Consistent spherical parameterisation for statistical shape modelling

We have described previously a method of automatically constructing statistical models of shape. The method treats model-building as an optimisation problem by re-parameterising each shape so as to minimise the description length of the training set. The approach requires an explicit parameterisation of each shape, which is straightforward in 2D, but non-trivial in 3D. It is necessary to provide some parameterisation of the training set to initialise the optimisation. An inappropriate initial parameterisation can cause the optimisation to converge at a slower rate or stop it from converging to a satisfactory solution. In this paper we describe a method of producing a consistent parameterisation for a given set of surfaces. The consistent parameterisations were used to initialise the model-building algorithm and produced results that were significantly better than alternative approaches