Cortical flat mapping is a method that takes advantage of the two-dimensional
sheet topology of the cortical surface. It has been mainly used to visualize
functional and anatomical data of the human brain. All flattening approaches
require a triangulated surface mesh that represents the cortical surface and
this surface must be a topologically correct 2-manifold (i.e. a topological
sphere or disc). Since few algorithms are available for creating topologically
correct cortical surfaces and widely used algorithms, such as the marching cubes
or marching tetraheda algorithm, generate surfaces with topological errors,
there is a need for methods that can detect and repair topological problems in
surfaces. I will discuss the software package TopoCV that I have written which
automatically detects and corrects topological errors in triangulated surfaces.
It can read in and output surfaces in a variety of file formats (including byu,
obj, vtk and CARET and FreeSurfer formats). Once a surface has been verified to
be topologically correct, it can be "flattened". I will also discuss the
software CirclePack which can be used for computing approximations to conformal
maps in Euclidean, hyperbolic and spherical geometries. This software has been
successfully used to flatten cortical surfaces and I will discuss some of the
neuroscientific applications where we are using conformal flattening. I will
also discuss some of the novel shape metrics that a theoretical-based conformal
method such as CirclePack can offer as compared to other numerical conformal
methods. Links for downloading TopoCV and CirclePack are available at
http://www.math.fsu.edu/~mhurdal.
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