2nd International Conference on Medical Image Computing and
Computer-Assisted Invervention (MICCAI'99)
September 19-22, 1999
Quasi-Conformally Flat Mapping the Human Cerebellum
Monica K. Hurdal1, Philip L. Bowers1,
Ken Stephenson2, De Witt L. Sumners1,
Kelly Rehm3,4, Kirt Schaper3,
David A. Rottenberg3,4
1Dept. of Mathematics, Florida State University, Tallahassee, FL
2Dept. of Mathematics, University of Tennessee, Knoxville, TN
3PET Imaging Center, VA Medical Center, Minneapolis, MN, 55417,
4Dept. of Radiology, University of Minnesota, Minneapolis, MN,
We present a novel approach to creating flat maps of the brain. It is
impossible to flatten a curved surface in 3D space without
metric and areal distortion; however, the Riemann Mapping Theorem implies
that it is theoretically possible to preserve conformal (angular)
information under flattening. Our approach attempts to preserve the
conformal structure between the original cortical surface in 3-space and
the flattened surface. We demonstrate this with data from the human
cerebellum and we produce maps in the conventional Euclidean plane, as well
as in the hyperbolic plane and on a sphere.
Conformal mappings are
uniquely determined once certain normalizations have been chosen, and this
allows one to impose a coordinate system on the surface when flattening in
the hyperbolic or spherical setting. Unlike existing methods, our approach
does not require that cuts be introduced in the original surface. In
addition, hyperbolic and spherical maps allow the map focus to be transformed
interactively to correspond to any anatomical landmark.
REPRINT VERSION: 8 pages with 3 color figures
gzipped postscript 1495 K File
or available as:
M. K. Hurdal, P. L. Bowers, K. Stephenson, D. W. L. Sumners, K. Rehm,
K. Schaper, D. A. Rottenberg, Quasi-conformally flat mapping the human
cerebellum, in C. Taylor and A. Colchester (eds), Medical Image
Computing and Computer-Assisted Intervention - MICCAI'99, Vol. 1679 of
Lecture Notes in Computer Science, Springer, Berlin, pp. 279-286, 1999.
Updated July 1999.
Copyright 1999 by Monica K. Hurdal. All rights reserved.