  We consider the problem of modelling noisy but highly symmetric shapes that
can be viewed as hierarchies of whole-part relationships in which higher level
objects are composed of transformed collections of lower level objects. To this
end, we propose the stochastic wreath process, a fully generative probabilistic
model of drawings. Following Leyton's "Generative Theory of Shape", we
represent shapes as sequences of transformation groups composed through a
wreath product.
  This representation emphasizes the maximization of transfer --- the idea that
the most compact and meaningful representation of a given shape is achieved by
maximizing the re-use of existing building blocks or parts.
  The proposed stochastic wreath process extends Leyton's theory by defining a
probability distribution over geometric shapes in terms of noise processes that
are aligned with the generative group structure of the shape. We propose an
inference scheme for recovering the generative history of given images in terms
of the wreath process using reversible jump Markov chain Monte Carlo methods
and Approximate Bayesian Computation. In the context of sketching we
demonstrate the feasibility and limitations of this approach on model-generated
and real data.
