On estimating 3-D incompressible motion

In this paper we present a new method for estimating the 3-D motion of an incompressible or nearly incompressible body from a set of noisy and possibly sparse measurements. This problem occurs in applications such as the estimation of heart motion and fluid flow. Our method is based on a stochastic motion model where the incompressibility condition is modeled as a correlation between certain components of the displacement or velocity field gradient. This model, which we call the correlation model, allows for local fluctuations in volume, and provides a framework for incorporating a priori knowledge of the directions of expansion and contraction. We derive an optimal estimate equation based on the correlation model, which under certain conditions reduces to that obtained by other authors using a regularisation approach. Computer simulations are presented that demonstrate the correlation model method