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Hierarchical algorithm

The results from the first CIV processing (CIV1) can be improved in an iterative way by a succession of false vector removal (fix), interpolation to make a new guess, and CIV processing with reduced search zone, using the estimate from the previous processing. By this method convergence to local correlation maxima can be obtained, with displacements mutually consistent with their neighborhood.

Furthermore, in the second CIV processing (CIV2), the prior knowledge of the local deformation rate and rotation is used to refine the pattern matching, see fig.10. During the time lapse \( t\), the local displacement differs from the pure translation by \( sB_{x}t/2 \) (or \( sB_{y}t/2) \) at the edge of the pattern-box. Deformation will deeply affect CIV when this shift becomes of the same order as the apparent particle size \( \delta \), or image correlation length. Estimating \( s \) from a typical velocity \( U \) as \( s\sim U/L \), we get that deformation effects are important for \( B_{x}d/2L>\delta \). Since \( \delta \sim 1 \) pixel, with a displacement \( d= \) 10 pixels, this corresponds to \( B_{x}>0.2L \).

Figure 10:
\resizebox*{0.6\textwidth}{!}{\includegraphics{deform.eps}}

To describe such deformation, it is necessary to interpolate the image itself between the integer pixel values. This is done by a spline interpolation of the image intensity in the pattern-box.

Taking into account this deformation effect allows, as well as prior information, allows to increase the time interval, and therefore the precision. The use of prior information may also allow to reduce the pattern-box and increase the spatial resolution.


next up previous contents
Next: Data format Up: Processing software: Previous: Velocity interpolation (patch):   Contents
Joel Sommeria 2003-02-14