Variational Approaches to Image Fluid Flow Estimation With Physical Priors

We present several variational approaches for fluid flow estimation from image sequences in experimental fluid dynamics. These approaches enable the contextual data analysis of particle images based on physical constraints, including bounds on the variation of divergence and vorticity of flow patterns, vanishing divergence for incompressible flows, and iterative estimation-prediction schemes based on vorticity transport for spatiotemporal regularization. All approaches amount to solving convex optimization problems that have unique solutions. They can be computed by standard numerical algorithms exploiting sparsity even for large-scale problems. We also present recent results on the physically consistent denoising of corrupted three-dimensional fluid flow estimates.