Surface fitting
Constructive
manifolds are very well-suited to surface fitting a) because an
approximate shape can be made that correctly captures the needed
degrees of freedom b) each chart can be fit individually and c)
(depending on the surface representation) have built-in hierarchical
and smoothing properties.
Surface fitting is also related to parameterization. Constructive
manifolds separate out the problem of topology representation from
geometry. The surface fitting problem is then broken into three steps:
- Build a manifold with the same topology as the data (preferably
using charts that correctly capture the complexity distribution of the data).
- Put the manifold in 1-1 correspondence with the data. This is the parameterization step; note that, unlike the majority of parameterization techniques, this does not require cutting the surface into planar pieces. At this stage it is also possible to introduce correspondence constraints.
- Add geometry to the manifold so that it fits the data. This can be done hierarchically.
We are currently exploring methods for going straight from MRI or
CT data to a manifold surface, taking advantage of the fact that we
know the basic shape we're looking for.
We are also looking at the problem of consistent parameterizations so
that we can quantitatively describe surface variation of a class of
shapes.
See also: editing, representation, and comparison.
Papers
- Converting
implicit surfaces to parametric ones using a cute trick involving
axis-aligned cuts. Uses S-Patches, an n-sided patch developed by Charles Loop and Tony deRose.
- Fitting canonical
manifolds to existing meshes.
- Fitting
manifolds to bone data.
- Using fitted manifolds to look at joint contact areas and ligament lengths.
- Using fitted manifolds to look at inter-bone distances under movement.
- Using fitted
manifolds to look at joint contact areas and ligament lengths under
movement (a pre-cursor to the paper above).
- Fitting a manifold to a point data set. Goes from a set of unordered points to a smooth, analytic surface.
Students