Research Project

Fast Solutions to Variational Optimization Problems in Image Processing

Speaker:Alexandros Iliopoulos
ailiop at
Date: Friday, May 4, 2012
Time: 4:30pm - 5:30pm
Location: D344 LSRC, Duke
Carlo Tomasi, Nikos Pitsianis


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 Euler-Lagrange (E-L) equations. Traditional methods approach this problem almost exclusively through the E-L 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 real-time 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 E-L 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