A new energy-based method for 3D motion estimation of incompressible PIV flows

Estimation of motion has many applications in fluid analysis. A lot of work has been carried out using Particle Image Velocimetry (PIV) to design experiments which capture and measure the flow motion using 2D images. Recent technological advances allow capturing 3D PIV image sequences of moving particles. In this paper, we deal with incompressible fluid flows which are a large class of physical real flows. We propose a new three-dimensional energy-based technique which estimates the flow motion preserving the incompressibility of the flow. We add the incompressibility constraint to the energy and we solve the constrained minimisation problem using a generalised Lagrange multipliers technique. The discretization of the energy yields to a challenging discrete optimisation problem. The performance of the proposed technique is measured and illustrated using numerical simulations.