Multi-scale optical flow including normalized mutual information for planar deformable lung motion estimation from 4D CT

A novel energy function for computing planar optical flow from X-ray CT images was presented and reported in detail in [1]. The technique combines four terms: brightness constancy, gradient constancy, continuity equation based on mass conservation, and discontinuity-preserving spatio-temporal smoothness. Both qualitative and quantitative evaluation of the proposed method demonstrated that the method results in significantly better angular errors than previous well-known techniques for optical flow estimation. A multi-scale approach to motion field computation based on this framework is presented in this paper. The proposed approach significantly speeds up the calculations, realizing computational savings. Additionally, an approach to determination of optimum values of scalar weights in the energy function is herein proposed. Normalized mutual information measured between the first image warped with the estimated motion and the second image is used to determine the optimum value for weighting parameters.