Template Matching Image Analysis for MTV

In 2D Molecular Tagging Velocimetry (MTV), tags are written into a fluid flow with a laser grid and imaged at discrete times.

These images are analyzed to calculate Lagrangian displacement vectors, often by direct cross correlation. The cross correlation method is inherited from particle imaging velocimetry, where the correlated images contain a random pattern of particles. A template matching method can be applied, which takes advantage of the known geometry of laser written tag grids in MTV. Grid intersections are explicitly located in each image by correlation with a template with several linear and rotational degrees of freedom, as shown below.

The template is a continuous mathematical function, so the correlation may be optimized at arbitrary sub-pixel resolution. The template is smooth at the spatial scale of the image noise, so random error is substantially suppressed. Under typical experimental conditions at low imaging resolution, displacement uncertainty is reduced by a factor of 5 compared to the direct cross correlation method. Due to the rotational degrees of freedom, displacement uncertainty is insensitive to highly deformed grids, thus permitting longer delay times and increasing the relative accuracy and dynamic range of the measurement. In addition, measured rotational displacements yield velocity gradients which improve the fidelity of interpolated velocity maps.

A template matching method is presented for the reduction of 2D MTV data which explicitly extracts available displacement information from undisplaced and displaced grid images. In simulated data from a rotational Poiseuille flow at low imaging resolution and signal to noise ratios above 8, displacement error less than 0.05 pixels rms is demonstrated, about a factor of 5 improvement over the commonly used direct cross correlation method. Template matching measures both linear and rotational displacements, and is shown to be insensitive to large grid deformations. This permits measurements with high dynamic range. A technique is developed to integrate the linear and rotational measurements into an interpolated velocity map. This interpolation is sensitive to MTV grid orientation relative to physical velocity gradients.

Adapted from:
M. C. Ramsey, R. W. Pitz, “Template matching for improved accuracy in molecular tagging velocimetry,” Experiments in Fluids, 51, pp. 811-819, 2011. http://dx.doi.org/10.1007/s00348-011-1098-y