Summary: Polyrigid and Polyaffine Transformations: a
Novel Geometrical Tool to Deal with
Non-Rigid Deformations. Application to the
registration of histological slices.
Vincent Arsigny, Xavier Pennec, Nicholas Ayache
INRIA Sophia, Epidaure team, 2004 Route des Lucioles, F-06902 Sophia-Antipolis
We describe in this paper a novel kind of geometrical transformations, named poly-
rigid and polyaffine. These transformations efficiently code for locally rigid or affine
deformations with a small number of intuitive parameters. They can describe com-
pactly large rigid or affine movements, unlike most free-form deformation classes.
Very flexible, this tool can be readily adapted to a large variety of situations, simply
by tuning the number of rigid or affine components and the number of parameters
describing their regions of influence.
The displacement of each spatial position is defined by a continuous trajectory
that follows a differential equation which averages the influence of each rigid or
affine component. We show that the resulting transformations are diffeomorphisms,
smooth with respect to their parameters. We devise a new and flexible numerical
scheme to allow a trade-off between computational efficiency and closeness to the