Optical Flow Estimation of a Fluid Based on a Physical Model

An estimation of 3D velocity field including occluded parts without maxing tracer to the fluid had not only never been proposed but also impossible by the conventional computer vision algorithm. In this paper, we propose a new method of three dimensional optical flow of the fluid based on physical model, where some boundary conditions are given from a priori knowledge of the flow configuration. Optical flow is obtained by minimizing the mean square errors of a basic constraint and the matching error terms with visual data using Euler equations. Here, Navier-Stokes motion equations and the differences between occluded data and observable data are employed as the basic constrains. we verify the effectiveness of our proposed method by applying our algorithm to simulated data with partly artificially deleted and recovering the lacking data. Next, applying our method to the fluid of observable surface data and the knowledge of boundary conditions, we demonstrate that 3D optical flow are obtained by proposed algorithm.