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SUMMARY:Computational Conformal / Quasi-conformal Geometry and Its Applica
 tions - Chan\, T (HKUST)
DTSTART:20110822T084500Z
DTEND:20110822T093000Z
UID:TALK32427@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Conformal (C) / Quasi-conformal (QC) geometry has a long histo
 ry in pure mathematics\, and is an active field in both modern geometry an
 d modern physics. Recently\, with the rapid development of 3D digital scan
 ning technology\, the demand for effective geometric processing and shape 
 analysis is ever increasing. Computational conformal / quasi-conformal geo
 metry plays an important role for these purposes. Applications can be foun
 d in different areas such as medical imaging\, computer visions and comput
 er graphics.\n\nIn this talk\, I will first give an overview of how confor
 mal geometry can be applied in medical imaging and computer graphics. Exam
 ples include brain registration and texture mapping\, where the mappings a
 re constructed to be as conformal as possible to reduce geometric distorti
 ons. In reality\, most registrations and surface mappings involve non-conf
 ormal distortions\, which require more general theories to study. A direct
  generalization of conformal mapping is quasiconformal mapping\, where the
  mapping is allowed to have bounded conformality distortions. In the secon
 d part of my talk\, theories of quasicoformal geometry and its application
 s will be presented. In particular\, I will talk about how QC can be used 
 for registration of biological surfaces\, shape analysis\, medical morphom
 etry and the inpainting of surface diffeomorphism.\n\n
LOCATION:Seminar Room 1\, Newton Institute
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