3D CONGRUENCY – THE POINT CLOUD PROBLEM

Prof. Dr.-Ing. habil. Thomas A. Wunderlich

Technical University of Munich

Department of Civil, Geo and Environmental

Engineering

Chair of Geodesy

Monitoring by TLS – practicing

unfinished theories

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• Deformation Analysis

• Challenges

• Theoretical Models

• Applications

• Critical Evaluation

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Although theories are unfinished yet:

practice started already!

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Principal task: proof of significant geometrical

changes of an object between two observation epochs

• Rigid body movements (translations, rotations, tilt) or/and

• Change in shape (bending, buckling, torsion)

One of the two epochs may be predetermined by an as-planned or an as-built

geometry from CAD or BIM (s1= ? mm)

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Classic congruence analysis of networks[Pelzer, 1971]

• Checking identical approximate coordinates and

free adjustment of both eopochs (discrete points)

• Testing comparable accuracy of both epochs – if

true: calculation of common s0

• Setting up vector of coordinate differences and the

corresponding cofactor matrix

• Global test of congruency – in case of zero

hypothesis rejection (T>F): tests to prove stable

control points, datum transformation on

approximate coord. of those points

• 2nd step of analysis: locating displaced object

points one by one, applying forward or backward

strategy

• Statement of object point deformations in direction

and magnitude - generalization

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Why discretization/generalization and not

straightforward monitoring by TLS?

Processing immense point quantities (up to millions or billions)

• Thinning out to mitigate processing load and time frequently proves necessary

• or alternative deriving representative points → again discretization of distinct points

No identical points from epoch to epoch

In contrast to conventional observation of single points, which are pegged, signalized

and can be aimed at repeatable, laser points of a point cloud will not hit identical object

spots in different epochs

No unambiguous assignment of points from different epochs to one another

While we have a definite geometric assignment between the coordinate realizations of

a discrete object point in two epochs, there are various specifications (models of

assignment) conceivable concerning point clouds

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1 -2 Bilder zum Zwischentitel

Models of assignment (I)

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Models of assignment (II)[Vosselman & Maas, 2010]

• Point to Point (P2P)

range images, virtual targets, grids

• Point to Surface (P2S)

triangulation (e.g. TIN - triangulated irregular networks), tiling

implicite functions (analytical surfaces)

explicite functions (free-form surfaces, e.g. B-splines, NURBS)

• Surface to Surface (S2S)

best-fit of entire surfaces (ICP - iterative closest point algorithms)

best-fit of surface segments

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P2P virtual targets: highway bridge Freimann[Schäfer, 2008, 2009, 2017]

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P2P grid: lock gate Gabcikovo[Schäfer et al., 2004]

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P2S TIN: oldtimer check before/after

transport[Wasmeier, 2016]

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P2S tiling: NATM-tunnel Stuttgart[Ohlmann-Lauber, 2010]

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P2S implicit functions – ellipsoid Futuro-

House[Ratke, 2006]

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S2S implicit functions – cylinder industry

chimneys[Kregar et al., 2015]

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P2S explicit functions – B-spline surface

model[Braun, 2011]

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Critical evaluation – potential for

improvement (I)

Areal, but maybe limited deformation statement

• sometimes only rigid body movements derivable

• frequently reduction to one dimension instead of 3d statement

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3d deformations by surface structure

matching of tiles[Chmelina et al., 2012]

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Critical evaluation – potential for

improvement (II)

Areal, but maybe limited deformation statement

• sometimes only rigid body movements derivable

• frequently reduction to one dimension instead of 3d statement

Possible new parameters to characterize deformations hardly used

• e.g. differences of areas, differences of volumes (local, total)

• exception: change of focal length at radio telescope [Uni Bonn]

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Paraboloid parameter radio telescope

Effelsberg[Holst & Kuhlmann, 2011, 2014, 2015]

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Critical evaluation – potential for

improvement (III)

Areal, but maybe limited deformation statement

• sometimes only rigid body movements derivable

• frequently reduction to one dimension instead of 3d statement

Possible new parameters to characterize deformations hardly used

• e.g. differences of areas, differences of volumes (local, total)

• exception: change of focal length at radio telescope [Uni Bonn]

Tests of Significance?

• current research object except rare attempts in PhD theses

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Test of representative points at dam

Okertal[Eling, 2009]

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Fusion of image and scan evaluation

(RGB+D) [Wagner, 2016]

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functional

interpolation of ranges

(depth image) at the

locations of identical

object points for both

epochs

stitched images

mapped to

panoramic sphere;

identification of

identical points in

two epochs

Concept of rigorous deformation analysis

using laser scans and camera images – MS60[Wagner, Wiedemann, Wunderlich, 2017]

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matched image

points of 1 & 2

scan points 1

control points

scan points 2

interpolated

ranges

object

Free station

epoch 1Free station

epoch 2

THANK YOU FOR YOUR ATTENTION – MUITO OBRIGADA

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Hammelburg bridge – load test (14.09.2017)

• Task: crack detetction (position & width), solution camera images + control pints

observed by TPS eingemessen (non-stable stationsl, free stationing in each epoch

by means of stable benchmarks)

• Superior solution; RGB+D: all from one instrumentt,

full 3D-deformations derivable

39

Regions of

RGB+D captures