the 0.015mm resolution.
The modeling accuracy depends on the rotational
and translational positioning, and distance-sensing.
The mal-aligned positioning results in a shape
distortion, but still generates topologically stable
models.
4 CONCLUDING REMARKS
A simple, automatic, geometrically accurate,
topologically stable, robust and noise-resistive object
modeling, with matrix format meshes, to be followed
by quantitative 3D shape processing, is proposed.
Most of the reconstruction procedures from the
unorganized set of points are based on the principle:
“retrieving surface topology from surface geometry.”
In general, “retrieving topology from geometry,”
where appropriate distance-based criteria are used for
the modeling, is not easy especially in the presence of
noise even in the dense data-sets. Our topology, on
the contrary, is not dependent on geometry. In our
procedure, “topology is first assigned in the scanning
stage and geometry follows.” The noise problem is
inherent in the triangulation scanning, which is fatal
in the ICP algorithm due to point-connection
(topology) ambiguities caused by the problem, is
solved using the matrix format smoothing operators
for practical usage in the exchange for some spatial
resolution reduction.
The matrix format of the modeled data is intuitive
and easy to apply to the quantitative shape
modification using the various matrix type 3D shape
modification operators, which recursively include
thus modeled results with the same matrix format.
The 3D shape models are fused together by
convolution. The data format is compatible with that
of the BEM/FEM. The desired meshing, not limited
to triangular, but quadrilateral, hexagonal, and even
n-gonal meshes, is possible in the same way.
A Boolean operation with multi-directional
modeling is currently underway. We expect
considerable utility in the practical approximate
modeling and 3D shape processing.
REFERENCES
Blais, F., 2004, Review of 20 Years of Range Sensor
Development, Journal of Electronic Imaging, 13 (1),
231-240.
Boissonnat, J., 1984, Geometric Structures for Three-
Dimensional Shape Representation, ACM Transactions
on Graphics, 3 (4), 266-286.
Chen, F., Brown, G., Song, M., 2000, Overview of
Three-Dimensional Shape Measurement Using Optical
Methods, Optical Engineering, 39 (1), 10-22.
Dey, T., Goswami, S., 2004, Provable Surface Re-
construction from Noisy Samples, Annual Symposium
on Computational Geometry, In Proceedings of 20th
Annual Symposium on Computational Geometry,
330-339.
Doi, J., Sato, W., Miyamoto, Y., Ando, S., Yamanaka, M.,
2004, Reuse of a Geometric Model for Shape
Approximation, In Proceedings of 2004 IEEE
International Conference on Information Reuse and
Integration (IRI 2004), 174- 179.
Forsyth, D., Ponce, J., 2003, Computer Vision - A modern
Approach, Prentice Hall, New Jersey.
Godin, G., Beraldin, J., Taylor, J., Cournoyer, L.,
El-Hakim, S., Baribeau, R., Blais, F., Boulanger, P.,
Domey, J., Picard, M., Active Optical 3D Imaging for
Heritage Applications IEEE Computer Graphics and
Applications, 22, 24-36, 2002.
Hartley, H.,. Zisserman, A., 2000, Multiple View Geometry
in Computer Vision, Cambridge Univ. Press,
Cambridge, UK..
Levoy,
M., Pulli, K., Curless, B., Rusinkiewicz, S., Koller,
D., Pereira, L., Ginzton, M., Anderson, S., Davis, J.,
Ginsberg, J., Shade, J., Fulk, D., The Digital
Michelangelo Project; 3D Scanning of Large Statues,
In Proceedings of Siggraph 2000, 131-144, 2000.
Mantyla, M., 1988, An Introduction to Solid Modeling,
Computer Science Press, Rockville, Maryland.
Paul J., Besl, P., McKay, D., 1992, A Method for
Registration of 3-D Shapes, IEEE Transactions on
Pattern Analysis and Machine Intelligence, 14 (2),
239-256.
Pauly, M., Keiser, R., Kobbelt, L., Gross, M., 2003, Shape
Modeling with Point-Sampled Geometry, ACM
Transactions on Graphics (TOG), 22 (3), Special issue:
Proceedings of ACM SIGGRAPH, 641-650.
Rusinkiewicz, S.,. Levoy, M., 2001, Efficient Variants of
the ICP Algorithm, In Proceedings of the 3rd
International Conference on 3-D Digital Imaging and
Modeling (3DIM ’01), 145-152.
Scott, W., Roth, G., Rivest, J., 2003, View Planning for
Automated Three-Dimensional Object Reconstruction
and Inspection, ACM Computing Surveys, 35(1),
64-96.
Simple3D, 2005, 3D Scanners, Digitizers, and Software
for Making 3D Models and 3D Measurements,
http://www. simple3d.com/
Turk, G., Levoy, M., 1994, Zippered Polygon Meshes from
Range Images, In Proceedings of SIGGRAPH 1994,
311- 318.
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