On a Mathematical Midsagittal Contour Model of Tongue

A mathematical model of tongue in the midsagittal plane is constructed. A tongue contour is modeled as a flexible elastic beam, for which the elastic line equation is numerically solved for the given boundary conditions and the distributed external forces. The database of tongue contours collected from the solutions of the elastic line equation is clustered into 16 classes using the K-means clustering algorithm. The resulting tongue contour is modeled as a linear combination of the cluster centroids and coefficients for any centroid that satisfy several constraints related to mechanical and kinematic properties of tongue. The model is tested on the database that contains tongue surface measurements for various sounds. The approximation error is within the data measurement error for all cases.