Models for distributions of shapes contained within images can be widely used
in biomedical applications ranging from tumor tracking for targeted radiation
therapy to classifying cells in a blood sample. Our focus is on hierarchical
probability models for the shape and size of simply connected 2D closed curves,
avoiding the need to specify landmarks through modeling the entire curve while
borrowing information across curves for related objects. Prevalent approaches
follow a fundamentally different strategy in providing an initial point
estimate of the curve and/or locations of landmarks, which are then fed into
subsequent statistical analyses. Such two-stage methods ignore uncertainty in
the first stage, and do not allow borrowing of information across objects in
estimating object shapes and sizes. Our fully Bayesian hierarchical model is
based on multiscale deformations within a linear combination of cyclic basis
characterization, which facilitates automatic alignment of the different curves
accounting for uncertainty. The characterization is shown to be highly flexible
in representing 2D closed curves, leading to a nonparametric Bayesian prior
with large support. Efficient Markov chain Monte Carlo methods are developed
for simultaneous analysis of many objects. The methods are evaluated through
simulation examples and applied to yeast cell imaging data.