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SUMMARY:The elastic metric for surfaces and its use - Ian Jermyn (Durham U
 niversity)
DTSTART:20171115T113000Z
DTEND:20171115T121500Z
UID:TALK95086@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Shape analysis requires methods for measuring distances betwee
 n shapes\, to define summary statistics\, for example\, or Gaussian-like d
 istributions. One way to construct such distances is to specify a Riemanni
 an metric on an appropriate space of maps\, and then define shape distance
  as geodesic distance in a quotient space. For shapes in two dimensions\, 
 the &#39\;elastic metric&#39\; combines tractability with intuitive appeal
 \, with special cases that dramatically simplify computations while still 
 producing state of the art results. For shapes in three dimensions\, the s
 ituation is less clear. It is unknown whether the full elastic metric admi
 ts simplifying representations\, and while a reduced version of the metric
  does\, the resulting transform is difficult to invert\, and its usefulnes
 s has therefore been questionable.  In this talk\, I will motivate the ela
 stic metric for shapes in three dimensions\, elucidate its interesting str
 ucture and its relation to the two-dimensional case\, and describe what is
  known about the representation used to construct it. I will then focus on
  the reduced metric. This admits a representation that greatly simplifies 
 computations\, but which is probably not invertible. I will describe recen
 t work that constructs an approximate right inverse for this representatio
 n\, and show how\, despite the theoretical uncertainty\, this leads in pra
 ctice to excellent results in shape analysis problems.  This is joint work
  with Anuj Srivastava\, Sebastian Kurtek\, Hamid Laga\, and Qian Xie.
LOCATION:Seminar Room 1\, Newton Institute
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