[Insight-users] Deformable Surface Registration

[Arnaud GELAS]

Hi Somi,

As Karthik pointed, if both meshes are homeomorphic to a sphere you can 
first use a spherical parameterization and can follow the provided 
reference.

A more general method (that could also handle this particular case), is 
to first generate a "cut graph" on your mesh that will be used as 
boundary for a planar parameterization. Note that if you constraint the 
boundary to be a square in the plane, and if you associate to any point, 
or triangle information like 3D coordinates, curvature, you can generate 
a 2D image. Finally you can apply any registration method to register 
the 2 parameterizations.

Regarding this last method, you can find an explanation how to compute 
the cut graph in the following paper:
http://www.cs.sunysb.edu/~gu/publications/pdf/2002/ComputeConformalStructure.pdf
Computing Conformal Structures Of Surfaces
Xianfeng Gu and Shing-tung Yau, Communications in Information and 
Systems, 2002, Volume 2, 121--146

For the planar parameterization, you can find details at
http://www.insight-journal.org/browse/publication/202
"Parameterization of discrete surfaces", Gelas A. and Gouaillard A.


Arnaud


On 07/31/2009 01:00 AM, Karthik Krishnan wrote:
> There are methods for both
> - Point set to point set registration
> - mesh to mesh registration
>
> The former includes ICP. Please see the examples/tests in ITK. Search 
> for IterativeClosestPoint*.cxx
>
> The latter is expected to be added to ITK in the near future. You can 
> find the source / details at
>
> http://www.insight-journal.com/browse/publication/645
> "Rotational Registration of Spherical Surfaces Represented as QuadEdge 
> Meshes", Ibanez L., Audette M., Yeo B.T., Golland P.
>
> The mesh here is specific for the case of spherical meshes (points on 
> a 2D manifold, and can be associated with the surface of a sphere) and 
> the transform is specific to a Rotation transform.
>
> On Thu, Jul 30, 2009 at 11:44 PM, somi <seesomi at gmail.com 
> <mailto:seesomi at gmail.com>> wrote:
>
>     Hi,
>     Is there a functionality in ITK for deformable surface
>     registration (similar to 3D/2D volume/image registration) for
>     registering 2 surfaces ?
>     I want to register Mesh A to Mesh B, the number of vertices in
>     Mesh A and B might be different.
>     If there is a functionality, does it support multi-resolution
>     registering ?
>
>     I would really appreciate if someone could give me some pointers.
>
>     Best Regards,
>     Somi
>
>
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