Variational second order flow estimation for PIV sequences

Abstract

We present in this paper a variational approach to accurately estimate simultaneously the velocity field and its derivatives directly from PIV image sequences. Our method differs from other techniques that have been presented in the literature in the fact that the energy minimization used to estimate the particles motion depends on a second order Taylor development of the flow. In this way, we are not only able to compute the motion vector field, but we also obtain an accurate estimation of their derivatives. Hence, we avoid the use of numerical schemes to compute the derivatives from the estimated flow that usually yield to numerical amplification of the inherent uncertainty on the estimated flow. The performance of our approach is illustrated with the estimation of the motion vector field and the vorticity on both synthetic and real PIV datasets.

Cardiac flow component analysis

“…Numerical differential operators based on single-level differential operators have been described in various literature [29][30][31][32][33]. We shall examine the approximation of the gradient of a function based on a point of differentiation with reference to a velocity field.…”

Variational fluid flow measurements from image sequences: synopsis and perspectives

“…This local scheme (17) has been applied to flow field measurements by Okuno & Nakaoka (1991), Sugii et al (2000) and Yamamoto & Uemura (2009) technique has been extended for the recovery of the velocity fields and its derivative, and has been assessed on PIV images by Alvarez et al (2008). Solutions to this least squares estimation problem through an eigenvalue analysis (16) comprises the so called structure tensor approaches (Bigün et al, 1991;Jähne, 1993).…”

Strain analysis by a total generalized variation regularized optical flow model

“…In particular, optical flow models with priors containing higher order derivatives of the flow were successfully used, e.g. in [1,6,15,20,24,32,33,35,36].…”

“…Although it seems natural to apply ideas from variational optical flow models also for strain analysis, such methods have rarely been addressed in the literature. The papers [1,15] aim at computing derivatives simultaneously to the optical flow field but are not related to engineering applications. The computation of the (Lagrangian) strain tensor by a variational method was addressed in [19].…”