IGARSS, 24-29 July 2011, Vancouver, Canada (Session FR2.T03)
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 University
2 Graduate Institute of Electronics Engineering, National Taiwan University
Outline

Introduction

Using In-Situ Conjugate Features

Weighted NISLT Approach

Quality Assessment

Numerical Validation

Conclusion
NTUCvE Surveying Engineering Group
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.
x
x
 
 
 y   sR  y   t
z
z
 2
 1
s: scale
R: rotation matrix
t: translation vector
1
2
1
2
1
Station 1
Station 2
2
Using In-Situ Features
Obtaining the transformation parameters

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.
Using In-Situ Features
Obtaining the transformation parameters

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.
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
Slope surfaces and edges
Bridge pillars
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:
Scale parameter
 dx 
12
T
-1
s  (l k Pl k ) l k P 
 dx12


dx13
dx13
T
dx ij 

dx ij 

where dxij and dx’ij are coordinate differences (vectors) in the original and
transformed systems, P is the weight matrix, lk is a kx1 unity vector.
Weighted NISLT Approach
Rotational parameters
G = (PX)T (PX)( XT PT PX)1 = Sa Λa VaT
R = S a VaT
where ΔX and ΔX’ are the matrices by stacking all the normalized row
vectors in the original and transformed systems.
Translational parameters
 ( x1 ' sRx1 )T 


T
( x ' sRx2 ) 
t  (l n T Pl n )1 l n P  2



T
( xn ' sRxn ) 
Weighted NISLT Approach
Characteristics of weighted NISLT approach
- Closed-form solution, requires no initial
18
Affine by Least-squares
Simlarity by Least-squares
Affine by Proposed
Similarity by Proposed
16
values nor iterative computations 
highly efficient compared to
Process Time (seconds)

14
12
10
8
6
4
LSQ-based approaches.
2
0
0
100
200
300
400
500
600
700
800
900
1000
Number of Reference Points
- 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.
Quality Assessment

Classical point-based approach:
Registration quality is typically evaluated by the post-fit residuals for
point coordinates after applying the estimated parameters.
n

RMSV =
εTi εi
i 1
n
εi : post-fit residual vector of point i
n : 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:
Absolute Consistency (qa)
Relative Similarity (qr)
np
qa 
v
i 1
nl
T
i
vi
np
Positional alignment
qr 

i 1
2
i
nl
Geometric similarity
v i : post-fit residual vector of conjugate point i or the vector between point i ‘s
projected points on two conjugate features.
 i : the angle between two conjugate vectors (directional vectors, normal
vectors, or eigenvectors) after the registration.
n p , nl : the numbers of conjugate points and conjugate vectors
Quality Assessment

Interpretation of a registration solution:
(a) Moderate qa, good qr.
(b) Moderate qa and qr.
(c) Poor qa, good qr.
(a)
(c)
(b)
(d) Poor qa and qr.
(d)
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.
S2
S1
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.
Thanks for your attention
For more information, please contact:
Jen-Yu Han, Ph.D.
Department of Civil Engineering, National Taiwan University
Email: [email protected] Phone: +886-2-33664347
Website: http://homepage.ntu.edu.tw/~jenyuhan