The authors have developed an advanced procedure for sub-pixel analysis, which utilize the higher-order expansions of spatio-temporal gradients of visualized flow image. Present approach stands on an innovative idea of the measurement principle using multi-frame images and multi-dimensional objectives. In this paper, an advanced procedure on gradient method has been proposed. The contribution of higher-order derivatives to the constraint equation was considered, and the multi-step higher-order algorithm is established. Proposed constraint equation contains non-linear terms, and corresponding numerical solution is employed. The evaluation by means of VSJ standard image shows the excellent performance of present method, and twenty percent accuracy improvement in comparison with the conventional first-order approach was obtained. Present approach contributes to improving the limitation of measurement resolution greatly.

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