Maximum-likelihood estimation for the offset normal shape distributions using EM

 

Statistical shape analysis is an interdisciplinary area of research which has important applications in biology, medicine, archaeology and image analysis. The shape of an object is defined as the geometrical information left after standardisizing in terms of rotation, translation and size. In practice, the shape of objects from a given population can be encoded within a finite set of points called landmarks, selected according to some biological, mathematical or geometrical significance.

This talk reports a method for performing maximum likelihood estimation of parameters of the offset normal shape distribution. This distribution is defined as that induced by the shape of a Gaussian distributed random configuration with vertices representing the location of a set of landmarks in the plane. This represents an important parameterized family of distributions for shape analysis and is introduced by Dryden and Mardia in 1991.

The proposed method consists of an EM algorithm whose update steps resemble those of the widely used general procrustes algorithm. Our method 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.