BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//talks.cam.ac.uk//v3//EN
BEGIN:VTIMEZONE
TZID:Europe/London
BEGIN:DAYLIGHT
TZOFFSETFROM:+0000
TZOFFSETTO:+0100
TZNAME:BST
DTSTART:19700329T010000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0100
TZOFFSETTO:+0000
TZNAME:GMT
DTSTART:19701025T020000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
CATEGORIES:Applied and Computational Analysis
SUMMARY:Discrete geodesic calculus in shape space - Martin
Rumpf\, Institute for Numerical Simulation\, Univ
ersity of Bonn
DTSTART;TZID=Europe/London:20111117T150000
DTEND;TZID=Europe/London:20111117T160000
UID:TALK33714AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/33714
DESCRIPTION:Based on a local approximation of the Riemannian d
istance on a manifold by a computationally cheap d
issimilarity measure a time discrete geodesic calc
ulus is developed and applications to shape space
are explored.\nThereby\, the dissimilarity measure
is derived from a spring type energy whose Hessia
n reproduces the underlying Riemannian metric. Usi
ng this measure to define length and energy on dis
crete paths on the manifold a discrete analog of c
lassical geodesic calculus can be developed. \nThe
notion of discrete geodesics defined as energy mi
nimizing paths gives rise to discrete logarithmic
and exponential maps and enables to introduce a t
ime discrete parallel transport as well.\nThe rela
tion of this time discrete to the actual\, time co
ntinuous Riemannian calculus is explored and the n
ew concept is applied to a shape space in which sh
apes are considered as boundary contours of physi
cal objects consisting of viscous material. The fl
exibility and computational efficiency of the appr
oach is demonstrated for topology preserving morph
ing\, the interplay of paths in shape space and lo
cal shape variations as associated generators\, th
e extrapolation of paths\, and the transfer of geo
metric features.
LOCATION:MR14\, CMS
CONTACT:Carola-Bibiane Schoenlieb
END:VEVENT
END:VCALENDAR