)1 0.8 0.6 0.4 0.2 -2 -1 1

2

1.5

1

k(d)

0.5

d2-0.5

1

2

3

4

5



Example using Gaussian kernel function2.5

6

2

4

1.5

2

1

10.5

2

3

4

5

-2

-41 -0.5 2 3 4 5

-6

x = (1, 2, 2.5, 3, 4 ) z = (1, 2, 1.75, 2, 0 )

m = K 1z = ( 0.29, 5.07, 6.49, 5.76, 1.53)

f (x) k (d ) = e d-2 -1

2.5

2

1.5

21 0.8 0.6 0.4 0.2 11

d2

0.5

1 -0.5

2

3

4

5



Statistical interpretation of Gaussian kernel function Interpretation as covariance of laser points Pi , Pk having distance d

C ( Pi Pk ) := C (d ) = C (0) e

d c

2

C(0)

C(d)

d

Statistical surface description: close points have high covariance Need to determine C(0), c



Determination of parameters of covariance function After removal of trend (see later), zi coordinates contain measurement error ri systematic error si

zi = si + ri Variance of zi :

Vzz

=

1 1 zi zi = ( si si + 2 si ri + ri ri ) n n 1 ( si si + ri ri ) = Vss + Vrr n



Determination of parameters of covariance function Determination of empirical covariances Cj Sort point pairs into buckets, according to their distance

d j dCj = 1 nj

Pi Pk

< d j + d1 nj

In each bucket, determine empirical covariances

zi z k

s s

i k

Determine C(0)2 C (0) = Vss = Vzz Vrr = Vzz Z

(using estimate Z of height error)

Determine cj for each bucket from

C j = C ( 0) e

dj cj

2

solve for c j

Determine c as weighted mean of cjClaus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006


Interpolation and filtering After having determined Gaussian kernel function, interpolation is just as before:

f ( P ) = c T C 1z c T = C ( PP ) C ( PP2 ) L C ( PPn ) 1

(

)

z T = ( z1

z2 L zn )

C (0) C ( P P2 ) C ( P Pn ) 1 1 C ( P2 P ) C (0) C ( P2 Pn ) 1 C = O M C ( P P ) C ( P P ) L C (0) n 1 n 2 What happens if we replace C by

Vzz Vss = C (0)C(d) d

Vzz C ( P P2 ) C ( P Pn ) 1 1 C ( P2 P ) Vzz C ( P2 Pn ) 1 C = O M C(P P ) C(P P ) L Vzz n 1 n 2



Interpolation and filtering Note from earlier:2 Vzz = Vss + Vrr = C (0) + Z

C = C + z2 I n2.5

using C

2.5

using C

2

2

1.5

1.5

1

1

0.5

0.5

1 -0.5

2

3

4

5-0.5

1

2

3

4

5

Interpolation and filtering: considers measurement errors Allows weighting of measurements using individual Vzz ,iClaus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006


Hierarchic robust interpolation Kraus & Pfeifer 1998, Pfeifer et al. 2001 Before application, remove trend surface, e.g. by estimation of a low-degree polynomial After trend removal, 3 stages of refinement: Interpolation + filtering as just explained Robust interpolation compute weights for individual points (see next slides) Hierarchic robust interpolation if gross errors occur in large clusters compute data pyramid, use surfaces obtained in coarse level to accept points within tolerance band in higher resolution level



Robust interpolation2 Initial interpolation using unit weights i2 = 0

Outlier, probably vegetation Interpolation follows outlier

Result of interpolation + filtering

(Source: I.P.F. TU Vienna)

Trend surfaceClaus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006


Robust interpolation Calculate filter values = oriented distance from surface to measured point Compute histogram of filter values Usually, asymmetric: many points above surface, few points below surface

(Source: I.P.F. TU Vienna)Claus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006


Robust interpolation Use asymmetric weight function (a,b different for left & right branch)

pi =

1 + (a f i g )

1

b

, =2 i

02pi

a, b parameters, g shift determined from histogram Also remove points which are too far off the surface

cutoff

(Source: I.P.F. TU Vienna) Claus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006


Robust interpolation

Initial interpolation

Refined interpolation




Filter results in forested area




Progressive TIN densification



TIN densification (Axelsson, 2000) Start using sparse seed points lowest points in a large grid, based on largest structure, e.g. 50-100 m Densify iteratively from below calculate required thresholds from points currently included in the TIN add points to the TIN if they are within thresholds Threshold computation based on median values of surface normal angles and elevation differences. Uses histograms for computation of median.



