Ultrasound imaging is a helpful tool to observe tongue movements without interfering with natural speech. There exist a variety of models to quantify tongue shape based on contours extracted from ultrasound images. However, these can be affected by poor image quality, e.g., when parts of the tongue are missing from the images due to imaging artifacts. In this study, we investigate the effects of various contour extraction errors on the accuracy and consistency of different shape measures. We developed exponential and polynomial contour perturbation models, then simulated missing tongue tip and root, and investigated the impact of these perturbations on shape measures based on the discrete Fourier transform (DFT), modified curvature index (MCI), and triangular fitting. This was applied to a set of CV utterances collected from healthy and impaired speakers. Results demonstrate the effectiveness of DFT and triangular fitting in clustering different phonemes despite the added noise. A high degree of correlation was found between the DFT coefficients of the perturbed and original tongue contours. There is also a trade-off between the robustness of the model and sensitivity to minor actual differences in tongue shape. Sometimes, these slight differences help group tongue shapes that differ, e.g., due to coarticulation effects. Therefore, we have attempted to improve the precision of the DFT model by adding palatal contact information.