Another aspect of my research is improving the usability of flat maps and developing new methods for obtaining new and useful information from the maps. This includes new analysis and visualization methods. I have been collaborating with Dr. David Banks and Kevin Kurtz in the Computer Science Department at Florida State University in this regard.
Here are some flat maps of the cerebral cortex that I created.
corresponds to the right cerebral hemisphere of the "Visible Man" from
The National Library of Medicine's Visible Human
Project. This data was kindly provided by
David Van Essen at the
Washington University School of Medicine. This
surface consists of 103,845 triangles and 52,360 vertices.
For this data, a boundary cut along
the corpus collosum and four extraneous cuts along various fissures
have been introduced to create a surface boundary. Although these
extraneous cuts are not need for the circle packing approach, they are of
interest to other neuroscientific researchers.
When using my quasi-conformal method for creating flat maps, there are
no intermediate cortical maps produced in the flattening process.
The circle packing approach yields a single, final flat map which is a
quasi-conformal map of the cortical surface. We used
Open Inventor to interactively morph between the original cortical surface
mesh in R3 and the precomputed flat map in R2.
A texture map of the circle packing flat map was imposed on the
original cortical surface. This serves the additional purpose of being
able to observe the circle deformations that occur when the circles
from the circle packing flat map are taken back onto the original surface.
Linear interpolation was used to
compute the morphing that takes the cortical surface onto the
precomputed flat map.
It should be emphasized that the quasi-conformal map is not computed via
this morphing process --- a different morphing algorithm
will produce different intermediate maps, with only the original
surface and the final flat map remaining the same.
A Quicktime movie shows this morphing
process. Here are some frames from the movie.
Because of the complexity and folds of the brain, it was difficult to navigate
on the flat map. To address this problem, we created a bump mapped image of
the flat map which shades the flat map using the surface normal in
R3. This gives an indication of where the
folds and fissures of the brain are located on the flat map.
The following images show the enhanced flat map, and this Quicktime movie shows the morphing process using the bump map coloring.
These are some of the ways that we are working on enhancing the usability of the flat maps. These types of approaches assist neuroscientific researchers in understanding the deformations and curvature changes that the original surface undergoes to obtain the final quasi-conformal flat map and gives them a more intuitive feel for navigating on the flat maps.
Images and animations were created with the assistance of Kevin Kurtz and David Banks (Department of Computer Science and School of Computational Science and Information Technology, Florida State University). This work was supported in part by NSF Grant 0083898 "Realistic Illumination for Scalar Field and Vector Field Visualization" (D. Banks, PI) and FSU 2000 Planning Grant "Brain Visualization" (D. Banks, PI). David Van Essen, Heather Drury and James Dickson from Washington University School of Medicine, St. Louis are acknowledged for providing the Visible Man data.