TIN densification Add one point at a time in each triangle facet Accept based on distance and angle threshold Special case for discontinuous surfaces (urban areas) threshold values easily exceeded use mirroring of point at closest point in TIN triangle to compute deviation

d

d mirror d



Segmentation based filtering

Note: the slides of this section were provided by George Sithole / George Vosselman based on their talk Filtering of airborne laser scanner data based on segmented point clouds given at the laser scanning workshop 2005 in EnschedeClaus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006


Filter designProblem analysis Smooth surface assumption does not hold Lack of context information Filter as a local operator Point-wise filtering

New filter approach Use continuous surface instead of smooth surface Filter continuous segments of points instead of points

Claus Brenner Slide provided by George Sithole, George Vosselman International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006


Segment based filtering

Texture based image segmentation

Point cloud segmentation into continuous surfaces



Profile segmentation

Delaunay Delaunay Triangulation Triangulation

Minimum Minimum Spanning Tree Spanning Tree

Proximity Proximity Thresholding Thresholding

Remove Remove Dangling Edges Dangling Edges



Profile classificationRaised Raised

Lowered Lowered

Terraced Terraced

High High

Low Low



Combining profiles to segments



Combining profiles to segments



Segment classification

Based on majority of segment profile classifications



Bridge detection Select all terrain profiles Analyse profile segment classifications



Results in urban areaSegment based filtering

Type I error Type II error

Alg. 1 Alg. 2 Three other algorithms of the ISPRS filter test

Alg. 3



Results in quarrySegment based filtering

Type I error Type II error

Alg. 1

Alg. 2

Alg. 3



Quantitative resultsUrban sites (error %) Alg 1 Average 5.6 Median 4.3

Alg 2 7.0 6.7

Alg 3 14.0 12.2

New alg 6.0 4.3

Rural sites (error %) Alg 1 Average 3.6 Median 2.9

Alg 2 9.5 7.9

Alg 3 15.6 17.2

New alg 5.4 6.2



Conclusions for segment based filtering Segment-based filtering preserves discontinuities allows filtering of large objects can be combined with other filtering methods could be extended with other attributes (shape, size, colour) Segmentation in areas with low vegetation remains difficult Bridges can be recognised in bare earth segment Segmentation results may support manual editing



ISPRS filter test



ISPRS filter testComparison of filter algorithms, 2002-2004 8 sites, 8 participants Qualitative and quantitative evaluation

All filters do well on smooth terrain with vegetation and buildings. All filters have problems with rough terrain and complex city landscapes. In general, filters that compare points to locally estimated surfaces performed best. The problems caused by the scene complexities were larger than those caused by the reduced point density. Research on segmentation, quality assessment and usage of additional knowledge sources is recommended. Full report on http://www.geo.tudelft.nl/frs/isprs/filtertest/Claus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006


Extraction and modellingClaus Brenner with contributions from George Vosselman and Juha Hyypp

Institute of Cartography and Geoinformatics University of Hannover, Appelstr. 9a, 30167 Hannover, Germany [email protected] www.ikg.uni-hannover.de



Example laser scan data100

80

60

40

20

0 0 20 40 60 80 100

Data obtained by aerial laser scanning Example: approx. one measurement per m2 Regularized raster, mesh width 1m x 1m



Example laser scan data



Main applications

Derivation of DEMs Forest inventory Extraction of man-made objects Flood modelling Mapping of linear structures: dikes, roads, power line clearance Classification



Extraction and modelling

Introduction Feature extraction Derivatives Local polynomial fit and curvature analysis Planar faces Region growing, scan line grouping, RANSAC, Hough transform More complex shapes Building extraction Examples (data driven, model driven, integration of existing knowledge) Future developments: constraints & generalization see terrestrial scanning



Derivativesf ( x) DSM seen as a grayvalue image derivatives can be used to detect jumps in the DSM second derivatives may be used to detect discontinuities in slope Derivative masks from digital image processing can be used Note: derivative has metric interpretation

x f ( x) x

x



Derivatives: discrete operators Derivative operator based on difference quotientdf f ( x + x ) f ( x ) ( x) dx x

mask: (1 1) even mask length, linear phase noise: = 2 f 1.4 f Derivative operator based on average difference quotientdf 1 f ( x ) f ( x x ) f ( x + x ) f ( x ) f ( x + x ) f ( x x ) ( x) + = dx 2 x x 2 x

mask: 1 2 (1 0 1) = 1 2 (1 1) (1 1) odd mask length, zero phase noise: = 1 f 0.7 fClaus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006

2


Derivatives

Original DSM f ( x, y )

2 2 f ( x, y ) + f ( x, y ) x y

1

2



Derivatives

Original DSM f ( x, y )

