Quasi-conformally flat mapping the human cerebellum

Monica K. Hurdal, Philip L. Bowers, Ken Stephenson, Witt L. De Sumners, Kelly Rehm, Kirt Schaper, David A. Rottenberg

Research output: Chapter in Book/Report/Conference proceedingConference contribution

75 Scopus citations


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.

Original languageEnglish (US)
Title of host publicationMedical Image Computing and Computer-Assisted Intervention –MICCAI 1999 - 2nd International Conference, Proceedings
EditorsAlain Colchester, Chris Taylor
PublisherSpringer- Verlag
Number of pages9
ISBN (Print)354066503X, 9783540665038
StatePublished - Jan 1 1999
Event2nd International Conference on Medical Image Computing and Computer-Assisted Intervention, MICCAI 1999 - Cambridge, United Kingdom
Duration: Sep 19 1999Sep 22 1999

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference2nd International Conference on Medical Image Computing and Computer-Assisted Intervention, MICCAI 1999
Country/TerritoryUnited Kingdom

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1999.


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