On Calculation Schemes of Spatial Gradient for Spatio-temporal Derivative Method

Abstract

Some calculation schemes of spatial gradient for spatio-temporal derivative method, which was used for sub pixel displacement detection, were evaluated. It was found that the second-order accurate central finite difference scheme tends to underestimate the gradient of tracer-particle's intensity, so that it leads to overestimation of sub-pixel displacements. In this study, upstream and downstream finite difference scheme was proposed and evaluated. It was shown that the proposed scheme has high accuracy and is robust to noise.