2 2 f ( x, y ) + f ( x, y ) x y

1

2



Morphological operations: opening

300

300

250

250

200

200

150

150

100

100

50

50

0 0 50 100 150 200 250 300

0 0 50 100 150 200 250 300

Original DSM

DSM DTM



Morphological operations: opening

DSM DTM Height > 5 m and footprint > 50 m2 Height > 5 m

Orthophoto



Local estimation of polynomial functions Derivatives (especially second derivatives) are sensitive to noise Standard smoothing masks are not motivated geometrically Idea: for each discrete point, determine locally a best approximating polynomial function f (u ) then, derivatives f ( x) and f ( x) can be obtained from the derivatives of f (u ) and f (u )

f (u )

N

f (1)

uM K

0 1K M


U = { M , M + 1,K 0,1,K , M }


Local estimation of polynomial functions Scalar product

f , g := f (u ) g (u )uU

Polynomial base functions up to second order

0 (u ) := 1 1 (u ) := u 2 (u ) := u 2

M ( M + 1) 3

Properties of base functions (orthogonality)

i , j = 0 i j 0 , 0 = 2 M + 1 =: p0 1 , 1 = 1 3 M ( M + 1)(2M + 1) =: p1 2 , 2 = K =: p2Claus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006


Local estimation of polynomial functions Definition of normalized base functions

bi :=

i

pi

i , b j = ij

(Kronecker)

Second order approximation for functions of one variable

f (u ) = ai i (u )i =0 uU

2

withtrick: no need to invert since functions are orthogonal

ai := f , bi = f (u ) bi (u )

Second order approximation for functions in two variables

f (u , v) = aij :=

i + j 2

a

ij

i (u ) j (v)

with

( u , v )U 2Claus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006

f (u , v) bi (u ) b j (v)


Local estimation of polynomial functions Derivatives: f (u, v) = a00 + a10u + a01v M ( M + 1) M ( M + 1) + a20 u 2 + a11uv + a02 v 2 3 3

u v

f (u , v) f (u, v)

= a10 + a20 2u + a11 v = a01 + a02 2v + a11 u


f (0, 0) u f (0, 0) v 2 f (u, v) 2 u 2 f (u , v) u v 2 f (u , v) v 2

= a10 = a01 = 2a20 = a11 = 2a02


Local estimation of polynomial functions Example:M = 3 U = {3,K ,3} , p0 = 7, p1 = 28, p2 = 84

1 f (u ) 1 7 u =3 3 1 a1 = f , b1 = f (u ) u 28 u =3 a0 = f , b0 = a2 = f , b2 =u =3

3

3

f (u )

1 2 (u 4) 84

From this, the following convolution masks are obtained:1 (1 1 1 1 1 1 1) 7 1 d1 = ( 3 2 1 0 1 2 3 ) 28 1 d2 = ( 5 0 3 4 3 0 5 ) 84 d0 =Claus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006


Local estimation of polynomial functions Two-dimensional convolution masks are obtained as follows:T Du = d 0 d1 T Duu = 2d 0 d 2 T Dvv = 2d 2 d 0

Dv = d1T d 0

Duv = d1T d1 E.g. the second partial derivative with respect to u:

5 5 5 2 2 T f Duu * f , Duu = 2d 0 d 2 = 2 5 7 84 u 5 5 5

0 3 4 3 0 5 0 3 4 3 0 5 0 3 4 3 0 5 0 3 4 3 0 5 0 3 4 3 0 5 0 3 4 3 0 5 0 3 4 3 0 5



Differential geometry

N

x vUp q2 3

u

Regular parametrized surface:x : 2 U 3 U open, x differentiable, dxq injective

Normal vectorN (q) = xu xv (q) xu xv



Differential geometry First fundamental form in local coordinatesI = E (u ) 2 + 2 F u v + G (v) 2 E = xu , xu , F = xu , xv , G = xv , xv Second fundamental form in local coordinates

II = e (u ) 2 + 2 f u v + g (v) 2 e = N , xuu , f = N , xuv , g = N , xvv Gaussian curvature and mean curvature

N (q) =

xu xv (q) xu xv

eg f 2 K = 1 2 = EG F 2 1 eG 2 fF + gE H = ( 1 + 2 ) = 2 EG F 2

1 , 2 main curvaturesClaus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006


Differential geometry DSM is given as a graph z = f(u,v) From this, the following simplifications are obtained:z = f (u , v) u 1 0 x(u , v) = v , xu = 0 , xv = 1 f (u , v) fu fv E = xu , xu = 1 + f u2 etc. fu 1 f N= 2 v ( fu + f v2 + 1)1 2 1 f e = N , xuu = 2 uu ( fu + f v2 + 1)1 2 K, HClaus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006

etc.


