The first step in the volume morphing pipeline is warping the source
and target volumes 
and 
. Volume warping has been
the subject of several investigations in computer graphics, computer
vision, and medicine. Warping techniques can be coarsely classified
into two groups: (i) Techniques that allow only minimal user control,
consisting of at most a few scalar parameters. These algorithms
automatically determine similarities between two volumes, and then
seek the warp which transforms the first volume to the second one
[18]. (ii) Techniques in which user control consists
of manually specifying the warp for a collection of points in the
volume. The rest of the volume is then warped by interpolating the
warping function. This group of algorithms includes free-form
deformations [17], as well as semi-automatic medical
data alignment [18].
As stated in section 1.3, user control over the warps is crucial in designing good morphs. Point-to-point mapping methods [21], in the form of either regular lattices or scattered points [13], have worked in 2D. However, regular grids provide a cumbersome interface in 2D; in 3D they would likely become unmanageable. Also, prohibitively many scattered points are needed to adequately specify a 3D warp.
Our solution is a feature-based approach extending the work of [2] into the 3D domain. The next two sections will introduce our feature-based 3D warping and discuss the UI to feature specification.