Fluid flow and optical flow

Abstract

The connection between fluid flow and optical flow is explored in typical flow visualizations to provide a rational foundation for application of the optical flow method to image-based fluid velocity measurements. The projected-motion equations are derived, and the physics-based optical flow equation is given. In general, the optical flow is proportional to the path-averaged velocity of fluid or particles weighted with a relevant field quantity. The variational formulation and the corresponding EulerLagrange equation are given for optical flow computation. An error analysis for optical flow computation is provided, which is quantitatively examined by simulations on synthetic grid images. Direct comparisons between the optical flow method and the correlation-based method are made in simulations on synthetic particle images and experiments in a strongly excited turbulent jet.

OpenOpticalFlow: An Open Source Program for Extraction of Velocity Fields from Flow Visualization Images

“…To determine the optical flow, a variational formulation with a smoothness constraint is typically used [7,13]. Given g and f, we define a functional:…”

“…(3) with the Neumann condition ∂u/∂n = 0 on the image domain boundary ∂Ω for the optical flow [7,12].…”

“…The rational foundation for application of the optical flow method to fluid flow measurements is the quantitative connection between the optical flow and the fluid flow velocity for various flow visualizations. Liu and Shen [7] have derived the projected motion equations for various flow visualizations including laser-sheet-induced fluorescence images, transmittance images of passive scalar transport, schlieren, shadowgraph and transmittance images of density-varying flows, transmittance and scattering images of particulate flows, and laser-sheet-illuminated particle images. Further, these equations are recast into the physics-based optical flow equation in the image plane.…”

“…Digital flow visualization images are usually obtained by using cameras detecting radiation with a certain wavelength bandwidth from a fluid medium in a flow. Liu and Shen [7] have given the physics-based optical flow equation for different flow visualizations, which is written in in the image coordinates as:…”

“…The optical flow u = (u 1 , u 2 ) is proportional to the light-path-averaged velocity weighted with the field quantity ψ related to a visualizing medium [7]. In the special case where g∇·u = 0 and f = 0, Eq.…”