  A population quantity of interest in statistical shape analysis is the
location of landmarks, which are points that aid in reconstructing and
representing shapes of objects. We provide an automated, model-based approach
to inferring landmarks given a sample of shape data. The model is formulated
based on a linear reconstruction of the shape, passing through the specified
points, and a Bayesian inferential approach is described for estimating unknown
landmark locations. The question of how many landmarks to select is addressed
in two different ways: (1) by defining a criterion-based approach, and (2)
joint estimation of the number of landmarks along with their locations.
Efficient methods for posterior sampling are also discussed. We motivate our
approach using several simulated examples, as well as data obtained from
applications in computer vision and biology; additionally, we explore
placements and associated uncertainty in landmarks for various substructures
extracted from magnetic resonance image slices.
