An Expectation Maximization Algorithm for Inferring Offset-Normal Shape Distributions

The statistical theory of shape plays a prominent role in applications such as object recognition and medical imaging. An important parameterized family of probability densities defined on the locations of landmark-points is given by the offset-normal shape distributions introduced in [7]. In this paper we present an EM algorithm for learning the parameters of the offset-normal shape distribution from shape data. To improve model flexibility we also provide an EM algorithm to learn mixtures of offset-normal distributions. To deal with missing landmarks (e.g. due to occlusions), we extend the algorithm to train on incomplete data-sets. The algorithm is tested on a number of real-world data sets and on some artificially generated data. Experimentally, this seems to be the first algorithm for which estimation of the full covariance matrix causes no difficulties. In all experiments the estimated distribution provided an excellent approximation to the true offset-normal shape distribution.