- 83 -
can not be estimated. However, we can measure the bounding
cuboid and compare it with the dimensions of the model. Table
1 summarizes the results. The resulting models, shown from
three views, are depicted in Figure 16. All models are built with
an octree resolution of 256 3 and using 360 views.
Vessel #1
1
>
%
•
»
m
4
V
V
Sherd #1
Sherd ii2
Figure 16. 3D models of two vessels, two sherds and a cup
6. CONCLUSION
Many In this paper a combination of a Shape from Silhouette
method with a shape from Structured Light method was
presented, which create a 3D model of on object from images of
the object taken from different viewpoints. It showed to be a
simple and fast algorithm, which is able to reconstruct models
of arbitrarily shaped objects, as long as they do not have hidden
concavities, i.e., concavities not visible in any of the input
images. For concavities visible to the active system, results
show that the computed volumes provide the correct model. The
algorithm is simple, because it employs only simple matrix
operations for all the transformations and it is fast, because even
for highly detailed objects, a high resolution octree (256 3
voxels) and a high number of input views (36), the
computational time hardly exceeded 1 minute on a Pentium II.
Already for a smaller number of views (12) the constructed
models were very similar to the ones constructed from 36 views
and they took less than 25 seconds of computational time.
For archaeological applications, the object surface has to be
smoothed in order to be applicable to ceramic documentation,
for classification, however, the accuracy of the method
presented is sufficient since the projection of the decoration can
be calculated and the volume estimation is much more precise
than the estimated volume performed by archaeologists.
7. REFERENCES
[1] H. Baker. Three-dimensional modelling. In Proc. of 5' h Inti.
Conf. on AI, pages 649-655, 1977.
[2] P. Besl. Active, optical range imaging sensors. MVA,
1(2): 127-152,1988.
[3] H. H. Chen and T. S. Huang. A survey of construction and
manipulation of octrees. Computer Vision, Graphics, and
Image Processing, 43:409-431, 1988.
[4] C. H. Chien and J. K. Aggarwal. Volume/surface octrees
for the representation of three-dimensional objects. CVGIP,
36:100-113,1983.
[5] R. M. Haralick and L. G. Shapiro. Glossary of computer
vision terms. PR, 24(l):69-93, 1991.
[6] M. Kampel and R. Sablatnig. On 3d Modelling of
Archaeological Sherds. In Proceedings of International
Workshop on Synthetic-Natural Hybrid Coding and Three
Dimensional Imaging, Santorini, Greece, pages 95-98,
1999.
[7] M. Kampel and S. Tosovic. Turntable calibration for
automatic 3D-reconstruction. In R. Sablatnig, editor, Proc.
of 24th AAPR Workshop, pages 25- 31,2000.
[8] K. Kutulakos and S. Seitz. A theory of shape by space
carving. IJICV, 38(3): 197-216, 2000.
[9] C. Liska and R. Sablatnig. Estimating the next sensor
position based on surface characteristics. In ICPROO,
volume I, pages 538-541, 2000.
[10] W. N. Martin and J. K. Aggarwal. Volumetric description
of objects from multiple views. PAMI, 5(2): 150-158, 1983.
[11] C. Menard and R. Sablatnig. Computer based Acquisition
of Archaeological Finds: The First Step towards Automatic
Classification. In H. Kamermans and K. Fennema, editors,
Interfacing the Past, Computer Applications and
Quantitative Methods in Archaeology, number 28, pages
413-424, Leiden, March 1996. Analecta Praehistorica
Leidensia.
[12] V S. Nalwa. A Guided Tour Of Computer Vision.
AddisonWesley, 1993.
[13] W. Niem. Error analysis for silhouette-based 3D shape
estimation from multiple views. In N. Sarris and M.
Strintzis, editors, Proc. of Inti. Workshop on Synthetic-
Natural Hybrid Coding and 3D Imaging, pages 143-146,
1997.
[14] J. O'Rourke and N. Badler. Decomposition of
threedimensional objects into spheres. IEEE Transactions
on Pattern Analysis and Machine Intelligence, PAMI-1
(3):295-305, 1979.
[15] C. Orton, P. Tyers, and A. Vince. Pottery in Archaeology.
1993.
[16] M. Potmesil. Generating octree models of 3D objects from
their silhouettes in a sequence of images. CVGIP, 40:1-29,
1987.
[17] Y. Shirai. Three-Dimensional Computer Vision. Springer-
Verlag, 1987.
[18] S. K. Srivastava and N. Ahuja. Octree generation from
object silhouettes in perspective views. CVGIP, 49:68-84,
1990.
[19] R. Szeliski. Rapid octree construction from image
sequences. CVGIP: Image Understanding, 58(1 ):23-
32,1993.
[20] S. Tosovic. Lineare Hough-Transformation und
Drehtellerkalibrierung. Technical Report PRIP-TR-59,
Institute of Computer Aided Automation, Pattern
Recognition and Image Processing Group, Vienna
University of Technology, Austria, 1999.
[21 ]S. Tosovic and R. Sablatnig. 3d modeling of archaeological
vessels using shape from silhouette. In Proc. of Conf. on 3-
D Digital Imaging and Modeling, pages 51-58, 2001.
[22] J. Veenstra and N. Ahuja. Efficient octree generation from
silhouettes. In CVPR, pages 537-542, 1986.
8. ACKNOWLEDGEMENTS
This work was partly supported by the Austrian Science
Foundation (FWF) under grant PI 3385-INF, the European
Union under grant 1ST-1999-20273 and the Federal Ministry of
Education, Science and Culture.