Quasi-conformal Flat Maps of the Human Cerebellum
Thursday, October 12, 2000 - 11:30am - 12:15pm
Monica Hurdal (Florida State University)
There is great interest in trying to create flat maps of the cortical surface. It is believed that flat maps can assist in identifying and localizing functional foci obtained from PET and functional MRI data. Most current approaches attempt to minimize or reduce a combination of linear, areal and angular distortion between the flattened surface of the cortex and the original cortical sheet. However, it is impossible to flatten a surface without introducing linear and areal distortion. Nevertheless, the Riemann Mapping Theorem from mathematics states that angle-preserving (conformal) maps exist. A novel computational implementation will be discussed which creates conformal flat maps of the cortical surface using circle packings. This approach offers a number of advantages over existing approaches such as no cuts need to be introduced into the surface, the maps are mathematically unique, maps can be created in the Euclidean and hyperbolic planes and on a sphere, and canonical coordinate systems can be imposed on these maps.