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

Motion estimation has many applications in fluid analysis, and a lot of work has been carried out using Particle Image Velocimetry (PIV) to capture and measure the flow motion from sequences of 2D images. Recent technological advances allow capturing 3D PIV sequences of moving particles. In the context of 3D flow motion, the assumption of incompressibility is an important physical property that is satisfied by a large class of problems and experiments. Standard motion estimation techniques in computer vision do not take into account the physical constraints of the flow, which is a very interesting and challenging problem. In this paper, we propose a new variational motion estimation technique which includes the incompressibility of the flow as a constraint to the minimization problem. We analyze, from a theoretical point of view, the influence of this constraint and we design a new numerical algorithm for motion estimation which enforces it. The performance of the proposed technique is evaluated from numerical experiments on synthetic and real data.