Mechanical Regularization of Optical Flow: General Framework Using Finite-Elements

We present a general framework for regularization of optical flow by mechanical finite-element models derived from the theory of continuum mechanics. We enforce image-based local motion estimates as lumped body forces applied at mesh nodes of an underlying mechanical model. The lumped body forces are formulated as virtual springs displaced by local motion estimates. The choice of each virtual spring stiffness reflects local textural quality and associated local motion confidence. In this formulation, the choice of image similarity measure, local search algorithm, image-mechanics confidence coupling, and material mechanics is application and user specific. Complex nonlinear viscoelastic materials can be used for regularization, as the modularity of the framework facilitates the use of commercially available finite-element solvers. Results from synthetic uniaxial deformation of liver parenchyma are provided and compared to traditional image-based regularizers. We demonstrate that knowledge of underlying material mechanics significantly improves motion estimates, even in situations where mechanical boundary conditions are not known.