BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Stochastic Metamorphosis in Imaging Science - Darryl Holm (Imperia
 l College London)
DTSTART:20171214T160000Z
DTEND:20171214T170000Z
UID:TALK96640@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:In the pattern matching approach to imaging science\, the proc
 ess of metamorphosis in template matching with dynamical templates was int
 roduced in [7]. In [5] the metamorphosis equations of [7] were recast into
  the Euler-Poincar &#x301\;e variational framework of [4] and shown to con
 tain the equations for a perfect complex fluid [3].&nbsp\;  &nbsp\;  <br><
 br>This result related the data structure underlying the process of metamo
 rphosis in image matching to the physical concept of order parameter in th
 e theory of complex fluids [2]. In particular\, it cast the concept of Lag
 rangian paths in imaging science as deterministically evolving curves in t
 he space of diffeomorphisms acting on image data structure\, expressed in 
 Eulerian space. In contrast\, the landmarks in the standard LDDMM approach
  are Lagrangian.  &nbsp\;  <br><br>For the sake of introducing an Eulerian
  uncertainty quantification approach in imaging science\, we extend the me
 thod of metamorphosis to apply to image matching along stochastically evol
 ving time dependent curves on the space of diffeomorphisms. The approach I
 S guided by recent progress in developing stochastic Lie transport models 
 for uncertainty quantification in fluid dynamics in [6\, 1].  &nbsp\;  <br
 ><span><br>[1] D. O. Crisan\, F. Flandoli\, and D. D. Holm. Solution prope
 rties of a 3D stochastic Euler fluid equation. arXiv preprint arXiv:1704.0
 6989\, 2017. URL <a target="_blank" rel="nofollow" href="https://arxiv.org
 /abs/1704.06989">https://arxiv.org/abs/1704.06989</a>.</span>  [2] F. Gay-
 Balmaz\, D. D. Holm\, and T. S. Ratiu. Geometric dynamics of optimization.
  Comm. in Math. Sciences\, 11(1):163&ndash\;231\, 2013.  [3] D. D. Holm. E
 uler-Poincar&eacute\; dynamics of perfect complex fluids. In P. Newton\, P
 . Holmes\, and A. Weinstein\, editors\, Geometry\, Mechanics\, and Dynamic
 s: in honor of the 60th birthday of Jerrold E. Marsden\, pages 113&ndash\;
 167. Springer\, 2002.  [4] D. D. Holm\, J. E. Marsden\, and T. S. Ratiu. T
 he Euler&ndash\;Poincar &#x301\;e equations and semidirect products with a
 pplications to continuum theories. Adv. in Math.\, 137:1&ndash\;81\, 1998.
   [5] D. D. Holm\, A. Trouv&eacute\;\, and L. Younes. The Euler-Poincar &#
 x301\;e theory of metamorphosis. Quarterly of Applied Mathematics\, 67:661
 &ndash\;685\, 2009.  [6] Darryl D Holm. Variational principles for stochas
 tic fluid dynamics. Proceedings of the Royal Society of London A: Mathemat
 ical\, Physical and Engineering Sciences\, 471(2176):20140963\, 2015.  [7]
  A. Trouv&eacute\; and L. Younes. Metamorphoses through Lie group action. 
 Found. Comp. Math.\, 173&ndash\;198\, 2005.
LOCATION:Seminar Room 1\, Newton Institute
END:VEVENT
END:VCALENDAR