Morphing &
Registration
RBF surface representations offer
new possibilities for morphing, warping and registration.
Blending
The above example
illustrates the smooth blending properties of an RBF. Here a
single RBF describes two surfaces simultaneously. The surface on
the left corresponds to a particular iso-surface threshold, while
the surface on the right corresponds to another. The intervening
surfaces correspond to intermediate threshold values.
Registration
The point-wise
registration problem encountered in 2D and 3D imaging is similar
to the morphing problem. Registration requires matching landmarks
between two images and distorting one image to align with the
other. It is possible to do both rigid and non-rigid body registration
using RBFs. A least energy
solution is derived depending on the choice of basis
function.
Warping
A vector field
describing the mapping between homologous landmarks can be
described by an RBF which smoothly determines where intervening
surface points map to.