Surface types Surfaces can be classified depending on the sign of K and H Both signs can be coded into a single number (KH sign map)

khs := 3 (1 + sgn H ) + 1 + sgn K In practice, H=0 or K=0 will not be obtained, thus the following modified sign function is used:

1 x < sgn ( x) := 0 x 1 x >

sgn ( x)

x



Surface typeskhs K0

H0 6 7 8 4 1 Not possible 2



Application: curvature type classification

Type 03Simple discrete derivative operatorsClaus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006

Type 68


Application: curvature type classification

Type 03Local estimation of polynomial functionsClaus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006

Type 68


Region based segmentation Region based segmentation: partitioning of a region into disjoint subregions subregions evaluate true with respect to a given predicate P () subregions are maximal More precisely:

1.

URi =1

n

i

=R

2. 1 i n : Ri is connected 3. i j : Ri R j = 4. P ( Ri ) = true 5. i j : P ( Ri R j ) = false, if Ri , R j are neighborsClaus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006


Region based segmentation

1 5 9

2 6

3 7

4 8

1 5 9

2 6

3 7

4 8

R1 = {1, 2,3, 4, 7,8,12} R2 = {5, 6,10,11,15,16} R3 = {9,13,14}

10 11 12

10 11 12

13 14 15 16

13 14 15 16

How can the desired subregions be obtained? E.g.: cluster analysis split-and-merge region growing



Region growing

Start1 2 6 3 7 4 8 1 5 9 2 6 3 7 4 8 1 5 9 2 6 3 7 4 8

Search for seed region Found? Y Grow region as long as possible N End

5 9

10 11 12

10 11 12

10 11 12

13 14 15 16

13 14 15 16

13 14 15 16

1 5 9

2 6

3 7

4 8

1 5 9

2 6

3 7

4 8

1 5 9

2 6

3 7

4 8

10 11 12

10 11 12

10 11 12

13 14 15 16

13 14 15 16

13 14 15 16



Region growing Predicates for digital surface models distance of points from an estimated planeP : z = ax + by + c distance: d (i ) = axi + byi + c zi

normal vector orientationcos = N i , ( a, b,1)T

Disadvantages: the order of selection of seed regions affects the result iterative estimation of plane equation is time consuming Application: detection of planar regions in DSM, e.g. roof facesClaus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006


Region growing: examples



Scanline grouping (Jiang & Bunke, 1992) Subdivide each line into segments (e.g. using DouglasPeucker) Build seed region using consecutive segments Grow seed region by adding segments Postprocess

y0+2 y0+1 y0Claus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006



y0+2 y0+1 y0Claus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006



y0+3 y0+2 y0+1 y0Claus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006



y0+3 y0+2 y0+1 y0Claus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006


Scanline grouping segmentation: examples

DSM (Stuttgart, 1m)

Segmentation



Scanline grouping segmentation: examples

DSM (Stuttgart, 1m)

Segmentation



RANSAC (Random Sample Consensus, Fischler & Bolles 1981) Algorithm: Select minimum number of observations randomly (e.g. 3 points for a plane, 2 points for a line) = random sample Compute parameters based on these observations Find out the number N of compatible observations = consensus Select solution which has largest N

There is a formula for minimum number of draws required Very powerful algorithm, easy to implement



RANSAC example: find linear segmentsz

x z

x z

xClaus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006


RANSAC example: find linear segmentsz

x z

x z

xClaus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006


RANSAC for planar segmentation

etc.



Examples: region growing, RANSAC

Region growing

RANSAC



Examples: region growing, RANSAC

RANSAC

Region growing



Hough transform (PVC Hough, 1962)6

y

N

(x0,y0)

cos N = sin

c4 2

one specific line

1 2 3 4 5 6

x cos + y sin + c = 0c = ( x0 cos + y0 sin ) = c( )x-2 -4

Hough space-6

6

y

high count

4 2

1 -2 -4

2

3

4

5

6

x-6

accumulatorClaus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006


Hough transform Can be used for any parameterized object: planes, cylinders, Higher dimensions may become impractical (space, time) Sometimes sequential Hough transforms of lower dimension are feasible Global 3D Hough transform may be problematic

(source: George Vosselman)Claus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006


Building Reconstruction







(Source: Sony press release)Claus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006


Non photorealistic rendering (NPR)

Source: Prof. Dllner, Computer Graphics Systems, Hasso-Plattner Institute, PotsdamClaus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006


