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

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.