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SUMMARY:Efficient Preconditioning of Laplacian Matrices for Computer Graph
 ics - Dilip Krishnan\, MIT
DTSTART:20140106T110000Z
DTEND:20140106T120000Z
UID:TALK49542@talks.cam.ac.uk
CONTACT:Microsoft Research Cambridge Talks Admins
DESCRIPTION:We present a new multi-level preconditioning scheme for discre
 te Poisson equations that arise in various computer graphics applications 
 such as image colorization\, edge-preserving decomposition\, and geodesic 
 distances on three-dimensional meshes. Our approach interleaves the select
 ion of fine- and coarse-level variables with the removal of weak connectio
 ns between potential fine-level variables (sparsification) and the compens
 ation for these changes by strengthening nearby connections. By applying t
 hese operations before each elimination step and repeating the procedure r
 ecursively on the resulting smaller systems\, we obtain a highly efficient
  multi-level preconditioning scheme with linear time and memory requiremen
 ts. Our experiments demonstrate that our new scheme outperforms or is comp
 arable with other state-of-the-art methods\, both in terms of operation co
 unt and wall-clock time. This speedup is achieved by the new method's abil
 ity to reduce the condition number of irregular Laplacian matrices as well
  as homogeneous systems. It can therefore be used for a wide variety of pr
 oblems\, including 3D meshes\, without the need to carefully match the alg
 orithm to the problem characteristics.
LOCATION:Auditorium\, Microsoft Research Ltd\, 21 Station Road\, Cambridge
 \, CB1 2FB
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