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High-Quality Vector Field and Direct Jacobian Estimation
Gronát, Petr
In this paper, a correlation method for direct vorticity computation of the fluid velocity field is introduced. The correlation method allows an affine transformation of a correlation window. It is shown that Lagrangian field of displacements, considering the linear terms only, satisfies the requirements for affine transformation and using the Normalized-Cross-Correlation (NCC) together with affine transformation and Newton-Raphson iterative method, six parameters defining this transformation can be estimated. Using these parameters, both displacement and vorticity can be computed directly without differentiation of the vector field.
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High-Quality Vector Field and Direct Vorticity Estimation Uusing the Affine Correlation Method
Gronát, Petr
We present a correlation method for direct vorticity computation of the fluid velocity field. The correlation method allows the affine transformation of a correlation window. It is shown that Lagrangian field of displacements is locally affine considering linear terms only. Using the Normalized-Cross-Correlation (NCC) combined with affine transformation and Newton-Raphson iterative method, six parameters defining this transformation are estimated. Subsequently, using these parameters, both displacement and vorticity can be computed, hence, these properties are being obtained for every single pixel directly during the correlation procedure.
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Affine Correlation Method for Direct Vorticity, Skew and Displacement Estimation
Gronát, Petr
In this paper, a correlation method for direct vorticity computation of the fluid velocity field is introduced. The correlation method considering the affine transformation of a correlation window is presented. It is shown, that Lagrangian field of displacements, con- sidering the linear terms only, satis- fyes the requirements for affine transfor- mation. Using the Normalized–Cross– Correlation together with affine trans- formation and Newton-Raphson itera- tive method, six parameters defining the transformation can be estimated. Subse- quently, both displacement and vorticity can be computed using the above men- tioned parameters, hence, the vorticty is being obtained for every single point di- rectly during the correlation procedure.
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