International Archives of the Photo
grammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B7. Istanbul 2004
Figure 2: (a) left-search surface, (b) centre-template surface, (c)
right-search surface, (d) obtained 3D point cloud after LS3D
surface matching, (e) shaded view of the final. composite
surface.
The second experiment refers to the matching of two
overlapping 3D point clouds (Figure 3), which are a part of a
chapel in Wangen, Germany, and were scanned using IMAGER
5003 terrestrial laser scanner (Zoller+Frôhlich). Initial
approximations of the unknowns were provided by interactively
selecting 3 common points on the both surfaces before the
matching. Obtained results are given at part II of Table I. The
estimated oy gives valuable information about the sensor noise
level and the accuracy limit of the scanner as 71 7 mm.
Table 1: Experimental results
5 n i t d 50 Oi /Oy 167 O6, / Gy / Oy
sec mm mm mm e
LL. P 2497.7 06 15 0.9 0.15/0.07/0.05 0.96/2.44/1.90
B 9. da 0.19 0.15/0.07/0.05 0.96/2.42/1.91
IR P 32856 0:5, 1.5: 021 0.13/0.03/0.05 0.68/2.25/1.73
B 6 1.4 0.21 0.13/0.03/0.05 0.69/2.26/1.75
Il P-13461 5o 380-0 1.74 0.23/0.62/0.01 0.69/0.17/0.46
B 4:56 1.72 0.22/0.61/0.01 0.69/0.17/0.46
-R: right face surface, II: laser scanner data
I-L: left face surface ,
Jlane, B: bi-linear surface, n: number of
s: surface representation, P: |
employed points, i: iterations, t: process time, d: point spacing
arametric bi-linear surface representation gives a slightly
The p
a better a posteriori sigma value
better convergence rate and
than the triangle plane representation, while increasing the
The standard deviation of the z-
computational expenses.
ion vector shows the excellent data
component of the translati
content in the depth direction, but the relative precision is
highly optimistic, which is ~1/1000 of the point spacing.
Since LS3D reveals the sensor noise level and accuracy
potential of any kind of surface measurement method or device,
it should be used for comparison and validation studies.
Ee
ON
: a
nm cmm
HET OI RHET
M réal
ii ghia
fr
(a) (b)
Figure 3: (a) top - template surface patch, (a) bottom - search
surface patch, (b) overlay of the shaded surfaces.
4. CONCLUSIONS
LSM is a fundamental measurement algorithm, and has been
applied to a great variety of data matching problems due to its
strong mathematical model. Two well-known ones are LS image
matching in 2D pixel space, and LS multiple cuboid matching
in 3D voxel space. The LS3D is bridging the conceptual gap
between the LS image matching and the LS cuboid matching.
This new 3D surface matching technique is a generalization of
the least squares 2D image matching concept and offers high
flexibility for any kind of 3D surface correspondence problem,
as well as monitoring capabilities for the analysis of the quality
of the final results by means of precision and reliability
criterions. Another powerful aspect of this proposed method is
its ability to handle multi-resolution, multi-temporal, multi-
scale, and multi-sensor data sets. The technique can be applied
to a great variety of data co-registration problems. In addition
time dependent (temporal) variations of the object surface can
be inspected, tracked, and localized using the statistical analysis
tools of the method.
ACKNOWLEDGEMENT
The author would like to thank Dr. Nicola D'Apuzzo for
providing the face surface data sets, which were measured by
use of his own software Viewrriplet GTK v0.9€. The laser
scanner data set is courtesy of Zoller+Frôhlich GmbH
Elektrotechnik (Wangen, Germany).
REFERENCES
Bergevin, R., Soucy, M., Gagnon, H.. Laurendeau, D., 1996.
Towards a general multi-view registration technique. [EEE
c
Pattern Analysis and Machine Intelligence, 18(5), pp. 540-547.
,
Besl, P.J., and McKay, N.D., 1992. A method for registration of
3D shapes. /EEE Pattern Analysis and Machine Intelligence,
14(2), pp. 239-256.
Campbell, R.J., and Flynn, P.J., 2001. A survey of free form
object representation and recognition techniques. Computer
Vision and Image Understanding, 81(2), pp. 166-210.
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