[Insight-developers] Parameterization of surfaces meshes

[Alexandre GOUAILLARD]

Hi guys,

Good news, our code for parameterization of surface meshes is now ready to
transfert to ITK.

Spherical (possibly conformal) parameterization has been used intensively
for brain mapping, but is unfortunatly limited to zenus zero surfaces. A
conformal flatennign filter is actually in /Review, but it uses a spherical
parameterization to begin with, so it suffers from the same limitations.

We have implemented most of the (border-fixed) parameterization you can find
out there in a framework. We provide a simple algorithm that can extract a
"cut graph" from surfaces meshes of ANY genus. Cutting the surface open alng
this cut graph allows you to parameterize it. You can choose what kind of
border transform you want both in term of shape (usually disk or
square-shaped domain, but any convex domain will do) and in term of energy
minimization. Same goes for the parametrization itself, and finally the code
is templated over the matrix solver.

This last point is quite important, as different solvers will give you very
different speed depending on your specific case. It is also important, as
only vnl, which is quite a slow solver, is usable natively from ITK, so you
are more likely to use anything else. Templating over the solver let you do
so without modifying the algorithm itself (a-la C-GAL).

The firsts results illustrate our point:
Parameterization of one surface mesh with vnl:   6.1 s
Parameterization of the same mesh with  TAUCS:   0.27s

Expect a submission of a roughly 4 pages paper around end of november 2007.

We are also working out the best way (integration vs. compilation flag) of
using TAUCS with ITK. TAUCS copyright owner agreed on a BSD licence, but we
still need to check if the librairies TAUCS is build onto have suitable
licence, and if it would make sens for ITK to intergrate it.

If you have any comment, any idea, or if you wanna give a look at the code
beforehands, don't hesitate to send me an e-mail. We are sending this e-mail
to gather attention and thus have people reviewing the paper quickly,
hopefully reducing the amount of time needed to transfer the code into
/Review.

The work is based on previous publications (see below). This version is
written on top of itkQuadEdgeMesh, a new datasrtucture dedicated to surface
meshes. It has been enterely re-written by Arnaud Gelas (BioImaging Lab,
Singapore).

Alex.

A. GOUAILLARD, A. GELAS,  S. VALETTE,  E. BOIX and R. PROST,
³Curvature-based Adaptive Remeshing for Wavelet-Based Multires. 3D Meshes².
In Proc. of International Conference on Image Processing ICIP¹05,  Genova,
September 11th-14th 2005. Vol. 1,  pp 1033-1036.

A. GOUAILLARD, A. GELAS, T. KANAI, R. PROST,
« Image Processing and Computer Graphics: Illustrated Complementaries ».
JSF 2004, 4-5 Nov., Yoyogi, Tokyo.

A. GOUAILLARD, A. GELAS, S. VALETTE, E. BOIX, R. PROST,
³Remeshing Algorithm for Multiresolution Prior Model in Segmentation."
In Proc. of International Conference on Image Processing, ICIPŒ04,
Singapore, October 24~27 October 2003, pp. 2753-2756.