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3-D localization of reference marks: for each trinocular
view, all visible fiducial marks are located with subpixel
accuracy. A point-matching is then performed over such
points and, wherever a matching is found, the back-
projected point is determined. By doing so, we obtain, for
each trinocular view, the 3D camera-coordinates of a
subset of the fiducial marks. Some a-priori knowledge on
the relative position of the targets in the scene will help
identifying and labeling them. After labeling them, the
reference points can be matched throughout different
triplets, thus allowing us to compute the camera motion
between them. As described above, the rigid motion that
best overlaps targets of different triplets is taken as the
relative motion of the camera system from one triplet to
another. This operation is carried out for all the
consecutive pairs of views. By using camera motion, the
coordinates of all 3D edges can now be converted into a
common reference frame. At this point, if camera motion
has been accurately estimated, a simple merging of 3D
edges obtained from each triplet provides a complete
description of the observed object.
3-D surface interpolation: In some cases it is highly
desirable to obtain a 3D model whose shape is described
by a closed surface rather than by edges. Moreover, for
applications like image synthesis or virtual reality, there is
a need for 3D models where besides the shape, also the
original pictorial information on the surface (texture) is
recovered. For this reason, the last processing step, is
the construction of a surface that, by passing through all
edges, approximates the object surface. The 3D surface
is obtained using an optimized surface interpolation
technique which, in fact, is a discretization of the thin-
plate spline algorithm (Discrete Smooth Interpolation [5]).
This technique allows the presence of local
discontinuities in the interpolated surface, while
performing a spline-like interpolation on smooth surface
regions. This technique is particularly suitable for
interpolation of 3D shape information, being the shape
information typically characterized by edges and depth
discontinuities (i.e. at object borders).
The operation of recovering the original pictorial
information (texture) is done through a back-projection of
the luminance information associated to the original
images (from the original viewpoint to the scene space).
Roughly speaking, the images are projected on the
interpolate surface in a similar way as a “slide projector”
would do it. In order to obtain good quality results from
this texture mapping operation, particular care must be
used in compensating the different conditions of
illumination for the different viewpoints of the original
images. The quality of the texture mapping is also
affected by the quality of camera calibration and camera
motion estimation, which normally causes undesirable
errors in overlapping the texture from different viewpoints.
5. EXPERIMENTAL RESULTS
Some examples of application of the system are
presented in this paper. Two sample objects, a fish-
shaped hand-crafted object and a toy train engine, have
been used to test the proposed full-3D reconstruction
procedure. Each object has been placed on a low-cost
moving support in front of the trinocular camera system.
509
The cameras are placed at the vertices of a triangle in
order to avoid matching ambiguities and to guarantee
favorable conditions in the relative epipolar geometry.
Figures 2 and 5 show, for each object, one of the original
images taken by the camera system.
Figure 3 shows, for the object "train", a view of the 3D
edges localized in one trinocular shot. Thanks to the
accuracy of the 3D edge reconstruction and camera
calibration algorithms, with this technique it has been
possible to achieve a relative accuracy of 200/300 ppm in
the 3D location of edges.
Figures 4 and 6 show the obtained reconstruction after
merging the 3D edges obtained from all trinocular views.
As we can see, edges from different triplets merge in a
very precise fashion, which confirms the quality of the
camera motion estimation. The maximum diameter of the
bundles of homologous edges results as being smaller
than 0.5 mm, which corresponds to a relative precision of
300/400 ppm.
Figure 7 shows, for the object "fish", a synthetic
perspective view of the reconstructed surface of the
object, where the pictorial information has been mapped
from the original images through texture-mapping. The
fidelity of the rendering and the sharpness of the
projected texture prove the good quality of the proposed
texture-mapping procedure.
6. CONCLUSIONS
The experimental results have shown that, in spite of the
low cost of the system, the achieved level of accuracy is
quite high. In fact, consider just one trinocular view, the
3D co-ordinates of visible sharp edges can be computed
with a precision of about 200/300 ppm. When
considering a series of trinocular views for a complete
reconstruction of the scene, the accuracy remains nearly
unchanged (300/400 ppm), which emphasizes the quality
of the camera motion estimate.
Further improvements of the proposed reconstruction
method are currently under development, especially
those related to the 3D edge-merging process and the
problem of "full-3D" interpolation of surfaces of complex
volumes. In particular, we are focusing on the integration
of volumetric reconstruction methods and the above
technique.
REFERENCES:
[1] C. Braccini, G. Gambardella, A. Grattarola, S.
Zappatore: "Motion estimation of rigid bodies: effects
of the rigidity constraints." EURASIP, 1986. Signal
Processing lll: theories and applications. pp. 645-
648.
[2] T.S. Huang, O.D. Faugeras: "Some properties of the
E matrix in two-view motion estimation." /EEE Trans
on Pattern Analysis and Machine Intelligence. Vol.
11, No. 12, Dec. 1989, pp. 1310-1312.
[3] S. Soatto, R. Frezza, P. Perona: “Motion estimation
on the Essential Manifold.” In: Computer Vision -
ECCV '94. Third European Conference on Computer
Vision. Proceedings. Vol.ll., Stockholm, Sweden, 2-
6, May 1994. pp. 61-72.
[4] Tsai, R.Y., 1987. A Versatile Camera Calibration
Technique for High-Accuracy 3D Machine Vision
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996
