Mesh Discussion for Core 1

Topics for discussion regarding Meshes in ITK.

Thursday, June 19th, 3-3:30pm ET

Participants:

• Will Schroeder,
• Luis Ibanez,
• Andrey Fedorov,
• Polina Golland,
• Thomas Yeo
• Alex Gouillard

Goal

• The goal is to figure out what's there and what needs to be done to make meshes usable for algorithm development.

Tools Needed

• Thomas: I am listing some tools that might be necessary for people working with meshes in ITK (the viewpoint is probably biased towards my needs). I might also be referring to meshes as representing surfaces depending on the contexts.

Registration

1. Need to interpolate values residing on the vertices of a mesh onto a set of points (which could belong to another mesh). I can give more specific examples in my problems if clarifications needed.

1. Given a point lying on a face (triangle/tetrahedron) of a mesh, compute the spatial gradient at that point, i.e., how will the interpolated value changes as the point position changes.

1. Does ParametricSpaceToImageSpaceMeshFilter already accomplished this? Found this on the documentation page, but it's unclear if it doing point (1) above.

Mesh Parameterization

1. Given a mesh, impose a parametric (e.g., planar, spherical) coordinate system. This is necessary for registration.

1. Different possible metric for such a parametrization: metric distortion, conformal, etc.

Given a Mesh Representing a Surface

1. Compute differential geometric properties, e.g., first and second fundamental forms (mean and gaussian curvature)

1. For mesh representing cortical surface, computing sulcal depth

Closed 2D Surface Analysis

1. Spherical Harmonic Transform - Spherical Harmonics are the basis of spherical filtering.

1. Wavelets - I thought Delphine's work was to be imported into ITK. They must have needed to do perform interpolation and impose a spherical coordinate system...

Obtaining the Mesh in the First Place

1. In the context of the brain: white matter segmentation, topology correction, mesh generation.