A Variational Approach for 3D Motion Estimation of Incompressible PIV Flows

Abstract

Estimation of motion has many applications in fluid analysis. Lots of work has been carried out using Particle Image Velocimetry 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 context, we propose a new threedimensional variational (energy-based) technique. Our technique is based on solenoidal projection to take into account the incompressibility of the real flow. It uses the result of standard flow motion estimation techniques like iterative cross-correlation or pyramidal optical flow as an initialization, and improves significantly their accuracies. The performance of the proposed technique is measured and illustrated using numerical simulations.

An Optical Flow-Based Approach for Minimally Divergent Velocimetry Data Interpolation

“…In the conventional optical flow method there are two constraints, brightness and smoothness [45]. Optical flow-based methods have been promising in the area of fluid flow estimation in PIV [46–51]. For example, in [47], incompressibility of the flow is added as a constraint in the optical flow minimization problem.…”

An optical flow-based approach for the interpolation of minimally divergent velocimetry data

“…In the conventional optical flow method there are two constraints, brightness and smoothness [45]. Optical flow-based methods have been promising in the area of fluid flow estimation in PIV [46][47][48][49][50][51]. For example, in [47], incompressibility of the flow is added as a constraint in the optical flow minimization problem.…”

Identification of velocity fields for geophysical fluids from a sequence of images

“…A variational approach is presented in [2] where a cost function similar to ours is minimized in the context of incompressible fluids, but an initial guess provided by cross-correlation is required. Some authors replace the constant brightness assumption by an integrated continuity equation [12,8] in order to take into account the spreading of intensity sources.…”