  Incorporating shape information is essential for the delineation of many
organs and anatomical structures in medical images. While previous work has
mainly focused on parametric spatial transformations applied on reference
template shapes, in this paper, we address the Bayesian inference of parametric
shape models for segmenting medical images with the objective to provide
interpretable results. The proposed framework defines a likelihood appearance
probability and a prior label probability based on a generic shape function
through a logistic function. A reference length parameter defined in the
sigmoid controls the trade-off between shape and appearance information. The
inference of shape parameters is performed within an Expectation-Maximisation
approach where a Gauss-Newton optimization stage allows to provide an
approximation of the posterior probability of shape parameters. This framework
is applied to the segmentation of cochlea structures from clinical CT images
constrained by a 10 parameter shape model. It is evaluated on three different
datasets, one of which includes more than 200 patient images. The results show
performances comparable to supervised methods and better than previously
proposed unsupervised ones. It also enables an analysis of parameter
distributions and the quantification of segmentation uncertainty including the
effect of the shape model.
