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Tongue surface measurements from midsagittal ultrasound scans are effectively arcs with deviations representing tongue shape, but smoothing-spline analysis of variances (SSANOVAs) assume variance around a horizontal line. Therefore, calculating SSANOVA average curves of tongue traces in Cartesian Coordinates [Davidson, J. Acoust. Soc. Am. (1), 407–415 (2006)] creates errors that are compounded at tongue tip and root where average tongue shape deviates most from a horizontal line. This paper introduces a method for transforming data into polar coordinates similar to the technique by Mielke [J. Acoust. Soc. Am. (5), 2858–2869 (2015)], but using the virtual origin of a radial ultrasound transducer as the polar origin—allowing data conversion in a manner that is robust against between-subject and between-session variability.


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