In this paper, we propose a novel representation of prior knowledge for image segmentation, using diffusion wavelets that can reflect arbitrary continuous interdependencies in shape data. The application of diffusion wavelets has, so far, largely been confined to signal processing. In our approach, and in contrast to state-of-the-art methods, we optimize the coefficients, the number and the position of landmarks, and the object topology - the domain on which the wavelets are defined - during the model learning phase, in a coarse-to-fine manner. The resulting paradigm supports hierarchies both in the model and the search space, can encode complex geometric and photometric dependencies of the structure of interest, and can deal with arbitrary topologies. We report results on two challenging medical data sets, that illustrate the impact of the soft parameterization and the potential of the diffusion operator.

In this paper, we propose a novel approach to model shape variations. It encodes sparsity, exploits geometric redundancy, and accounts for the different degrees of local variation and image support. In this context we consider a control-point based shape representation. Their sparse distribution is derived based on a shape model metric learned from the training data, and the ambiguity of local appearance with regard to segmentation changes. The resulting sparse model of the object improves reconstruction and search behavior, in particular for data that exhibit a heterogeneous distribution of image information and shape complexity. Furthermore, it goes beyond conventional image-based segmentation approaches since it is able to identify reliable image structures which are then encoded within the model and used to determine the optimal segmentation map. We report promising experimental results comparing our approach with standard models on MRI data of calf muscles - an application where traditional image-based methods fail - and CT data of the left heart ventricle.