Correlation

Image correlation is the key step of Particle Imaging Velocimetry. This is where successive images are evaluated and displacements are calculated.  How does it work?

The images are separated into numerous smaller sub-areas or interrogation windows. It is the interrogation windows that are correlated not the entire images. The correlation of an interrogation image with another in the successive image yields one single vector, assigned to the point at the center of the interrogation area. When the image is separated into NxM interrogation areas along its x and y axes, we obtain NxM vectors.

To obtain a denser velocity grid, the interrogation areas may be overlapping. A common value is 50% overlap, but I have used up to 75% when employing a single pass procedure.

 

FIGURE_1-F

Correlation of successive images. (a) the image is correlated in sub-areas. (b) two sub-areas at successive times are correlated. (c) correlation map shows how well the two sub-images fit one another when shifted along x- and y-axes. (d) a Gaussian curve is fitted to the correlation map to find the position of the peak with sub-pixel precision.

 

FIGURE_2

Multi-pass with window deformation. (a) first pass with overlap 50% yields the gray vectors and the blue one at the center. (b) Vectors from the first pass are interpolated to a smaller grid (red vectors). Interpolated vectors are employed to pre-shift and deform the interrogation area of the second pass. Correlation of shifted and deformed interrogation area yields a corrector to the interpolated first pass (predictor).

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