Augmented reality car navigation

Source: press release, Siemens AG, 30.09.2005



Engravings by Merian

Matthus Merian d. ., 1593-1650 Martin Zeiller Topographia, 1642ff., 30 Bd., 100 maps, 2150 views



Partial tasks for building reconstructionRaw data Result

building reconstruction

Detection

Structuring

Geometric Reconstruction

Semantic AttributationGebude { { Gebude ID == 541 ID 541 Nutzungsart == Gewerblich Nutzungsart Gewerblich Gebude { { Gebude Stockwerke ==55 Stockwerke ID == 541 541 ID Stellpltze = 2 Stellpltze = 2 Nutzungsart == Gewerblich Nutzungsart Gewerblich { Fassadenmaterial == { Gebude { { Fassadenmaterial Gebude Stockwerke ==55 Stockwerke KH315 F1 == ID == 541 F1 ID 541 Stellpltze == KH315 Stellpltze 2 Nutzungsart ==F2 ==2 F2 KH221 KH221 Nutzungsart Gewerblich { Gewerblich Fassadenmaterial == { Fassadenmaterial KH315 Stockwerke ==5F3 == KH315 Stockwerke KH315 5F3 F1 == KH315 F1 EF951 Stellpltze == 2F4 == EF951 Stellpltze =2 F4 F2 = KH221 KH221 F2 } Fassadenmaterial == { Fassadenmaterial { F3 ==} KH315 KH315 F3 ffentlich = { F1 == KH315 F1 KH315EF951 F4 ==ffentlich = { F4 { Artztpraxis, Link @3398472 } F2 == KH221EF951 F2 } KH221 { Artztpraxis, Link @3398472 } F3 ==} KH315 { { Restaurant, Link @0274832 } KH315 Restaurant, Link @0274832 } F3 ffentlich = { } F4 ==ffentlich = { F4 EF951 } EF951 { {Artztpraxis, Link @3398472 } } } Artztpraxis, Link @3398472 }} } { Restaurant, Link @0274832 } Restaurant, ffentlich{Gebude { { Link @0274832 } == { { ffentlich Gebude }} ID Link @3398472 } { {Artztpraxis,== 542 @3398472 } ID 542 } Artztpraxis, Link } Nutzungsart == Wohn { { Restaurant, Link @0274832 } Restaurant, Link @0274832 } Nutzungsart Wohn Gebude { Stockwerke ==22 } } Gebude { Stockwerke ID == 542 542 ID Stellpltze = 0 }} Stellpltze = 0 Nutzungsart == Wohn Nutzungsart Wohn Gebude { { } } Gebude Stockwerke ==22 Stockwerke ID == 542 ID 542 Stellpltze == 0 Stellpltze 0 Nutzungsart == Wohn Nutzungsart Wohn }} Stockwerke ==22 Stockwerke Stellpltze == 0 Stellpltze 0 }}



Geometric building modelsBuilding Model

Parametric

General

Primitive

Combined

Prismatic

Polyhedral

Ruled

Freeform



Boundary representation vs. CSG

Topology hard

easy

Boundary representation (BREP)

Constructive solid geometry (CSG) Claus Brenner



Data driven reconstructionObject contains straight edges Object contains rectangles Object is red

Original image Edge extraction Grouping into rectangles Filtering using spectral signature

Object has minimum size

Filtering using size, grouping



Model driven reconstruction

Model database Original imageExplicit models



Example: data driven



Data driven approach Assumptions: Roof described by planar faces Height jump edges parallel or perpendicular to main building orientation

Steps: Plane detection Initial face outlining in TIN Reconstruction of building outline Reconstruction of roof face edges(Slide provided by George Vosselman) Claus Brenner International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006


Initial roof facesHeight data Connected components

Rough face outlines



Reconstruction of roof outline

Union of faces

Approximation by straight lines main building direction minimum edge size most points inside building



Reconstruction of face edges Ridges and valleys Intersection of planes of adjacent roof faces Roof outline Intersection of planes with adjacent walls Height jumps inside roof surface Straight lines aligned to main building directions



Reconstruction of 3D building Merging edges to faces Joining parallel edges Intersection of other edges Extraction of terrain height



Example: model driven



Demo: ATOP

Claus Brenner Can be downloaded from: http://www.ikg.uni-hannover.de/3d-citymodels International Summer School Digital Recording and 3D Modeling, Aghios Nikolaos, Crete, Greece, 24-29 April 2006


Integration of existing knowledge: Using existing 2D ground plans



Using existing 2D ground plans

Solves detection problem Helps with structuring Helps to select model in model driven approach (How?)

Helps wit

aerial laser scanning

Documents