Area preserving parameterisation of shapes with spherical topology

Statistical shape models are powerful tools for model-based segmentation and have been successfully applied to the segmentation of various structures in medical images. Though the segmentation algorithms based on statistical shape models are simple, finding corresponding landmarks for the construction of the models is a challenging optimisation task. State-of-the-art algorithms that solve the correspondence problem require a representation of the training shapes in a suitable parameter space. The mapping of a shape to a parameter space can introduce large area distortions so that simple sampling techniques can not reconstruct the original shapes sufficiently well. In this paper, we propose an algorithm to construct area preserving parameterisations of shapes with spherical topology. Using our approach, good reconstructions of the original shapes can be achieved by uniform sampling. In contrast to previously published methods that use a black box optimisation approach, we exploit knowledge about the shortcomings of initial parameterisations.