Research Project
Fast Solutions to Variational Optimization Problems in Image Processing
Speaker:  Alexandros Iliopoulos
ailiop at cs.duke.edu 
Date: 
Friday, May 4, 2012 
Time: 
4:30pm  5:30pm 
Location: 
D344 LSRC, Duke 

Carlo Tomasi, Nikos Pitsianis 


Abstract
Energy minimization problems arise naturally in a lot of graphics and
vision applications, such as image editing, surface deforming or
variational motion registration, as they allow one to compute a
"natural" effect of a set of given actions on the image data. The
minimization problem can be expressed as the variational minimization of
the energy functional, or as a system of partial differential equations
known as the EulerLagrange (EL) equations. Traditional methods approach
this problem almost exclusively through the EL system, which is linear for
the case of the energy functional. However, this entails computing all
stationary functionals, only one of which is the desired minimizer
(analogously, one could talk about local and global minima). This can be an
inhibiting factor for many realtime applications, for which efficiency (in
both performance and accuracy) is instrumental.
We propose to explore the use of the Conjugate Gradient (CG) method in a
hierarchical fashion, operating on both the the Variational and the EL
forms, in order to compute the optimal solution while avoiding divergence
towards false candidate solutions. The CG method implicitly leverages the
spectral properties of the system it is applied to and could be useful in
filtering out unnecessary spectral components to obtain a coarse direction
towards the true minimizer. Also, different discretization models
that lead to a sparse gradient representation of the system will be
considered.
Advisor(s): Xiaobai Sun