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 used primarily to visualize functional and anatomical data of the human brain. All flattening approaches require a triangulated surface mesh representing the cortical surface, and this surface must be a topologically correct two-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 tetrahedra methods generate surfaces with topological errors, there is a need for tools that can detect and repair such problems. I will discuss the software package TopoCV, which automatically detects and corrects topological errors in triangulated surfaces. It can read and output surfaces in a variety of file formats, including BYU, OBJ, VTK, 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 to compute approximations to conformal maps in Euclidean, hyperbolic, and spherical geometries. This software has been successfully used to flatten cortical surfaces, and I will describe several neuroscientific applications in which conformal flattening is employed.
In addition, I will discuss some of the novel shape metrics that a theory-based conformal method such as CirclePack can provide compared with other numerical conformal mapping approaches.
An example includes a cortical hemisphere and its corresponding spherical, hyperbolic, and Euclidean flat maps generated using the software TopoCV and CirclePack.
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