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A new methodology to analyze two-component molecular tagging velocimetry image pairs is presented. Velocity measurements with high spatial resolution are achieved by determining grid displacements at the intersections as well as along the grid lines using a multivariate adaptive regression splines parameterization along the segments connecting adjacent grid intersections. The methodology can detect the orientation of the grid, contains redundant steps for increased reliability, and handles cases where parts of the grid are missing, indicating potential for automation. Initial demonstration of the algorithm's performance was illustrated using synthetic data sets derived from Computational Fluid Dynamics simulations and compared to Hough-transform and cross-correlation methodologies. Besides providing comparable results in terms of precision and accuracy to previously reported methodologies, the analysis …