
Elastic Prior Shape Models of 3D Objects for Bayesian Image Analysis 357
FIGURE 17.6
Comparison of geodesics in the pre-shape space and shape space.
for an optimal rotation over SO(3) using Procrustes analysis. Then, given
this rotation, one searches for an optimal re-parameter ization over Γ using
a gradient descent algorithm [13]. This results in an optimal rotation and
re-parameterization of the second surface denoted by f
∗
2
= O
∗
(f
2
◦ γ
∗
). The
second step is to compute the geodesic path between f
1
and f
∗
2
using path
straightening, and to measure its length. We have found that the exact and
approximate solutions are very similar in practice.
We demonstra ...