Finding the control parameters of an articulatory model that result in given acoustics is an important problem in speech research. However, one should also be able to derive the same parameters from measured articulatory data. In this paper, a method to estimate the control parameters of model by Maeda from electromagnetic articulography (EMA) data, which allows the derivation of full sagittal vocal tract slices from sparse flesh-point information, is presented. First, the articulatory grid system involved in the model's definition is adapted to the speaker involved in the experiment, and EMA data are registered to it automatically. Then, articulatory variables that correspond to measurements defined by Maeda on the grid are extracted. An initial solution for the articulatory control parameters is found by a least-squares method, under constraints ensuring vocal tract shape naturalness. Dynamic smoothness of the parameter trajectories is then imposed by a variational regularization method. Generated vocal tract slices for vowels are compared with slices appearing in magnetic resonance imaging images of the same speaker or found in the literature. Formants synthesized on the basis of these generated slices are adequately close to those tracked in real speech recorded concurrently with EMA.