We present a divide-and-conquer method that efficiently finds a near-optimal distribution of sensing locations for free-form surface digitization. We formulate a next-best-point problem and transform the uncertainty of a B-spline surface into a higher-dimensional B-spline surface. This technique allows the use of the convex hull and subdivision properties of B-spline surfaces in the divide-and-conquer algorithm. It thus greatly reduces the search time for determining the next best sensing location.

1.
Kim
,
P.
, and
Ding
,
Y.
, 2004, “
Optimal Design of Fixture Layout in Multistation Assembly Processes
,”
IEEE. Trans. Autom. Sci. Eng.
1545-5955,
1
(
2
), pp.
133
145
.
2.
Li
,
Y. F.
, and
Liu
,
Z. G.
, 2003, “
Method for Determining the Probing Points for Efficient Measurement and Reconstruction of Free-Form Surfaces
,”
Meas. Sci. Technol.
0957-0233,
14
(
8
), pp.
1280
1288
.
3.
Wang
,
Y.
, and
Pelinescu
,
D. M.
, 2001, “
Optimizing Fixture Layout in a Point-Set Domain
,”
IEEE Trans. Rob. Autom.
1042-296X,
17
(
3
), pp.
312
323
.
4.
Xiong
,
Z.
,
Wang
,
M. Y.
, and
Li
,
Z.
, 2004, “
A Near-Optimal Probing Strategy for Workpiece Localization
,”
IEEE Trans. Rob. Autom.
1042-296X,
20
(
4
), pp.
668
676
.
5.
Yau
,
H.
, 1998, “
Uncertainty Analysis in Geometric Best Fit
,”
Int. J. Mach. Tools Manuf.
0890-6955,
38
, pp.
1323
1342
.
6.
Konstantinos
,
A. T.
,
Peter
,
K. A.
, and
Roger
,
T.
, 1995, “
A Survey of Sensor Planning in Computer Vision
,”
IEEE Trans. Rob. Autom.
1042-296X,
11
(
1
), pp.
86
104
.
7.
Lee
,
K. H.
, and
Park
,
H. P.
, 2000, “
Automated Inspection Planning of Free-Form Shape Parts by Laser Scanning
,”
Rob. Comput.-Integr. Manufact.
0736-5845,
16
(
4
), pp.
201
210
.
8.
Pito
,
R.
, 1999, “
A Solution to the Next Nest View Problem for Automated Surface Acquisition
,”
IEEE Trans. Pattern Anal. Mach. Intell.
0162-8828,
21
(
10
), pp.
1016
1030
.
9.
Qian
,
X.
, and
Harding
,
K. G.
, 2003, “
A Computational Approach for Optimal Sensor Setup
,”
Opt. Eng. (Bellingham)
0091-3286,
42
(
5
), pp.
1238
1248
.
10.
Richard
,
P.
, and
Ruzena
,
B.
, 1995, “
A Solution to the Next Best View Problem for Automated CAD Model Acquisition of Free-Form Objects Using Range Cameras
,”
Proc. SPIE
0277-786X
2598
, pp.
78
89
.
11.
Sheng
,
W.
,
Xi
,
N.
,
Song
,
M.
,
Chen
,
Y.
, and
Rankin
,
J. S.
, 2000, “
Automated CAD-Guided Automobile Part Dimensional Inspection
,”
Proc. IEEE International Conference of Robotics and Automation
, Vol.
2
, pp.
1157
1162
.
12.
Spyridi
,
A. J.
, 1994, “
Automatic Generation of High Level Inspection Plans for Coordinate Measuring Machines
,” Ph.D. dissertation, University of Southern California, Los Angeles, CA.
13.
Elkott
,
D. F.
,
Elmaraghy
,
H. A.
, and
Elmaraghy
,
W. H.
, 2002, “
Automatic Sampling for CMM Inspection Planning of Free-Form Surfaces
,”
Int. J. Prod. Res.
0020-7543,
40
(
11
), pp.
2653
2676
.
14.
Whaite
,
P.
, and
Ferrie
,
F. P.
, 1997, “
Autonomous Exploration: Driven by Uncertainty
,”
IEEE Trans. Pattern Anal. Mach. Intell.
0162-8828,
19
(
3
), pp.
193
205
.
15.
Li
,
Y. F.
, and
Liu
,
Z. G.
, 2003, “
Uncertainty-Driven Viewpoint Planning for 3D Object Measurements
,”
Proceedings of the 2003 IEEE International Conference on Robotics and Automation
, Vol.
1
, pp.
127
132
.
16.
Wang
,
Y.
, and
Nagarkar
,
S.
, 1997, “
Optimal Sensor Location Design in Automated Coordinate Checking Fixtures
,” in the
Proceedings of IEEE International Symposium on Assembly and Task Planning (ISATP’97)
, pp.
140
145
.
17.
Xiong
,
Z.
,
Wang
,
M. Y.
, and
Li
,
Z.
, 2003, “
A Computer-Aided Probing Strategy for Workpiece Localization
,” in
Proceedings of the 2003 IEEE International Conference on Robotics & Automation
, Vol.
3
, pp.
3941
3946
.
18.
Fedorov
,
V. V.
, 1972,
Theory of Optimal Experiments
,
W.
Studden
and
E. M.
Klimbo
, eds.,
Academic
,
New York
.
19.
Nguyen
,
N. K.
, 1992, “
A Review of Some Exchange Algorithms for Constructing Discrete D-optimal Designs
,”
Comput. Stat. Data Anal.
0167-9473,
14
(
4
), pp.
489
498
.
20.
Liu
,
C.
,
Ding
,
Y.
, and
Chen
,
Y.
, 2005, “
Optimal Coordinate Sensor Placements for Estimating Mean and Variance Components of Variation Sources
,”
IIE Trans.
0740-817X,
37
, pp.
877
889
.
21.
Piegl
,
L.
, and
Tiller
,
W.
, 1995,
The NURBS Book
,
Springer
,
New York
.
22.
Kullback
,
S.
, 1968,
Information Theory and Statistics
,
Dover
,
New York
.
23.
Huang
,
Y.
, and
Qian
,
X.
, 2007, “
A Dynamic Sensing-and-Modeling Approach to 3D Point- and Area-Sensor Integration
,”
ASME J. Manuf. Sci. Eng.
1087-1357,
129
, pp.
623
635
.
You do not currently have access to this content.