Finding standard dental arch forms from a nationwide standard occlusion study using a Gaussian functional mixture model

Orthodontists are interested in finding a set of standard arch forms for clinical orthodontic practice. In this paper, we propose a functional clustering method for the dental arches based on a mixture of U-shaped curves. We decide the number of clusters (equivalently, mixture components) using the Bayesian information criterion and the jump criterion based on a given distortion function. We apply our method to clustering the dental arch data from the nationwide standard occlusion study conducted in Korea from 1997 to 2005. The data are composed of dental arches of 306 subjects with normal occlusion selected from 15,836 young adults. We also provide the comparison of the proposed method to other existing methods.