We present here results for three real image
sequences. Occluding contours were tracked using snakes
[Ber 94,Kas 88] (see figures 10(b), 11(b) and 12(b)). The first image sequence consists of 27 images of a tea
pot which were taken
with unknown camera motions. Therefore a preliminary calibration step is needed. This was done using a calibration pattern which is present in every
image (see figure 10(a)).
First, discrete points on rims are recovered if they are not close,
according to a threshold, to points where a1 and a-1 are
equal. The resulting points are then used to
construct a triangular mesh with respect to contour information:
two 3D points are connected if and only if they are on two
consecutive rims. A
ray-tracer is then used to render the surface. Finally, in order to estimate the accuracy
of the reconstruction, the rendered surface is projected onto original
images. This is done by use of the perspective projection matrix
computed during the calibration step. The
results of the different steps of the reconstruction process are shown
in figure 10.
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The reconstructed tea pot shown in this figure is incomplete. This
results from the fact that the total camera rotation during the
sequence is not sufficient to allow a global perception of the
surface. In fact, we reconstruct only what we see
and thus a partial surface description may be obtained, depending on
the total amount of rotation. This points out that a
surface model based on triangular facets is well adapted to modelise
the reconstructed surface since it does not require any a priori
information on the surface. Thus, it allows partial as well as
complete surface representations without any parametric or topologic information.
In next examples, real image sequences of a vase and a calabash were
taken using a rotating turntable (see figures
11(a) and 12(a)). The rotation angle between two
successive images is of 10 degrees for the vase sequence and of 7
degrees for the calabash sequence. Except for the calibration step which
was performed before the sequences were taken, the reconstruction process is the
same as in the previous example. Results are shown in figures
12 and 13.
Figures 10(f), 11(f) and 12(f) show that reconstructed surfaces are coherent. It should also be noticed that region of the surfaces where a-1 is close to a1 are still well reconstructed. This is due to the fact that even if these regions correspond to points on one rim for which the reconstruction is ill-conditioned, they may also correspond to points on other rims for which the reconstruction is well-conditioned. Such regions correspond, for the sequences presented, to points which are located at the top and the bottom of the surfaces. Figures 10(c), 11(c) and 12(c) show that the reconstructed rims cover also these regions.
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