Construction of groupwise consistent shape parameterizations by propagation

Prior knowledge can highly improve the accuracy of segmentation algorithms for 3D medical images. A popular method for describing the variability of shape of organs are statistical shape models. One of the greatest challenges in statistical shape modeling is to compute a representation of the training shapes as vectors of corresponding landmarks, which is required to train the model. Many algorithms for extracting such landmark vectors work on parameter space representations of the unnormalized training shapes. These algorithms are sensitive to inconsistent parameterizations: If corresponding regions in the training shapes are mapped to different areas of the parameter space, convergence time increases or the algorithms even fail to converge. In order to improve robustness and decrease convergence time, it is crucial that the training shapes are parameterized in a consistent manner. We present a novel algorithm for the construction of groupwise consistent parameterizations for a set of training shapes with genus-0 topology. Our algorithm firstly computes an area-preserving parameterization of a single reference shape, which is then propagated to all other shapes in the training set. As the parameter space propagation is controlled by approximate correspondences derived from a shape alignment algorithm, the resulting parameterizations are consistent. Additionally, the area-preservation property of the reference parameterization is likewise propagated such that all training shapes can be reconstructed from the generated parameterizations with a simple uniform sampling technique. Though our algorithm considers consistency as an additional constraint, it is faster than computing parameterizations for each training shape independently from scratch.