Image Processing Reference

In-Depth Information

Figure 4.8:
Screen capture of the semi-automated system that was delivered to Team Alinghi to compute

the 3D shape of their sails after training sessions.

integrated into a semi-automated system, depicted by Fig.
4.8
, that was designed to recover the 3D

shape of sails and delivered to the Team Alinghi, the syndicate that won the America's Cup in 2003

and 2007. For a surface such as the one of Fig.
4.8
that is modeled by a 1200-vertex mesh, involving

3600 degrees of freedom, 30 to 40 modes are typically enough to model smooth deformations.

By reducing the number of variables to be optimized, the modal representation makes it

easy to integrate additional information sources, which require the minimization of a nonlinear

criterion. However, while effective, this kind of approach suffers from the fact that a non-convex

objective function must be minimized and that, therefore, convergence to a desirable local optimum

cannot be guaranteed. When using correspondences alone, this limitation can be removed as fol-

lows
Salzmann
et al.
[
2008a
]. Recall that the 3D mesh representing the surface must be such that

the vector
x
obtained by stacking the coordinates of its vertices must satisfy the linear system of

Eq.
4.1
. Injecting the formulation of Eq.
4.6
into Eq.
4.1
means that the weights
c
must be solution

of

MSc

=−

Mx
0
.

(4.7)

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