Quality Assessment for LIDAR Point Cloud Registration using In-Situ

Conjugate Features

Jen-Yu Han1, Hui-Ping Tserng1, Chih-Ting Lin2

1 Department of Civil Engineering, National Taiwan University2 Graduate Institute of Electronics Engineering, National Taiwan University

IGARSS, 24-29 July 2011, Vancouver, Canada (Session FR2.T03)

NTUCvE Surveying Engineering Group

Outline

Introduction

Using In-Situ Conjugate Features

Weighted NISLT Approach

Quality Assessment

Numerical Validation

Conclusion

Introduction

Light Detection and Ranging (LIDAR) is capable of acquiring 3D spatial information in a fast and automatic manner.

Can be equipped on platforms of various kinds (air-borne, mobile, and terrestrial).

Usually requires multiple scans in order to construct a complete and accurate 3D model.

Reason 1: Incompleteness due

to obstructions

Reason 2: Error magnification due

to projective geometry

Introduction (cont’d)

Incompleteness due to obstructions

Many obstructions could occur when the LIDAR point cloud is collected from a single station.

Only partial information is acquired for the 3D object.

Introduction (cont’d)

Error magnification due to projective geometry

Point coordinates are based on range and angular measurements both of which contain errors.

As a result, the quality will become lower for outer regions.

Introduction (cont’d)

Registration of LIDAR datasets from multiple stations

Each dataset is defined in an arbitrary local reference frame.

A 3D similarity transformation model is usually postulated to relate the datasets defined in different reference frames.

2 1

x x

y s y

z z

R t

s: scale R: rotation matrixt: translation vector

Station 1 Station 2

1

1

1

2

2

2

Using In-Situ Features

Classic approach: point-based least-squares approach- Find (>=3) conjugate points in two LIDAR datasets- Perform least-squares parameter estimations

Requires extra effort to set up identifiable targets (e.g. control spheres or reflective sticks) or perform feature extractions.

Requires a set of good initial values and iterative computations to obtain reliable parameter estimates.

Obtaining the transformation parameters

Using In-Situ Features

Proposed approach: using directly in-situ features

Extended feature types

- Definite features Points: vectors between points Lines: directional vectors Planar patches: normal vectors

- Indefinite features Groups of points: eigenvectors of the tensor field constructed by a group of point.

Obtaining the transformation parameters

With these extended feature types, it becomes possible to use the geometric components that are already inherent in the scanned object.

Using In-Situ Features

In-situ features usable for LIDAR dataset registrations

Highway surfaces Bridge pillars

Slope surfaces and edges Structure edges and rails

No need to set up control targets reduce the cost for field work.

Weighted NISLT Approach Once feature correspondence is established, the

transformation parameters are estimated by the weighted NISLT (Non-Iterative Solutions for Linear Transformations) technique:

ij12 13T -1k k k

12 13 ij

dxdx dx)

dx dx dxs

l Pl l P (

T

Scale parameter

where dxij and dx’ij are coordinate differences (vectors) in the original and transformed systems, is the weight matrix, lk is a kx1 unity vector. P

Weighted NISLT Approach

Rotational parameters

where ΔX and ΔX’ are the matrices by stacking all the normalized row vectors in the original and transformed systems.

T T T 1 T( ) ( ) ) a a a G = P X P X X P P X = S Λ V(

Ta aR = S V

Translational parameters

T1 1

TT 1 2 2

T

( ' )

( ' )(

( ' )

n n n

n n

x s x

x s x

x s x

R

Rt l Pl ) l P

R

Weighted NISLT Approach Characteristics of weighted NISLT approach

- Closed-form solution, requires no initial

values nor iterative computations

highly efficient compared to

LSQ-based approaches.

- Weighted parameter estimation model uncertainties of input

observables can be realistically taken into consideration.

- Accepts input observables of different kinds (e.g. vectors between

points, directional vectors of linear features, normal vectors of

planar features, and eigenvectors of groups of points) make

possible a direct use of various in-situ geometric features.

