Cortical Surface Correction and Conformal Flat Mapping: TopoCV and CirclePack

Monica Hurdal
Florida State University
Mathematics

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.