Conformal and Area-Preserving Maps for Surface Warping and Image Registration

Allen Tannenbaum
Georgia Institute of Technology
School of Electrical and Computer Engineering

In this talk, we will outline some recent work using conformal
and area-preserving mappings for problems in surface warping and
image registration. We consider a novel 3D
visualization technique based on surface flattening for virtual
colonoscopy. Such visualization methods could be important in
virtual colonoscopy since they have the potential for non-invasively
determining the presence of polyps and other pathologies.
This conformal flattening method will also be employed for flattening
the brain on the sphere for visualization in functional MR.
The conformal mapping is an attempt to preserve the
appearance of the surface through the preservation of angles.
However, in some applications it is desirable to be able to
preserve areas instead of angles, so that the sizes of
surface structures are accurately represented in the plane. This
leads us to the theory of area-preserving mappings, and Monge-Kantorovich
optimal transport for surface warping and image registration.

Joint work with Steve Haker, S. Angenent, and R. Kikinis.


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