0 100 200 300 400 500 600 700 800 900 1000

0

2

4

6

8

10

12

14

16

18

Number of Reference Points

Pro

cess

Tim

e (s

econ

ds)

Affine by Least-squares

Simlarity by Least-squares

Affine by Proposed

Similarity by Proposed

Quality Assessment

Classical point-based approach:

Registration quality is typically evaluated by the post-fit residuals for point coordinates after applying the estimated parameters.

1

nTi i

iRMSVn

ε ε

=iε : post-fit residual vector of point in : number of conjugate points

This index gives a vague interpretation on the obtained result since it represents only the positional agreement between two datasets geometrical similarity is not considered!!

Quality Assessment

Proposed approach:

Here features of various kinds are used for a registration. The quality is then evaluated based on the following two indexes:

1

pnTi i

ia

p

qn

v v

: post-fit residual vector of conjugate point i or the vector between point i ‘s projected points on two conjugate features.

: the angle between two conjugate vectors (directional vectors, normal vectors, or eigenvectors) after the registration.

: the numbers of conjugate points and conjugate vectors

Absolute Consistency (qa) Relative Similarity (qr)

2

1

ln

ii

rl

qn

iv

i

,p ln n

Positional alignment Geometric similarity

Quality Assessment

Interpretation of a registration solution:

(a) (b)

(c) (d)

(a) Moderate qa, good qr.

(b) Moderate qa and qr.

(c) Poor qa, good qr.

(d) Poor qa and qr.

The quality of a registration solution can be explicitly defined by the proposed two indexes qa and qr.

Numerical Validation

Data collection:

A case study was performed for a 250m-long reinforced concrete (RC) bridge in Taipei City.

Two LIDAR stations (S1, S2) were set up about 80m away from the bridge.

S2S1

Numerical Validation

Data collection (cont’d):

LIDAR point cloud was collected at each station using a Trimble® GS200 Terrestrial Laser Scanner.

Resolution for the scanned points of the bridge was roughly between 0.02m ~ 0.04m.

No control sphere or reflective stick was set up in the scanned area.

Trimble GS200 Laser Scanner

- Range: 2m~200m

- Accuracy: range = 6 mm @ 100 m

angular = 6 mm @ 100 m

- Max. Density: 3mm@100m

Numerical Validation

Collected datasets and in-situ features used for registration

Two sets of LIDAR point clouds were collected at the two stations.

Since no control point was available, in-situ features were selected from the datasets and used for a registration.

Two pillars, a rail and a beam surface were used as conjugate features.

Station 1 Station 2

Numerical Validation

NISLT registration

The eigenvectors of conjugate features were used as observables while solving for the transformation parameters based on the proposed weighted NISLT approach.

Station 1 Station 2

Numerical Validation

Registration results (integrated point clouds)

Shown in true colors

Shown in blue for points collected at station 1 and in red for points collected at station 2

Numerical Validation

Registration results (integrated point clouds)

S1 S2

Integrated

Numerical Validation

Registration results (quality assessment)

- Absolute consistency (qa) = 3.81cm.

- Relative similarity (qr) = 1.864e-4 .

- qr is equivalent to a 3.73cm positional distortion for an object of

size 200m. Equally accurate in terms of positional agreement and

geometric similarity.

- Both values are within a reasonable range considering the

2cm~4cm resolution of the original LIDAR datasets the

registration quality is mostly dependent on the point resolution in

this case.

Conclusion

The proposed approach increases the number of usable features for a registration solution the cost for LIDAR field work can be significantly reduced.

The weighted NISLT enables an efficient parameter estimation when in-situ hybrid conjugate features are used.

The two quality indexes (absolute consistency and relative similarity) give a complete and explicit quality indication for a registration solution.

An automatic approach for selecting qualified in-situ features should be developed in the future.

For more information, please contact:

Jen-Yu Han, Ph.D. Department of Civil Engineering, National Taiwan University Email: jyhan@ntu.edu.tw Phone: +886-2-33664347 Website: http://homepage.ntu.edu.tw/~jenyuhan

Thanks for your attention