Maximum Likelihood Estimation for the Offset-Normal Shape Distributions Using EM

The offset-normal shape distribution is defined as the induced shape distribution of a Gaussian distributed random configuration in the plane. Such distributions were introduced by Dryden and Mardia (1991) and represent an important parameterized family of shape distributions for shape analysis. This article reports a method for performing maximum likelihood estimation of parameters involved. The method consists of an EM algorithm with simple update rules and is shown to be easily applicable in many practical examples. We also show the necessary adjustments needed for using this algorithm for shape regression, missing landmark data, and mixtures of offset-normal shape distributions.