3D optical flow computation using a parallel variational multigrid scheme with application to cardiac C-arm CT motion

  • Authors:

  • El Mostafa Kalmoun;Harald Köstler;Ulrich Rüde

  • Affiliations:

  • Cadi Ayyad University, National School of Applied Science, Marrakesh, Morocco;University of Erlangen-Nuremberg, Department of Computer Science 10, Erlangen, Germany;University of Erlangen-Nuremberg, Department of Computer Science 10, Erlangen, Germany

  • Venue:
  • Image and Vision Computing
  • Year:
  • 2007

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Abstract

Motivated by recent applications to 3D medical motion estimation, we consider the problem of 3D optical flow computation in real time. The 3D optical flow model is derived from a straightforward extension of the 2D Horn-Schunck model and discretized using standard finite differences. We compare memory costs and convergence rates of four numerical schemes: Gauss-Seidel and multigrid with three different strategies of coarse grid operators discretization: direct coarsening, lumping and Galerkin approaches. Experimental results to compute 3D motion from cardiac C-arm CT images demonstrate that our variational multi-grid based on Galerkin discretization outperforms significantly the Gauss-Seidel method. The parallel implementation of the proposed scheme using domain partitioning shows that the algorithm scales well up to 32 processors on a cluster of AMD Opteron CPUs which consists of four-way nodes connected by an Infiniband network.