Statistical shape models learned from a population of previously observed training shapes are nowadays widely used in medical image analysis to aid segmentation or classification. However, providing an appropriate and representative training population of preferably manual segmentations is typically either very labor-intensive or even impossible. Therefore, statistical shape models in practice frequently suffer from the high-dimension-low-sample-size (HDLSS) problem resulting in models with insufficient expressiveness.
In this paper, a novel approach for learning representative multi-resolution multi-object statistical shape models from a small number of training samples that adequately model the variability of each individual object as well as their interrelations is presented. The method is based on the assumption of locality, which means that local shape variations have limited effects in distant areas and, therefore, can be modeled independently. This locality assumption is integrated into the standard statistical shape modeling framework by manipulating the sample covariance matrix (non-zero covariances between distant landmarks are set to zero). To allow for multi-object modeling, a method for computing distances between points located on different object shapes is proposed. Furthermore, different levels of locality are introduced by deriving a multi-resolution scheme, which is equipped with a method to combine variability information modeled at different levels into a single shape model. This combined representation of global and local variability in a single shape model allows the use of the classical active shape model strategy for model-based image segmentation.
An extensive evaluation based on a public data base of 247 chest radiographs is performed to show the modeling and segmentation capabilities of the proposed approach in single- and multi-object HDLSS scenarios. The new approach is not only compared to the classical shape modeling method but also to three state-of-the-art shape modeling approaches specifically designed to cope with the HDLSS problem. The results show that the new approach significantly outperforms all other approaches in terms of generalization ability and model-based segmentation accuracy.