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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:The elastic metric for surfaces and its use - Ian
Jermyn (Durham University)
DTSTART;TZID=Europe/London:20171115T113000
DTEND;TZID=Europe/London:20171115T121500
UID:TALK95086AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/95086
DESCRIPTION:Shape analysis requires methods for measuring dist
ances between shapes\, to define summary statistic
s\, for example\, or Gaussian-like distributions.
One way to construct such distances is to specify
a Riemannian metric on an appropriate space of map
s\, and then define shape distance as geodesic dis
tance in a quotient space. For shapes in two dimen
sions\, the '\;elastic metric'\; combines tr
actability with intuitive appeal\, with special ca
ses that dramatically simplify computations while
still producing state of the art results. For shap
es in three dimensions\, the situation is less cle
ar. It is unknown whether the full elastic metric
admits simplifying representations\, and while a r
educed version of the metric does\, the resulting
transform is difficult to invert\, and its usefuln
ess has therefore been questionable. In this talk
\, I will motivate the elastic metric for shapes i
n three dimensions\, elucidate its interesting str
ucture and its relation to the two-dimensional cas
e\, and describe what is known about the represent
ation used to construct it. I will then focus on t
he reduced metric. This admits a representation th
at greatly simplifies computations\, but which is
probably not invertible. I will describe recent wo
rk that constructs an approximate right inverse fo
r this representation\, and show how\, despite the
theoretical uncertainty\, this leads in practice
to excellent results in shape analysis problems.
This is joint work with Anuj Srivastava\, Sebastia
n Kurtek\, Hamid Laga\, and Qian Xie.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:info@newton.ac.uk
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