Discrete Orthogonal Decomposition and Variational Fluid Flow Estimation

We exploit the mimetic finite difference method introduced by Hyman and Shashkov to present a framework for estimating vector fields and related scalar fields (divergence, curl) of physical interest from image sequences. Our approach provides a basis for consistent definitions of higher-order differential operators, for the analysis and a novel stability result concerning second-order div-curl regularizers, for novel variational schemes to the estimation of solenoidal (divergence-free) image flows, and to convergent numerical methods in terms of subspace corrections.