http://www.ams.jhu.edu/~priebe/shc.html

The Spherical Homeomorphism Conjecture


The spherical homeomorphism conjecture is made in [1].
A proof is given in [2] for the special case of surfaces,
and the theorem is generalized in [3].


This investigation is described by Dana Mackenzie in
"Topologists Take Scalpel to Brain Scans,"
SIAM News, Vol 37, No 7, Sep 2004.


[1] D.W. Shattuck and R.M. Leahy, "Automated graph-based analysis and correction of cortical volume topology," IEEE Transactions on Medical Imaging, Volume 20, Number 11, pp. 1167-1177, November 2001. (access via IEEE Xplore)

[2] L. Abrams, D.E. Fishkind and C.E. Priebe, "A proof of the spherical homeomorphism conjecture for surfaces," IEEE Transactions on Medical Imaging, Volume 21, Number 12, pp. 1564-1566, December 2002. (access via IEEE Xplore)

[3] L. Abrams, D.E. Fishkind and C.E. Priebe, "The generalized spherical homeomorphism theorem for digital images," IEEE Transactions on Medical Imaging, Volume 23, Number 5, pp. 655-657, May 2004. (access via IEEE Xplore)

[4] L. Abrams and D.E. Fishkind, "A genus bound for digital image boundaries," SIAM J. Disc. Math., to appear. preprint

Seminars:
DEF seminar announcement March 2003
LA seminar announcement November 2003
DEF seminar announcement December 2004
  • Lowell Abrams <labrams@gwu.edu>
  • Donniell E. Fishkind <fishkind@ams.jhu.edu>
  • Carey E. Priebe <cep@jhu.edu>